Ali A. Ameri

The Ohio State University, Columbus, Ohio

Computational Work to Support FAP/SRW

Variable-Speed Power-Turbine Development

NASA/CR—2012-217434

April 2012
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Ali A. Ameri

The Ohio State University, Columbus, Ohio

Computational Work to Support FAP/SRW

Variable-Speed Power-Turbine Development

NASA/CR—2012-217434

April 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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subject to revision as analysis proceeds.
NASA/CR—2012-217434 1 

Computational Work to Support FAP/SRW Variable-Speed 

Power-Turbine Development 

Ali A. Ameri 

The Ohio State University 

Columbus, Ohio 43210 

Abstract 

The purpose of this report is to document the work done to enable a NASA CFD code to model the 

laminar/turbulent transition on a blade. The purpose of the present work is to down-select a transition 

model that would allow the flow simulation of a Variable-Speed Power-Turbine (VSPT) to be accurately 

performed. The modeling is to be ultimately performed to also account for the blade row interactions and 

effect on transition and therefore allow accurate accounting for losses. The present work is however 

limited to steady flows. The low Reynolds number k-ω model of Wilcox and a modified version of same 

will be used for modeling of transition on experimentally measured blade pressure and heat transfer. It 

will be shown that the k-ω model and its modified variant fail to simulate the transition with any degree of 

accuracy. A case is therefore made for more accurate transition models. Three-equation models based on 

the work of Mayle on Laminar Kinetic Energy were explored and the Walters and Leylek model which 

was thought to be in a more mature state of development is introduced and implemented in the Glenn-HT 

code. Two-dimensional flat plate results and three-dimensional results for flow over turbine blades and 

the resulting heat transfer and its transitional behavior are reported. It is shown that the transition 

simulation is much improved over the baseline k- model. 

Introduction 

The key goal of the Subsonic Rotary Wing project is to enhance utilization of civil rotorcraft to 

relieve airport congestion and throughput capacity. One concept that has been advocated for this purpose 

is the use of tilt rotors to allow vertical takeoff of rotorcraft. In order to bring about fuel efficiency the 

main-rotor speed varies from 100 percent at takeoff to 50 percent at cruise. This can be achieved by using 

a transmission driven by a power turbine with minimal speed change. To avoid the added weight of the 

transmission a variable speed power turbine can be used instead of the transmission or in combination. To 

investigate the penalties associated with this alternative, various analytic tools are required. Such analysis 

tools require the capability to perform the physical modeling of these turbines within their operating 

envelope. This envelope is characterized by low Reynolds numbers, a characteristic of the power turbines, 

and a wide variation in the incidence angles due to the variation in the shaft speed. Lessons from the 

operation of Low Pressure Turbines and studies carried out for Low Pressure Turbines may be a source 

for guidance. 

Low Pressure Turbines have been reported to suffer loss of efficiency at higher altitudes under cruise 

conditions. This condition corresponds to a condition of low Reynolds number. Such low Reynolds 

number condition gives rise to separation of the flow on the suction side of the blades and in the case of 

absence of reattachment on the blade would give rise to large losses of efficiency. For the Power Turbine 

we have the additional requirement to also obtain accurate performance estimates for separation caused 

by a negative incidence. In short, better guidance for the design of the Power Turbine may be obtained if 

accurate and reliable simulation tools are available. Even in the absence of separation, the state of the 

boundary layer has a large effect on the loss in total pressure and must be addressed. Boyle and Ameri 

(Ref. 1) have shown that the prediction of the state of the boundary layer has a significant impact on the 

accuracy of the prediction of losses. 
NASA/CR—2012-217434 2 

Research and development work on analytical tools such as CFD codes utilizing transition models 

have been ongoing. In recent years, advances in modeling have been reported that may benefit the present 

work (Refs. 2 to 6). 

