Ali A. Ameri

The Ohio State University, Columbus, Ohio

Paul W. Giel

Vantage Partners, LLC, Cleveland, Ohio

Ashlie B. McVetta

Glenn Research Center, Cleveland, Ohio

Validation of a CFD Methodology for Variable 

Speed Power Turbine Relevant Conditions

NASA/TM—2013-217860

May 2013

GT2013-95030
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Ali A. Ameri

The Ohio State University, Columbus, Ohio

Paul W. Giel

Vantage Partners, LLC, Cleveland, Ohio

Ashlie B. McVetta

Glenn Research Center, Cleveland, Ohio

Validation of a CFD Methodology for Variable 

Speed Power Turbine Relevant Conditions

NASA/TM—2013-217860

May 2013

GT2013-95030

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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NASA/TM—2013-217860 1 

Validation of a CFD Methodology for Variable Speed Power 

Turbine Relevant Conditions 

Ali A. Ameri 

The Ohio State University 

Columbus, Ohio 43235 

Paul W. Giel 

Vantage Partners, LLC 

Brook Park, Ohio 44142 

Ashlie B. McVetta 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

Analysis tools are needed to investigate aerodynamic 

performance of Variable-Speed Power Turbines (VSPT) for 

rotorcraft applications. The VSPT operates at low Reynolds 

numbers (transitional flow) and over a wide range of 

incidence. Previously, the capability of a published threeequation turbulence model to predict accurately the transition 

location for three-dimensional heat transfer problems was 

assessed. In this paper, the results of a post-diction exercise 

using a three-dimensional flow in a transonic linear cascade 

comprising VSPT blading are presented. The measured blade 

pressure distributions and exit total pressure and flow angles 

for two incidence angles corresponding to cruise (i = 5.8°) and 

takeoff (i = −36.7°) were used for this study. For the higher 

loading condition of cruise and the negative incidence 

condition of takeoff, overall agreement with data may be 

considered satisfactory but areas of needed improvement are 

also indicated. 

Nomenclature 

Cps static pressure coef., (P–Ps2/(Pt1–P2)

Cpt total pressure coef., (Pt1–Pt)/(Pt1–P2) 

Cx axial chord 

H blade span 

i incidence angle 

Mis Mach number based on isentropic expansion of inlet to 

exit static pressure 

k turbulent kinetic energy

P pressure 

Re Reynolds number based on Cx and isentropic exit 

conditions 

S pitch 

Tu turbulence intensity, u'

s u'z /U 2 2 

u' fluctuating component of velocity

U incoming free stream velocity

x axial coordinate 

y pitchwise coordinate

z spanwise coordinate

Greek 

β pitch angle (deg.) 

 upstream endwall boundary layer thickness 

 specific dissipation of turbulence 

Ω gradient of velocity at the wall 

Subscripts 

1 based on inlet condition 

2 based on exit condition 

t total value 

x local value, or axial value 

s streamwise component 

z spanwise component 

Introduction 

Development of civil rotorcraft to enhance airspace 

throughput capacity and diminish airport congestion is a key 

goal of NASA’s Rotary Wing Project. One concept that could 

contribute to those goals is the use of Large Civil Tilt-Rotor 

(LCTR) aircraft to enable vertical takeoff and landing as well 

as high speed cruise (Refs. 1 and 2). In order to optimize fuel 

efficiency, the main-rotor speed is varied from 100 percent at 

takeoff to 55 percent at cruise. This can be achieved by using a 

two-speed transmission driven by a power turbine with 

minimal turbine speed change (Ref. 3). In order to avoid the 
NASA/TM—2013-217860 2 

added weight and complexity of a two-speed transmission, a 

variable speed power turbine (VSPT) can be used with a fixed 

gear ratio transmission. Variations in the shaft speed of the 

VSPT lead to a wide (40° to 60°) range of incidence at 

Reynolds numbers in the laminar or transitional range 

(Ref. 4), resulting in flow conditions that are difficult to 

analyze accurately. VSPTs share the low Reynolds number 

conditions with low pressure turbines which have been 

reported to suffer loss of efficiency at higher altitudes under 

cruise conditions (Refs. 5 to 7). Such low Reynolds number 

conditions allow for the existence of laminar boundary layers 

on the blade surfaces. Laminar boundary layers are prone to 

separation, producing large losses and deviation if not 

reattached. Positive incidence increases blade loading and 

strengthens the vortical secondary flow structures, and can 

induce flow separation on the suction-side. Negative incidence 

unloads the blade and makes for a more two-dimensional 

flow. Three-dimensional pressure-side cove separation occurs 

under conditions of extreme negative incidence (Ref. 8). 