Use of trusted analytic tools can lead to understanding of the behavior of various designs and their 

operations under design and off-design conditions. Owing to the expected range of Reynolds numbers, the 

issue of transition will be paramount. The present report only addresses implementation of transition 

models and testing under steady conditions. It does not address the wake induced transition. That will be 

the subject of a future work. 

Transition Modeling Options 

Implementation of transition models in NASA codes is not a new endeavor. As an example Ameri 

and Arnone undertook this task as reported in Reference 7 by implementing the then available 

intermittency models in a three-dimensional code. One of the ways that transition is modeled is to use an 

algebraic transition criterion within a flow solver. Such transition models are sensitive to the state of the 

boundary layer and indicate the start and extent of the transition. The progress of transition is marked by 

an intermittency factor, which is zero for a laminar flow and unity for a fully turbulent flow. This type of 

modeling implemented as shown in Reference 7 worked rather well but its use was limited by the 

necessity of computing velocity-profile measures such as momentum thickness. These measures are not 

readily computable in three-dimensional passages and in codes which use general multi-block grids or 

unstructured grids. This method of modeling was therefore excluded from the options. 

Another option that was entertained was the idea of computing the flow in two stages. The method 

was to initially carry out a laminar flow computation and to note the point of separation. The second 

computation would then run the flow as laminar up to separation and then turn the flow turbulent at the 

point of separation. Again, this scheme was not picked because of lack of generality, as the mode of 

transition may not be separation-induced. 

A viable option involves using intermittency methods along with a two-equation turbulence model. 

Various researchers have taken up this approach. They appear to have settled on an additional transport 

equation for a Re Reynolds number based on momentum thickness type variable which obviates the 

need for computation of momentum thickness through boundary layer integration (Refs. 2, 3, and 6). 

Another option available is to use transport equations that are set up for transition and turbulence and 

model them in a phenomenological manner (Ref. 4) without the necessity to compute any boundary layer 

or integral quantities. In the work we have undertaken, and about to report, the transition prediction using 

the k- model in its original form and a modified form as well as a k- based three-equation model 

developed by Walters and Leylek (Ref. 5) which was developed with emphasis on transition in its 

development. The newer models were implemented in a NASA code called Glenn-HT and tested. We will 

report on the various aspects of implementation and the results obtained thus far. 

In the event that the performance of the model is not satisfactory, we will explore other options such 

as the intermittency models described. 

In the following, we will first describe the data chosen for testing of various models. Next, we will 

review the grid generated for the chosen blade model. We will then describe the attempts at prediction of 

the data. We will emphasize the transition model of Walters and Leylek, its description, implementation 

and the results obtained. 

Source of Transition Data 

As described earlier, the flow in turbine blade passages of VSPT is expected to have low Reynolds 

numbers and thus be subjected to flow transition and separation. Coding turbulence models requires 

access to data for verification. We have access to data for transition as occurs as by-pass and do not have 

access to data for separated flows. Suitability of the models to separation induced transition is not 

 
NASA/CR—2012-217434 3 

therefore specifically checked. In part two of this work as we vary the incidence angles, separation will be 

an important aspect of the flow. We will compare the losses under those conditions to the available data 

for losses. The separation aspect may be an important aspect to investigate in the future. 

Data of Giel et al. 

The data used for this part of our work is from the experiment of Giel et al. (Ref. 8). They were 

obtained for an industry provided blade profile designated at NASA Glenn as “GE2.” Blade GE2 was a 

first stage turbine blade for a GE heavy frame power turbine (2500 °F class). Blade loading and nearly 

full-span heat transfer coefficient (Nusselt number) data were obtained. 

The design Reynolds number based on axial chord and exit conditions (designated by subscript ‘2’) 

was 2.68×106

. Data were also obtained at 50, 25, and 15 percent of the design value. The design pressure 

ratio was 1.443. Data were also obtained at −25 and 20 percent of this, and at inlet incidence angles of 

5. Eight cases were presented in the paper, but data are available for a total of 13 cases. The nominal 

15 percent value for Re2 = 375,000 is used in this report. The case designated as 15 percent is data we will 

work with in this report. 

Table 1 lists the blade dimensions and some pertinent data. 

TABLE 1.—GEOMETRIC DATA FOR GE2 

Figure 1, taken from (Ref. 8), clearly demonstrates the effect of Reynolds number on midspan suction 

surface flow transition. The plot shows clearly the transition from laminar to turbulent blade heat transfer 

as evidenced by a steep rise in heat transfer on the suction side and by curving up the heat transfer curve 

(Nusselt number) on the pressure side. 

In this work the mid-span data is used for two-dimensional computations. The inlet turbulence was 

specified as measured at 13 percent and the pressure ratio and the Reynolds number were matched to the 

experimental conditions. Wall Temperature was specified as constant for the simulation runs. 

For the three-dimensional runs the span-wise boundary layer thickness is specified = 37 percent of 

span. 

Other Data 

We supplement the data for GE2 with flat plate laminar and heat transfer and friction factor data 

taken from literature (as presented in Ref. 9). The Mach number chosen was approximately 0.2 and the 

Reynolds number based on local streamwise position from the leading edge of the plate covers five 

decades on the log-log plots to be presented. The flat plate case is notional and is for a zero pressure 

gradient case. 
NASA/CR—2012-217434 4 

Figure 1.—Nusselt number variation for GE2 blade versus wetted distance on the blade 

surface for four different Reynolds numbers. 

Computational Grid 

The grids used for CFD computations are generated using a commercial software tool called GridPro 

(Program Development Corporation). The software uses an elliptic solver to smooth an initial 

algebraically generated grid. The software generates a multi-block grid. 

Two geometries were used for this work. A two-dimensional grid for a flat plate computation and 

two-dimensional grid for the Giel et al.’s GE2 geometry (Ref. 8). A three-dimensional grid is also 

generated for GE2 but the details and the results, to be obtained, will be presented in subsequent reports. 

As shown in Figure 2, the flat plate grid starts upstream of the flat plate. Grid is refined near the leading 

edge (shown in Fig. 2(b)) and expands proceeding downstream. It is highly refined in the cross-stream 

direction to allow resolution in the laminar subgrid regime (y+ = 1). The grid is generated in 16 blocks. 

For the GE2 blade, for the three-dimensional grid (results not presented in this report), taking 

advantage of the symmetry of the passage, only half of the passage is gridded. The grid was constructed 

using 100 blocks. This applied to both the two-dimensional and three-dimensional cases that were 

generated. As is the practice with grid generation when using the software GridPro, an inviscid grid is 

generated first and subsequently viscous grid is generated using clustering. Clustering was done for the 

blades’ surfaces (and the endwall surface for the three-dimensional grid). The spacing was chosen such 

that the first grid lines were at a dimensionless wall distance (y+

) of near unity. Figure 3(a) and (b) show a 

two-dimensional and three-dimensional grid for the computations to follow. The inlet plane was situated 

to match the measurement stations in the experiment namely, at one axial chord upstream of the blade. 

The exit plane was placed at a measuring station corresponding to approximately two axial chords 

downstream. 

The three-dimensional grid consists of 610,000 grid points with 65 grid points used in the spanwise 

direction. The two-dimensional grid consists of 9500 points. 

Results of the three-dimensional computations are not reported in this document and will be 

addressed in the future. 

 
NASA/CR—2012-217434 5 

(a) 

(b) 

Figure 2.—(a) Grid for the two-dimensional grid and (b) near leading edge of the plate. 

(a) 

(b) 

Figure 3.—(a) The midspan grid and (b) The full three-dimensional grid. 

 
NASA/CR—2012-217434 6 

Glenn-HT Computer Code 

The computer code used and modified in this work is the Glenn-HT code. The code has a Graphical 

User Interface where the capabilities are illustrated. The code can be described as follows.

Glenn-HT is FORTRAN90 code. It is designed to be a multi-physics code and presently is capable of 

performing solid conduction and compressible fluid flow. It is written in modular form and follows object 

oriented programming concepts. 