Computational Fluid Dynamics (CFD) computations (Ref. 9) 

of a blade in a linear cascade under large negative angles also 

exhibited vortical structures aligned in the spanwise direction 

on the pressure-side cove. Since the test blade was a linear 

cascade, the vortex realigned itself to flow direction near the 

midspan of the linear blade. For an actual turbine blade such a 

vortex would realign itself to the direction of the flow and spill 

out near the tip (Ref. 8). 

Accurate prediction of losses under the conditions noted 

above is a challenge for steady CFD. The state of the 

boundary layer (laminar, transitional, or turbulent) has a large 

effect on the aerodynamic losses and thus a realistic prediction 

of the flow depends on its accurate modeling; further, the 

impact of deterministic unsteadiness of upstream and adjacent 

blade rows, neglected in the present analysis, is known to have 

a measurable effect on loss levels of transitional flows 

(Ref. 6). Analysis tools are needed to investigate the penalties 

associated with maintaining efficient VSPT operation over a 

wide shaft-speed change. 

In a previous study (Ref. 9), the capabilities of a published 

transition/turbulence model, namely the Walters-Leylek 

Three-Equation model (Refs. 10 and 11), was assessed. Threedimensional heat transfer data on a blade were used to mark 

transition for the computational exercise. Subsequent to 

establishing satisfactory model performance as it pertained to 

transition, computed loss for the Energy Efficient Engine (E3

) 

blade set (Refs. 12 and 13) was presented. This first-stage 

high-pressure-turbine blade-tip profile geometry had been 

tested in a linear cascade with zero tip clearance and varying 

inlet incidence angle (Ref. 13). The total pressure deficits at 

the exit for a wide range of incidence angles were computed. 

It was noted that losses were generated by the endwall and 

blade boundary layers and were transported and augmented by 

the horseshoe and passage vortices. At high negative 

incidences, pressure-side separation and roll-up of the 

resulting vortex into a streamwise vortex was illustrated and 

for positive incidence, it was shown that secondary flows 

strengthen and widen as the loading on the blades increases 

with the incidence angle. Comparison with wake profiles at 

midspan (Ref. 13) for the E3

 blade using the present 

methodology was given in Reference 14 where the predictive 

capability using Walters-Leylek model was shown to be quite 

good for the incidence angles at the extreme limits. 

Transition Modeling 

In an earlier report (Ref. 9), results were obtained with 

Walters and Leylek turbulence model. It was noted that among 

the benefits of using this model was the freedom from having 

to compute near-wall integral quantities, which are difficult to 

evaluate in complex three-dimensional flows. Transport 

equations for transition and turbulence use phenomenological 

models, as opposed to empirically based models (Refs. 10 and 

11), and do not require computation of any boundary layer or 

integral quantities. In the work presented by Walters and 

Leylek (Ref. 11), a modified form of the k- model 

supplemented with a transport equation for the “laminar 

kinetic energy,” forms a three-equation model. A study 

conducted by Cutrone et al. (Ref. 15) consisting of several 

models, including other popular models, showed the threeequation model approach to be promising. Subsequent 

application (Ref. 16) to two-dimensional flows and to a threedimensional turbine cascade showed good agreement with 

experiments and superior comparison to other models 

attempted in that paper and an earlier report. It should be 

noted that in References 15 and 16, the model (Refs. 10 and 

11) was implemented without the submodel for natural 

transition, presumably in anticipation of high turbulence 

levels.

Objectives 

In the present study, the flow field in a three-dimensional 

transonic linear cascade was computed in order to assess 

pressure distribution, midspan loss levels and exit flow angles. 