The code solves the unsteady compressible Navier-Stokes equations using a multigrid scheme and 

dual time stepping. An explicit Runge-Kutta solver is used as a smoother. The code uses a Multi-block 

structured grid but the blocks can be arranged in an unstructured manner. It uses a finite volume 

formulation. The default solver uses a central difference convective scheme, 4th order artificial 

dissipation with eigenvalue scaling helps to dampen oscillations and 2nd order differencing is used near 

shocks. Second order upwind scheme is also available. The code has been used in numerous studies and is 

held to be a reliable tool. 

Parallel Computing 

The 100 blocks of the GE2 case or the 16 blocks of flat plate are assigned to multiple CPUs. The 

relative sizes of the blocks determine how many CPUs may be used in an efficient manner. In this work a 

maximum of 20 CPUs were used for the GE2 case and 8 for the flat plate. 

Modeling Effort

Initial attempt at modeling the heat transfer on the GE2 blade was with the k- model. Our attempt’s 

lack of success in obtaining good results led us to seek a better transition model. Our experience with the 

k- model and Walter-Leylek’ s

~ k--kl model is reported below.

K-Omega Model 

The low Reynolds number variant (Ref. 10) is implemented in the code. As shown in Figure 4, the 

modeling produced a laminar flow solution in the immediate vicinity of the stagnation point and as it has 

been the community’s experience, we observe that the model goes through transition prematurely. 

Figure 4 presents the heat transfer rate described in terms of Nusselt number on the GE2 blade at midspan. Computations using the low Reynolds number k- model designated as the default version shows 

good match with the data at the leading edge. The agreement deteriorates soon after as the flow becomes 

fully turbulent in a short distance. Wilcox, in his book (Ref. 10), describes a possible way of adjusting the 

transition process in his model. The manner in which the transition process occurs in the model is 

described through the illustration shown in Figure 5, in which the friction factor for flow over a flat plate 

is plotted. There are two locations on the graph marked as (Rex)k and (Rex) The following expressions 

are used to compute these two thresholds: The factor 90,000 is known as the minimum critical Reynolds 

number for infinitesimal disturbances (Rex)cr when adjusted yields constants for the model that do not 

violate basic rules.  and 

 are constants in the k- model that determine the location and extent of 

transition. 

 (Rex)k = (Rex)cr *(

 

 (Rex)  (Rex)cr *(

 
NASA/CR—2012-217434 7 

Figure 4.—Nusselt number on GE2 blade with k- model. The data is form (Ref. 8) for the 50 percent span. 

Figure 5.—A schematic of skin friction variation for a boundary 

layer undergoing transition from laminar to turbulent flow. 

The value of (Rex)k should be lower than (Rex) for transition to first begin and for the latter to 

stabilize the flow and not allow it to continue amplifying. We chose to multiply both of the two thresholds 

by a factor (“Fac”) and thus move the transition downstream. Values of (Rex)k and (Rex) of 90,000 and 

122,500 produce the constants that are the values given by Wilcox. 

If (Rex)cr is replaced by (Rex)cr /Fac, the new form would allow for moving the transition location 

downstream. As shown in Figure 4, the factor “Fac” causes the transition point to shift downstream. The 

fully turbulent flow results are not changed as would be required by this change. Unfortunately, although 

there is some effect on transition, the agreement with the data is not satisfactory and does not warrant 

adaptation as a remedy. 

 
NASA/CR—2012-217434 8 

Walters and Leylek Model 

To the author’s knowledge there are two types of models that allow for transition modeling in a flow 

field. One type is as described by Suzen and Hwang (Ref. 2) and have been improved in many 

publications such as those in References 2 and 3. These models cast transition correlations in the form of 

transport equations thus making them suitable for flow field computations. The other type, such as the 

model of Walters and Leylek (Refs. 4 and 5), was developed with the process of transition built-in from 

the start. Walters and Leylek report that in developing their model(s) their intention was for the model to 

be as “hands off” for the user, requiring no modification for different application cases. It is a 

phenomenological model as opposed to an empirically based model. It is a single point model and does 

not require non-local or integral quantities. That latter fact is important enough that we did not choose 

(and did not see how to implement) the model of Pacciani et al. (Ref. 6) because it requires quantities that 

were not “single point” although the results of application of the model to two-dimensional separated 

flows were shown to be quite promising. 