This was motivated by the availability of relevant VSPT threedimensional data recently obtained at the NASA Glenn 

Research Center (Ref. 17). Two distinct conditions were 

considered and sensitivity to grid density and to variables such 

as turbulence length scale and inlet boundary layer thickness 

was investigated. The objective was to verify the predictive 

capabilities (and limitations, thereof) of a method of 

computing flows of relevance to the VSPT. The method 

involves a RANS solution of the flow field using the 

turbulence/transition model of Walters and Leylek (Refs. 10 

and 11). The test article for the experimental program was a 

scaled two-dimensional extruded VSPT blade designed to 

meet the specified engine requirement (Ref. 18), and adapted 

for a cascade test (Ref. 17). The measurements were taken at 

various Reynolds numbers and Mach numbers, and covered a 

wide range of incidence angles. Blade pressure loading 

measurements at multiple span locations as well as exit total-
NASA/TM—2013-217860 3 

pressure surveys in the wake were performed. Prediction of 

the pressure distribution, which is routine for attached flows, 

is often a challenge when the boundary layer separation is 

involved. The flow in this cascade is strongly threedimensional due to the high flow turning and an inlet 

boundary layer that covers approximately one quarter of the 

span. 

The CFD work performed to compute the pressure 

distribution and total-pressure coefficient and exit angle for 

the VSPT blade geometry at the “cruise” and “takeoff” 

incidence angles, and comparison to the experimental data of 

McVetta et al. (Ref. 17) will be reviewed. 

VSPT Blade Experiment 

A description of the cascade and a summary of the 

conditions for the experimental measurements used for this 

numerical validation are provided here. 

NASA Glenn Transonic Turbine Blade Cascade Facility is 

shown in Figure 1. The cascade’s large scale and continuous 

run capability at engine relevant Mach numbers and Reynolds 

numbers have allowed for detailed heat transfer and 

aerodynamic studies on a wide range of turbine blades. The 

blade geometry used in this test was a scaled two-dimensional 

midspan section of the VSPT second stage rotor (Ref. 18) 

shown in Figure 2 and the blade description is given in 

Table 1. The cascade for this test was made up of nominally 

ten blade passages. The blades were attached to a disk that can 

be rotated to set inlet flow angles (from axial) in the range 

−17°  β1  78.8°. During this test, ten incidence angles were 

examined (Ref. 17). Detailed three-dimensional flowfield data 

were acquired at incidence angles of 5.8° (β1 = 40.0°) and 

−36.7° (β1 = −2.5°), which represent the cruise and takeoff 

flight mission points, respectively. These two mission points 

were used in the CFD verification for this current study. The 

angle settings are given in Table 2. The flow conditions listed 

in Table 3 are the nominal conditions under which the CFD 

tests were run. The lowest achievable tunnel Reynolds number 

condition was higher than those at cruise. In order to admit 

transitional flow appropriate to altitude conditions, no 

turbulence grid was used during this test (Ref. 17). In a 

previous study (Ref. 13) the inlet turbulence intensity without 

a turbulence grid was documented to range from 0.25 to 

0.40 percent. McVetta et al. (Ref. 17) suggest that future plans 

will include testing at higher turbulence intensity. 

To allow the determination of the inlet length scale of 

turbulence, the turbulence for the present experiments was 

measured at two stations 4.5 and 0.5 axial- chords upstream of 

the blade row. These data, which will be shown in the 

computational section of the paper, were used to compute a 

turbulence length scale for use as an inlet boundary condition 

for the computations. 

Table 3 provides the experimental conditions which can be 

used in the simulations.

Figure 1.—Overall view of NASA Glenn’s transonic cascade 

facility. 

Figure 2.—Blade geometry and exit survey plane location. 

 

5

6

4

3

passage

4

passage

5

passage

3

Sta. 0

Sta. 2

2.0

0.0

55.5 metal

1.0

y pitch

1=34.2 zero i

1=11.8 max i

1=2.5 t-o

1=40.0 cruise

y

x

x/C 1.070 x x/C = x =

0.415

i=5.8

i=46.0

i=36.7

z

x

 1

Cx

H

 1
NASA/TM—2013-217860 4 

TABLE 1.—BLADE DESCRIPTION 

Geometry Value 

Axial chord, Cx

True chord 

Pitch, S 

Span, H

Throat diameter 

Leading edge diameter 

Trailing edge diameter 

Stagger angle 

Inlet metal angle 

Uncovered turning 

Exit metal angle 

180.57 mm (7.109 in.) 

194.44 mm (7.655 in.) 

130.00 mm (5.119 in.) 

152.40 mm (6.000 in.) 

72.85 mm (2.868 in.) 

15.16 mm (0.597 in.) 

3.30 mm (0.130 in.) 

20.35° 

34.2° 

19.47° 

–55.54° 

TABLE 2.—ANGLE SETTINGS 

Inlet angle, 

β1 

Incidence angle, 

i

40.0° (Cruise) 5.8° 

−2.5° (Takeoff) −36.7° 

TABLE 3.—FLOW CONDITIONS USED IN THE SIMULATIONS 

Inlet 

angle, 

β1

Exit 

ReCx

Press. 

ratio 

Exit 

MIS

δinlet 

in.

Tuin%

at 

−5.0 Cx

Tuin%

at 

−0.5 Cx

40.0 536,000 1.412 0.72 1.44 0.4 0.3 

−2.5 532,000 1.348 0.67 1.50 a

0.4 a0.3

a

Measured for the 40 incidence but deemed valid for this case. 

As shown in Figure 2, the inlet conditions were measured at 

Station 0, located approximately 0.5 axial-chords upstream of 

the cascade. For the present study total-pressure and exit flow 

angle data were acquired using a five-hole pitch-yaw probe 

and a three-hole boundary layer probe. The probes were also 

installed in the Station 2 survey plane located approximately 

7.0 percent axial-chord downstream of the blade trailing edge. 

The survey probe traversed three blade passages and half the 

span of the blade. For the two inlet angles considered in this 

study, pitchwise/spanwise surveys were taken which consisted 

of 26 spanwise surveys with 62 pitchwise points. The overall 

estimated uncertainty in flow angle was 1.5 and the overall 

estimated uncertainty in total-pressure coefficient was 

0.8 percent (Ref. 17). 

The main measurement blades 4, 5, and 6, shown in 

Figure 2, were instrumented with static pressure taps at four 

spanwise locations. Blade 5 was fully instrumented with 

44 taps along 10, 15, 30, and 50 percent of span. 

Computational Method 

The computations of exit total pressure, exit flow angles and 

blade pressure distribution were made using the code GlennHT (Ref. 19) on structured grids. The transition/turbulence 

model of Walters and Leylek was used for the computations 

(Ref. 11). 

Glenn-HT Computer Code 

The computer code used in this work is the Glenn-HT code 

(Ref. 19). Glenn-HT is a Fortran 90 code. It uses structured 

multi-block grids. It is designed to be a multi-physics code and 

is currently capable of solving solid conduction and 

compressible fluid flow. To arrive at a steady solution, a 

finite- volume form of the unsteady compressible ReynoldsAveraged Navier-Stokes (RANS) equations are integrated in 

pseudo-time using an explicit Runge-Kutta solver in a 

multigrid driver. For the present exercise, the convective 

fluxes were discretized with a second order upwind scheme 

described in Reference 20. The diffusive terms were 

discretized using a second-order central differencing. The 

convective terms of the turbulence model equations were 

modelled using a first-order upwind method.

Computational Grid 

The grids used in this work were generated using GridPro 

(Program Development Corporation) (Ref. 21). The software 

used an elliptic solver to smooth an initial, algebraically 

generated, multi-block grid. 

For the VSPT blade, taking advantage of the symmetry of 

the passage for the three-dimensional grid, only half of the 

span was gridded. The grid was constructed using multiple 

blocks in three-dimensional. As is the practice with grid 

generation when using GridPro, an inviscid grid was generated 

first and subsequently viscous grid was generated by 

clustering. The grid was clustered near the blade and the 

endwall surfaces. The spacing was chosen such that the first 

grid line away from the wall was at a dimensionless wall 

distance (y

+

) of near unity. 

Two grids were generated: Grid1 had 2 million nodes and 

Grid2 has approximately 7 million nodes. Both Grid1 and 

Grid2 used a clustering factor of 1.1 away from the walls 

(space at the wall 210–5 Cx). Grid2 was further refined in the 

spanwise direction (by about a factor of 1.5) to better capture 

three-dimensional spanwise effects. The streamwise direction 

was further refined around the blade to allow enhanced 

resolution of possible transition and/or separation, flow 

structures in the pressure-side cove and trailing edge, and 

wake flow. Enhanced resolution of the trailing circle was 

achieved by using 16 points in Grid1 versus 24 points for 

Grid2 around the trailing edge circle. 

Figure 3 shows the three-dimensional grid corresponding to 

Grid2 described above. The inlet plane was situated about half 

an axial-chord upstream to coincide with the measurement 

stations (Tables 2 and 3). The downstream boundary was 

placed at 1.5 axial-chord distance downstream of the leading 

edge. A third grid was also used for ensuring grid convergence 

by coarsening Grid2 by a factor of 2 in each index direction. 
NASA/TM—2013-217860 5 

Figure 3.—Typical three-dimensional grid for VSPT. 