Turbulence models and some transition models rely upon turbulence diffusion and interaction with 

shear to promote transition. Experimental and computational evidence (Ref. 11) suggest that for the 

bypass transition that may not be the mechanism. The laminar profile starts being affected by free stream 

turbulence as low as 1 percent by shifting momentum from outer region to inner region near the wall. At 

the same time, large amplitude and low frequency streamwise fluctuations lead to increase in friction and 

wall heat transfer resulting in bypass transition as these streamwise fluctuations grow and breakdown. 

The low frequency aspect is critical. Shown by Moss and Oldfield (Ref. 12), the wall heat transfer does 

not respond to high frequency spectra in the free stream where as the low frequency oscillations produces 

an increase in the level of wall heat transfer. Called “Splat Mechanism,” described again by Bradshaw 

(Ref. 13). Volino and Simon (Ref. 14) showed, by measuring the spectra of fluctuations in the free stream 

and in the boundary layer, that –u’v’ in the boundary layer upstream (in the pre-transitional region) occurs 

at the same frequency as v’ in the upstream and thus is responsible for these oscillations. While the 

streamwise fluctuations do not change the mean velocity profile, they do lead to bypass transition. 

Boundary layer is selective to certain free stream eddy scales and low-frequency disturbances in the 

boundary layer are amplified by the mean shear. The dynamics embodied in these streamwise 

fluctuations, in the model of Walters and Leylek, is captured by a “Laminar Kinetic Energy” equation 

through a modification of the concept devised by Mayle and Schultz (Ref. 15). Splats occur only for 

eddies with large length scales relative to the wall distance. Walters and Leylek have distinguished a 

“wall limited” large scale and “non-wall limited,” or small scale eddies in the near wall region as shown 

from Figure 6 taken from Reference 4. The effective eddy size designated in that figure delineates 

between larger eddies that contribute to the laminar kinetic energy (kL) and smaller ones that contribute to 

the turbulence. Start of transition is initiated by transfer of energy from the laminar kinetic energy to the 

turbulent fluctuations once a threshold is reached. Additional measures are implemented in the model to 

allow for natural and mixed mode transition. The turbulence model originally (Ref. 4) consisted of 

transport equations for laminar and turbulent kinetic energy and rate of dissipation of kinetic energy of 

turbulence, kL, kT,  In a later paper (Ref. 5) the transport equations solved were modified to include 

the inverse turbulent time scale. It is suggested that the latter form leads to a better representation of the 

breakdown of laminar kinetic energy to turbulence. This form was implemented in the Glenn-HT code
NASA/CR—2012-217434 9 

Figure 6.—Delineation of scales relevant to production of laminar and turbulent kinetic energy. 

Some Aspects of the Implementation of the Model 

The model was implemented into NASA’s Glenn-HT code. As the code is primarily an explicit code, 

the model equations were also implemented in an explicit manner. There are particular considerations 

about the implementation of the present model that will be briefly addressed. 

 Computation of distance to the wall had to be added to the code as the FORTRAN 90 version of 

Glenn-HT did not include this computation. The basic k- model which was originally implemented 

in the code, does not use the distance to the wall. Computation of wall distance as implemented is 

exclusively done for blocks having a wall boundary. For blocks having more than one wall boundary, 

the harmonic average of the individual wall distances was used for the effective quantity. For blocks 

not having a wall boundary the wall distance was designated as “very large.” As such, some care 

needs to be exercised in the process of grid generation not to develop meshes that have blocks 

neighboring walls that are too thin. As the wall distance within a block spans several orders of 

magnitude, the practical implementation of this is not very restricting. 

 Three variables (instead of one) had to be defined for the eddy viscosity, turbulent thermal diffusivity 

and turbulence diffusion required by the model. The standard method is to use the eddy viscosity and 

use turbulent Prandtl number and Schmidt number to model other fluxes. 

 Additional model specific variables were defined to store the above and additional variables and to 

carry the “jacobian” of the source terms. 

 The model calls for Neumann boundary conditions for laminar kinetic energy, turbulent kinetic 

energy and rate of dissipation on the walls as well as Dirichlet boundary conditions for laminar and 

turbulent kinetic energies. This over-specification was thought to be unsound and as it is the standard 

practice, we decided to use Neumann boundary conditions for the kinetic energies and Dirichlet for 

the rate of dissipation. 

 As stated earlier the model equations were treated explicitly. Few of the source terms thought to be 

contributing to the stiffness of the equations were linearized and treated implicitly to help with that 

issue. This part of the code may require more work and pointwise coupling of the model equations 

maybe explored. As implemented presently, there is a severe reduction in CFL as it relates to the 

model equations. 

Source code is available on NASA computers upon request.
NASA/CR—2012-217434 10 

Results 

Flat Plate 

The plots of coefficient of friction (Cf) and Stanton number (St) for flow over a flat plate are shown in 

Figures 7 and 8. Figure 7 shows the variation of friction factor, Cf  w /(0.5  u∞

2

), or normalized wall 

shear stress by the dynamic head against the local Reynolds number. The figure presents two lines 

belonging to a specific inlet turbulence intensity and computed on two different grid refinement levels. 

The lines show that the results are converged in grid resolution and that the transition effect appears 

reasonable. Also, the results of Cf show very good match to both the theoretically based laminar flow 

solutions and measured turbulent flow values reported in Reference 9. 

Figure 7.—Friction factor on a flat plate computations with Walters-Leylek model and 

comparison with data from Reference 9. 

Figure 8.—Transitional Stanton number on a flat plate and comparison with to data from 

Reference 9. 

9

9 
NASA/CR—2012-217434 11 

The plot showing the variation of Stanton number with the local Reynolds number also shows a good 

match with the turbulent flow correlation reported in Reference 9. The plot of Stanton number of Figure 8 

includes two levels of grid resolution as well as two levels of turbulence intensity. Agreement with the 

laminar flow heat transfer is imperfect showing an enhancement that appears to increase with turbulence 

intensity. Although this effect is indeed plausible- owing to increase in laminar wall heat transfer due to 

free stream turbulence- the fact that the agreement with laminar flow improves upon grid refinement 

suggests that further increase in grid refinement may remove this seeming enhancement. The location of 

transition shows a physical movement upstream with increase in turbulence intensity which is physically 

correct. The results make enough physical sense that we can turn our attention to the blade results. 

GE2 Blade Comparisons 

Pressure 

Two-dimensional runs were made to compare with mid-span results of GE2 experiment. As is the 

case with Glenn-HT code, the computations are started on a coarse grid and once that solution has 

reasonably converged, the results are interpolated to a twice as refined grid and the iteration scheme is 

continued until convergence. The results of the “coarse” and “fine” grid are shown in Figures 9 and 10. 

Figure 9 shows the pressure distribution on the blade. Before discussing the agreement between the 

computations and the data, it should be remembered that in the experiment, the hub endwall had a very 

thick boundary layer and thus the pressure distribution from a two-dimensional computation should not 

match the three-dimensional run. Agreement with pressure will be reviewed when three-dimensional runs 

are made in the near future. 

Figure 9.—Pressure distribution at the midspan of GE2 blade and comparison 

to data from Reference 8. 
NASA/CR—2012-217434 12 

Figure 10.—Nusselt number at midspan of GE2 and comparison with experimental data of Giel et al. (Ref. 8) 

at 50 percent span. 