Boundary Conditions 

The information listed in Tables 2 and 3 were used to 

specify the boundary conditions. Briefly, the exit boundary 

condition was a constant pressure boundary condition and was 

set according to the pressure ratio shown in Table 3. At the 

inlet, the boundary layer thickness was used to estimate a 

friction velocity (Ref. 22). Using the law of the wall/wake, a 

velocity profile was obtained which was subsequently 

converted into a total pressure profile. In the free stream, the 

measured turbulence intensity and the turbulence length scale 

were used to specify the inlet conditions for the turbulence 

kinetic energy and specific dissipation (k and ). The laminar 

kinetic energy, a variable in the Walters-Leylek turbulence 

model, was set to a very small value. A stable and satisfactory 

profile was established by specifying the inlet conditions in 

the free stream and allowing turbulence quantities to be 

extrapolated upstream within the boundary layer. 

The turbulence length scale, as specified in computations of 

turbulent flows, represents the size of energy- containing 

eddies and is often specified as a percentage of a relevant 

length scale such as the passage span or blade axial chord. 

Values between 1 to 10 percent are customarily used. In the 

present study, available data were used to compute the length 

scale as described below. 

Length Scale Computation 

In order to ascertain the appropriate value for the length 

scale which establishes the decay rate, computations were 

made using a three-dimensional sliver grid similar to the grid 

in Figure 3 covering the blade but having the upstream 

boundary at −5.0 axial-chord upstream. By iteratively 

adjusting the upstream value of the turbulence length scale, 

the turbulence level at the second location at −0.5Cx was 

matched. The length scale computed at the second location 

was used as a boundary condition for the three-dimensional 

computations to follow. For the rest of the computations 

(including the takeoff incidence angle) for which the upstream 

boundary was placed at −0.5Cx, the measured turbulence 

intensity of 0.3 percent and length scale of 0.3 percent of span 

were used. 

Results 

Post-diction results for the cruise and takeoff conditions are 

presented in this section. Results will be presented for blade 

pressure distribution, total-pressure coefficients, and exit flow 

angle distribution. 

Cruise Angle 

As listed in Table 2, at the cruise angle, the blade was tested 

at a positive incidence (i = +5.8°). Although the Reynolds 

number is ReCx,2 = 5.3105

, absence of free-stream turbulence 

makes this case difficult to compute as the flow tends to be 

transitional and prone to separation.

Pressure Distribution 

A comparison of the computed and measured blade pressure 

distributions would indicate the efficacy of the transition 

model; the boundary layer flow tends to be transitional and 

prone to separation and, hence, the presence or absence of 

separation affects the pressure distribution. Separation effects 

were reflected in the blade surface pressure distribution 

making the experimental comparisons useful for evaluating 

the model. 

Grid resolution adequacy for prediction of blade loading, 

usually less of a factor for attached flows, was investigated via 

a grid resolution study and the solutions were found to be grid 

independent; thus, only one solution is shown. As seen in 

Figure 4 overall, good agreement is seen between the 

computation and the experimental data. The data at midspan 

(black circles) suggest a suction-side separation occurring at 

x/Cx = 0.7, as evidenced by a plateau. The computations (black 

line) fail to capture the plateau. At x/Cx = 0.7, a discontinuity 

in the slope of the computed suction-side pressure is noted. 

Figure 5, shows the magnitude of the velocity gradient at 

midspan on both the pressure and suction surfaces. On the 

suction-side, transition occurs at 40 percent axial-chord. Such 

early transition would reduce the potential for boundary-layer 

separation on the suction-side. On the pressure-side agreement 

with data is excellent. The pressure-side appears to have 

transitioned at 35 percent axial-chord. 

Pressure loadings at other span locations are important to 

examine for this three-dimensional flow due to the thick inlet 

boundary layer. It is observed that the computed loading as 

shown in Figure 4, agree well with data in other span 

locations. Although there is a dearth of data on the suctionside, near the trailing edge at other spanwise locations, the 

computations in Figure 4 appear to go through those data 

points. 
NASA/TM—2013-217860 6 

Figure 4.—Pressure distributions at cruise 

(i = 5.8) for four span locations and 

comparison with data (Ref. 17). 

Figure 5.—Computed dimensionless magnitude 

of the velocity gradient on the blade surface at 

midspan for cruise incidence. 