Nusselt Number 

In Figure 10, the ordinate is the Nusselt number and the abscissa is the normalized wetted distance on 

the suction side and pressure sides. Nusselt number is defined as: 

Nu hC / k Cx  x (3) 

where Cx is the axial chord of the blade k is the thermal conductivity of the fluid and h is the heat transfer 

coefficient defined as: 

  aw w

w

T T

q h   (4) 

in Equation (4), qw is the wall heat flux, Tw and Taw are the wall temperature and the recovery temperature, 

respectively. The Taw in the experiment (Ref. 8) was computed by an expression involving the recovery 

factor, 

1 3 Pr / r  (5) 

where Pr is the Prandtl number which is a physical property of the fluid. 

The equation for the recovery temperature is: 





 



     2

2

1 Taw Ts 1 r M (6) 
NASA/CR—2012-217434 13 

Where M is the isentropic Mach number and is computed from the local wall pressure and inlet total 

pressure. Ts is the isentropic static temperature corresponding to the given Mach number. Given the above 

and the wall heat flux, the Nusselt number (Nu) can be computed. 

Figure 10 shows the results for the coarse and fine grid solutions at midspan. The data is shown for 

comparison. There are two turbulence length scales used. The results for the smaller length scale, do not 

exhibits good agreement on the pressure side where the results appear to suddenly turn turbulent. The 

suction side heat transfer like the experimental data shows a transitional behavior for which the location and 

extent of the transition agrees with the data. The lack of agreement on the pressure side and better agreement 

on the suction side suggested that the length scale may be an issue as the pressure side is more prone to 

buffeting by the free stream turbulence. The length scale was increased to 0.05*Cx and the pressure side heat 

transfer improved greatly. Grid convergence has not been checked for the higher scale case. 

The solutions show that the model is working well and is capable of simulating the transition start and 

extent. As for the convergence behavior of the two-dimensional solution, the solution was quite slow and 

required that a small CFL be used for much of the progress of the solution. 

This issue needs further attention. 

Summary 

For the Variable-Speed Power-Turbine work, the flow transition process has been identified as an 

important process to accurately model. Computational work needs to address this question if the losses 

are to be predicted correctly. This work has surveyed the literature and has found two suitable candidates. 

One is intermittency type models (Refs. 2 and 3) and one involving a phenomenological model of the 

bypass transition. The present work describes the performance of the low Reynolds number k- model 

and the implementation and preliminary results from the Walters-Leylek model (Refs. 4 and 5) on a blade 

for which experimentally measured data is available. The model was implemented in NASA Glenn-HT 

code and tested as applied to a turbine blade test case. The location of transition was successfully 

predicted on the suction side and the transition modeling on the pressure side appears to be promising. 

Future Work 

Future work should look at further two-dimensional and three-dimensional applications of the model. 

For the two-dimensional cases, fine grid solution for the higher length scale should be obtained. Threedimensional solutions should allow for comparison against the pressure distribution and heat transfer on 

other span locations. Improvement in the robustness of the numerical scheme is another topic that 

deserves attention. Finally, losses need to be computed and compared with experimental data. 

References 

1. R.J. Boyle and Ali A. Ameri, “Grid Orthogonality Effects on Turbine Midspan Heat Transfer and 

Performance,” ASME Journal of Turbomachinery, 119, No. 1, pp. 31–38, Jan. 1997. 

2. Suzen, Y.B., and Huang, P.G., 2000, “Modeling of Flow Transition Using an Intermittency 

Transport Equation,” ASME Journal of Fluids Eng., 122, pp. 273–284. 

3. Steelant, J., and Dick, E., 2001, “Modeling of Laminar-Turbulent Transition for High Free-stream 

Turbulence,” ASME Journal of Fluids Eng., 123, pp. 22–30. 

4. Walters, D. Keith and Leylek, James H., 2004, “A New Model for Boundary Layer Transition 

Using a Single-Point RANS Approach,” ASME Journal of Turbomachinery, Volume 126, Issue 1, 

193. 