Exit Total Pressure 

Total pressure was surveyed at 7 percent chord downstream 

of the trailing edge in Reference 17. Figure 6(a) shows the 

measured contours and 6(b) shows the computed contours at 

the same axial position. The passage is periodic and the 

mismatch in location is due to the shape of the computational 

domain. Inspection of Figure 6(b) reveals major areas of 

elevated loss. One area is the loss core due to the pressure side 

leg of the horseshoe vortex, shown prominently, corresponds 

to the experimental data at (–0.55, 0.38). Another is the region 

in the wake of the blade, corresponding to the region (–0.55, 

0.5) due to the separated flow in the vicinity of midspan. And 

the third region is close to the hub and is due to the wake and 

endwall boundary layer interaction corresponding to 

Figure 6(a) near (–0.5, 0.02). Qualitative agreement exists 

between Figure 6(a) and (b). Quantitative agreement is good 

near the endwall. 

(a) 

(b) 

Figure 6.—Cpt contours for the cruise incidence 

(i = 5.8) at 0.07 axial-chord downstream of the 

trailing edge; (a) data from (Ref. 17) and (b) 

computed. 

Figure 7.—Total pressure loss 0.07 axial-chord downstream of 

midspan (Ref. 17) and comparison with CFD computations. 

Computed and measured midspan total pressure coefficient 

at midspan are compared in Figure 7. For the computational 

result, two computational grids using 2 and 7 million grid 

points were shown with good agreement. Comparison with 

experiment shows the lack of agreement coming from the 

early transition and absence of separation zone in the 

computations. 

 

Cptot: 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

y/S -1.0 -0.5 0.0

0.0

0.1

0.2

0.3

0.4

0.5

z

H

-1.0 -0.5 0.0

0.0

0.1

0.2

0.3

0.4

0.5

-1.0 -0.5 0.0

0.0

0.1

0.2

0.3

0.4

0.5
NASA/TM—2013-217860 7 

Figure 8.—Area averaged losses at 7 percent 

axial-chord downstream of the blade at 

cruise incidence. 

Figure 8 shows experimentally determined pitch-averaged 

total pressure coefficient for the cruise condition for two 

adjacent passages (to verify periodicity), and the integrated 

computational results. While the CFD results at the two grid 

resolutions agree well, the calculated total pressure coefficient 

at midspan is lower than measured, consistent with Figure 7. 

The total pressure coefficient was overpredicted below 

30 percent span. 

Exit Angle Comparison 

In Reference 17, the pitchwise mass-averaged exit flow 

angle, β, is presented. The computed angles were similarly 

mass-averaged and presented in Figure 9. The computational 

results for the two grids agree very well. Agreement between 

the experiments and CFD is to within a degree which is of the 

order of the measurement uncertainty. In the highly overturned 

region very near the endwall the agreement diminishes to 

within 2° to 2.5°, which is slightly outside the uncertainty 

range of the experiments.

Takeoff Angle 

At takeoff, the incidence angle is –36.7. 

Pressure Distribution 

Figure 10 shows the static pressure coefficient for the blade 

at highly negative incidence (−36.7°). The negative incidence 

gives rise to an inverted pressure distribution in the leading 

edge region of the blade. The loading reverts to nominal 

beyond 20 percent axial-chord from leading edge. The 

pressure distribution plot shows good agreement between the 

Figure 9.—Mass Averaged pitchwise exit angle 

at 7 percent axial-chord downstream of the 

blade at cruise incidence. 

Figure 10.—Pressure distribution at takeoff for 

four span locations and comparison with data 

from Reference 17. 

computations and the experiment. The two refined grids gave 

the same result and only one is shown. Magnitude of the 

velocity gradient at the blade surface, plotted in Figure 11, 

along the blade midspan, shows a local pressure-side 

separation bubble between x/Cx values of 0.05 to 0.075. A red 

semicircle highlights the bubble. In Figure 10, the location of 

the local minimum and the magnitude of the static pressure 

coefficient on the pressure-side are nicely captured and the 

profile downstream is also well represented. Good agreement 

with the data is shown for the suction surface. As at cruise 

incidence, the kink in the data near x/Cx = 0.7, presumably due 
NASA/TM—2013-217860 8 

Figure 11.—Computed dimensionless magnitude of 

the gradient of velocity at the blade surface at 

midspan for takeoff incidence. 

to separation, is missed. Inspection of the velocity gradient 

along the suction-side of the blade in Figure 11 indicates 

transition took place at 40 percent axial-chord and thus 

reduced the possibility of a downstream separation. 

Exit Total Pressure 

Figure 12(a) and (b) show the experimental and computed 

contour plots of the total-pressure coefficient at 7 percent 

chord downstream of the trailing edge. One of the 

consequences of the unloading of the blade is the weakened 

secondary flow system in the passage and reduced variation in 

pressure loading in the spanwise direction. The contours 

appear different than those for the takeoff incidence. The 

pressure-side leg of horseshoe vortex, in Figure 12(a), can be 

seen to be present in the lower portion of the blade span, at 

(–0.5, 0.15), due to the weakening of the passage vortex. The 

endwall wake interaction is still present and the total pressure 

coefficient local maximum is located at (–0.5, 0.02). The 

computed results agree qualitatively with the experiment and 

all those features are present and are generally in the correct 

relative positions.

Figure 13 shows the experimentally measured total pressure 

distribution across the wake at the midspan. The computations 

agree with the size of the wake at midspan as the integrated 

average shown in Figure 14 shows good agreement with the 

experimental data. 

Figure 14 shows the pitchwise integrated total-pressure 

coefficient at the x/Cx = 1.07 plane both experimentally and 

computationally. To help verify periodicity, two adjacent 

passages 4 and 5 were reported in Reference 17, as shown in 

the legend. The agreement between the computed grids is 

quite good, as is the agreement between the computed and the 

experimental results. This may be due to the absence of large 

secondary flow structures in the passage and the apparent 

absence or weakness of the suction-side separation bubble at 

midspan. 

(a) 

(b) 

Figure 12.—Cpt contours for the takeoff incidence (i = 

–36.7) at 0.07 axial-chord downstream of the trailing 

edge (a) from (Ref. 17) and (b) computed. 

Figure 13.—Total pressure loss 0.07 axial-chord 

downstream of midspan for the takeoff incidence 

(Ref. 17) and comparison with CFD computations. 

Cptot: 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

y/S -1.0 -0.5 0.0

0.0

0.1

0.2

0.3

0.4

0.5

z

H

-1.0 -0.5 0.0

0.0

0.1

0.2

0.3

0.4

0.5

-1.0 -0.5 0.0

0.0

0.1

0.2

0.3

0.4

0.5
NASA/TM—2013-217860 9 

Figure 14.—Area averaged losses at 7 percent 

axial chord downstream of the blade at cruise 

condition. 

Figure 15.—Mass Averaged pitch angle at 

7 percent axial chord downstream of the 

blade. 

Exit Angle Comparison 

The pitch angle, β, was also computed and compared to the 

measured values. The data and comparison to the CFD 

computations are presented in Figure 15. The agreement 

between the two grids is very good. The variance between the 

CFD and the measured values is no more than 2 except for 

very near the endwall where the apparent variance is larger. In 

the highly overturned region very near the endwall the 

agreement diminishes to within 2° to 2.5° which is slightly 

outside the uncertainty range of the experiments.

Summary 

For the VSPT, flow transition/separation has been identified 

as an important process. Large variations in incidence angles 

require models that can reasonably compute these flows. 

Numerical modeling of the three-dimensional flow in a twodimensional transonic linear cascade was performed at the two 

incidence angle conditions corresponding to takeoff and cruise 

for which experimental data (Ref. 17) were available. The 

inlet length scale, which determines the decay rate of 

turbulence, was determined from the data. Three-dimensional 

blade loadings agreed with the data except for the aft 

30 percent of the suction-side, where CFD missed a laminar 

separation. As for the total-pressure survey downstream of the 

blade, agreement with the data was obtained to within 

50 percent for the cruise incidence angle while for the takeoff 

incidence the agreement was excellent. Agreement with the 

exit flow angle measurements was good and was mostly 

within about a degree for the cruise angle and less than two 

degrees for the takeoff angle which is fair. Near the endwall the 

error was as high as 2.5. 

Further assessment of the Walter-Leylek model is necessary 

for the determination of the source of the deficiency in the 

transition submodel. 

References 

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2. Acree, C.W., Hyeonsoo, Y., and Sinsay, J.D., 2008, 

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

July 22-24.