5. Walters, D. Keith and Leylek, James H., “Computational Fluid Dynamics Study of Wake-Induced 

Transition on a Compressor-Like Flat Plate,” ASME Journal of Turbomachinery—January 2005—

Volume 127, Issue 1, 52 (12 pages). 
NASA/CR—2012-217434 14 

6. Pacciani R., Marconcini M., Fadai-Ghotbi A., Lardeau S., Leschziner, M.A., 2011, “Calculation of 

High-Lift Cascades in Low Pressure Turbine Conditions Using a Three-Equation Model,” ASME 

Journal of Turbomachinery, 133, 031016 (2011). ISSN 0889-504X. 

7. Ali A. Ameri, A. Arnone, “Transition Modeling Effects on Turbine Rotor Heat Transfer,” ASME 

Journal of Turbomachinery, 118, No. 2, pp. 307–313, Apr. 1996. 

8. Paul W. Giel, Ronald S. Bunker, G. James Van Fossen and Robert J. Boyle, “Heat Transfer 

Measurements and Predictions on a Power Generation Gas Turbine Blade,” NASA/TM—2000-

210021 and ASME 2000–GT–0209. 

9. Fundamentals of Heat Transfer, Incropera, Frank P.; DeWitt, David P. New York: Wiley, c1981. 

10. Wilcox, D.C., Turbulence Modeling for CFD, 3rd edition, DCW Industries, Inc., La Canada CA, 

2006. 

11. Volino, R.J., 1998, “A New Model for Free-Stream Turbulence Effects on Boundary Layers,” 

ASME J. of Turbomachinery, 120, pp. 613–620. 

12. R.W. Moss and M.L.G. Oldfield, 1996, “Effect of Free-Stream Turbulence on Flat-Plate Heat Flux 

Signals: Spectra and Eddy Transport Velocities,” ASME Journal of Turbomachinery, Volume 118, 

Issue 3, 461. 

13. Bradshaw, P., 1994, “Turbulence: The Chief Outstanding Difficulty of Our Subject,” Exp. Fluids, 

16, pp. 203–216. 

14. Volino, R.J., and Simon, T.W., 1997, “Boundary Layer Transition Under High Free-Stream 

Turbulence and Strong Acceleration Conditions: Part 2—Turbulent Transport Results,” ASME 

Journal of Heat Transfer, 119, pp. 427–432. 

15. Mayle, R.E., and Schulz, A., 1997, “The Path to Predicting Bypass Transition,” ASME Journal of 

Turbomachinery, 119, pp. 405–411. 
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Computational Work to Support FAP/SRW Variable-Speed Power-Turbine Development 

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14. ABSTRACT

The purpose of this report is to document the work done to enable a NASA CFD code to model the transition on a blade. The purpose of the 

present work is to down-select a transition model that would allow the flow simulation of a Variable-Speed Power-Turbine (VSPT) to be 

accurately performed. The modeling is to be ultimately performed to also account for the blade row interactions and effect on transition and 

therefore accurate accounting for losses. The present work is limited to steady flows. The low Reynolds number k-ω model of Wilcox and a 

modified version of same will be used for modeling of transition on experimentally measured blade pressure and heat transfer. It will be 

shown that the k-ω model and its modified variant fail to simulate the transition with any degree of accuracy. A case is therefore made for 

more accurate transition models. Three-equation models based on the work of Mayle on Laminar Kinetic Energy were explored and the 

Walters and Leylek model which was thought to be in a more mature state of development is introduced and implemented in the Glenn-HT 

code. Two-dimensional flat plate results and three-dimensional results for flow over turbine blades and the resulting heat transfer and its 

transitional behavior are reported. It is shown that the transition simulation is much improved over the baseline k-ω model.

15. SUBJECT TERMS

Power turbine; Low pressure turbine; Turbulence modeling; Heat transfer; Losses 

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