3. Stevens, M.A., Handschuh, R.F., Lewicki, D.G., 2009, 

“Variable/Multispeed Rotorcraft Drive System 

Concepts,” NASA/TM—2009-215456; also ARL-TR4728. 

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Challenges of a Variable-Speed Power Turbine for 

Large Civil Tilt-Rotor Application,” Proc. AHS Int. 

66th Annual Forum, May; also NASA/TM—2010-

216758, Aug. 

5. Gier, J., Franke, M., Hübner, N., Shröder, T., 2008, 

“Designing LP Turbines for Optimized Airfoil Lift,” 

ASME-GT2008-51101. 

6. Haselbach, F., Schiffer, H.-P., Horsman, M., Dressen, 

S., Harvey, N., Read, S., 2002, “The Application of 

Ultra High Lift Blading in the BR715 LP Turbine,” 

ASME Journal of Turbomachinery Volume 124, 45–

51. 

7. Hourmouziadis, J., 1989, “Aerodynamic Design of 

Low Pressure Turbines,” in Blading Design for Axial 

Turbomachines, AGARD-LS-167, pp. 8-1 to 8-40. 
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8. Welch, G.E., 2011, “Computational Assessment of the 

Aerodynamic Performance of a Variable-Speed 

Power Turbine for Large Civil Tilt-Rotor 

Application,” Proceedings AHS Int. Forum 67, May 3-

5; also NASA/TM—2011-217124. 

9. Ameri, A., 2012 “Use of Transition Modeling to 

Enable the Computation of Losses for the VariableSpeed Power Turbine,” GT2012-69591, Turbo Expo, 

Copenhagen, Denmark. 

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for Boundary Layer Transition Using a Single-Point 

RANS Approach,” ASME Journal of Turbomachinery, 

Volume 126, Issue 1, 193. 

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Fluid Dynamics Study of Wake-Induced Transition on 

a Compressor-Like Flat Plate,” ASME Journal of 

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Pressure Turbine Component Test Performance 

Report,” NASA CR-168289. 

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“Aerodynamics Investigation of Incidence Angle 

Effects in a Large Scale Transonic Turbine Cascade,” 

AIAA-2012-3879, July, 2012, Atlanta, GA., USA. 

14. Welch, G.E., McVetta, A.B., Stevens, M.A., Howard, 

S.A., Giel, P.W., Ameri, A.A., To, W., Skoch, G., J. 

and Thurman, D.R., 2012, “Variable-Speed Power 

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AHS Int. 68th Annual Forum, May 1-3; also 

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2007, “An evaluation of bypass transition models for 

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and Fluid Flow, 28, pp. 161–177. 

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M., 2008, “Predicting transition in two- and threedimensional separated flows,” Int. Journal of Heat and 

Fluid Flow, Volume 29, pp. 504-526. 

17. McVetta, A.B., Giel, P.W, Welch, G.E., 2013, 

“Aerodynamic Measurements of a Variable-Speed 

Power-Turbine Blade Section in a Transonic Turbine 

Cascade at Low Inlet Turbulence,” GT2013-94695, to 

be presented at 2013 ASME Turbo Expo. 

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Gegg, S., 2012, “Design Optimization of IncidenceTolerant Blading Relevant to Large Civil Tilt-Rotor 

Power Turbine Applications,” NASA/CR—2012-

217016, Dec. 

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Edition, McGraw-Hill Inc., New York. 

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Validation of a CFD Methodology for Variable Speed Power Turbine Relevant Conditions 

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14. ABSTRACT

Analysis tools are needed to investigate aerodynamic performance of Variable-Speed Power Turbines (VSPT) for rotorcraft applications. 

The VSPT operates at low Reynolds numbers (transitional flow) and over a wide range of incidence. Previously, the capability of a 

published three-equation turbulence model to predict accurately the transition location for three-dimensional heat transfer problems was 

assessed. In this paper, the results of a post-diction exercise using a three-dimensional flow in a transonic linear cascade comprising VSPT 

blading are presented. The measured blade pressure distributions and exit total pressure and flow angles for two incidence angles 

corresponding to cruise (i = 5.8°) and takeoff (i = −36.7°) were used for this study. For the higher loading condition of cruise and the 

negative incidence condition of takeoff, overall agreement with data may be considered satisfactory but areas of needed improvement are 

also indicated. 

15. SUBJECT TERMS

Power turbine; Low pressure turbine; Turbulence modeling; Computational Fluid Dynamics (CFD); Validation 

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