Samuel J. Vinci

Cleveland State University, Cleveland, Ohio

CFD Simulations for the Effect of Unsteady Wakes 

on the Boundary Layer of a Highly Loaded 

Low-Pressure Turbine Airfoil (L1A)

Final Report

NASA/CR—2012-217417

September 2012
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Samuel J. Vinci

Cleveland State University, Cleveland, Ohio

CFD Simulations for the Effect of Unsteady Wakes 

on the Boundary Layer of a Highly Loaded 

Low-Pressure Turbine Airfoil (L1A)

Final Report

NASA/CR—2012-217417

September 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared under NASA Interagency Agreement No. NNC07IA10I 

(through U.S. Navy Agreement No. N00189–07–P–A253)

Prepared under Grant No. DE–FC26 –06NT42853
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Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

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

Acknowledgments

The author gratefully acknowledges the National Aeronautics and Space Administration for sponsoring the work. Dr. Anthony 

J. Strazisar, Dr. James D. Heidmann, and Dr. David E. Ashpis of the NASA Glenn Research Center served as grant technical 

monitors. 
CFD SIMULATIONS FOR THE EFFECT OF UNSTEADY WAKES ON THE 

BOUNDARY LAYER OF A HIGHLY LOADED LOW PRESSURE TURBINE 

AIRFOIL (L1A)

SAMUEL J VINCI

ABSTRACT

The study of a very high lift, low-pressure turbine airfoil in the presence of unsteady 

wakes was performed computationally and compared against experimental results. The 

experiments were conducted in a low speed wind tunnel under high (4.9%) and then low 

(0.6%) freestream turbulence intensity conditions with a flow coefficient (ζ) of 0.7. The 

experiments were done on a linear cascade with wakes that were produced from moving 

rods upstream of the cascade. The flow coefficient was kept at 0.7 while the rod to blade 

spacing was changed from 1 to 1.6 to 2 blade spacings. These cases were conducted for 

Reynolds number equal to 25,000 and 50,000, based on the suction surface length and the 

nominal exit velocity from the cascade. 

The experimental and computational data have shown that in cases without wakes, 

the boundary layer separated and did not reattach. The CFD was done with LES and 

URANS utilizing the finite-volume code ANSYS Fluent under the same freestream 

turbulence and Reynolds number conditions as the experiment but only at a rod to blade 

spacing of 1. 

With wakes, separation was largely suppressed, particularly if the wake passing 

frequency was sufficiently high. This was validated in the 3D CFD efforts by comparing 

the experimental results for the pressure coefficients and velocity profiles, which were 

reasonable for all cases examined. The 2D CFD efforts failed to capture the three 

NASA/CR—2012-217417 LLL
dimensionality effects of the wake and thus were less consistent with the experimental 

data. The effect of the freestream turbulence intensity levels also showed a little more 

consistency with the experimental data at higher intensities when compared with the low 

intensity cases. 

As a further computational study, cases were run to simulate higher wake passing 

frequencies which were not run experimentally. The results of these computational cases 

showed that an initial 25% increase from the experimental wake passing frequency of 

F=0.548 greatly reduced the size of the separation bubble, nearly completely suppressing 

it, however an additional 33% increase on top of this did not prove to have much of an 

effect.

NASA/CR—2012-217417 LY
TABLE OF CONTENTS

Page

ABSTRACT........................................................................................ iii 

LIST OF TABLES................................................................................. iv 

LIST OF FIGURES............................................................................... v 

NOMENCLATURE............................................................................... vi 

CHAPTER

I. INTRODUCTION............................................................... 1 

II. LITERATURE REVIEW....................................................... 3 

III. EXPERIMENTAL FACILITY AND MEASUREMENTS................ 7 

IV. NUMERICAL MODELS AND DOMAIN.................................. 10 

V. RESULTS AND DISCUSSION............................................... 17 

2D Results........................................................................ 23 

3D Results........................................................................ 28 

 Re = 25,000, F=0.513 

Low Free Stream Turbulence Intensity..................... 30 

High Free Stream Turbulence Intensity .................... 36 

 Re = 50,000, F =0.548 

Low Free Stream Turbulence Intensity..................... 42 

High Free Stream Turbulence Intensity..................... 68 

 

NASA/CR—2012-217417 Y
Re50,000, High Free Stream Turbulence Intensity 

 F = 0.698........................................................ 84 

 F = 0.917........................................................ 95 

VI. CONCLUSION.................................................................. 107 

VII. BIBLIOGRAPHY............................................................... 110 

NASA/CR—2012-217417 YL
LIST OF TABLES

 Table Page

I. Cascade Parameters............................................................... 9 

II. Grid Refinement Parameters.................................................... 13 

III. CFD Test Matrix.................................................................. 15 

NASA/CR—2012-217417 YLL
LIST OF FIGURES

Figure Page

1. a. Schematic of Experimental Facility............................................. 8 

b. Schematic of Computational Domains and Mesh: a) 2D Domain b) 

Refined Rod Mesh c) 3D Computational Domain............................. 14 

2. Rod Wake Velocity Magnitude Contours for Re 50,000: Comparison 

between Course (a) and Refined 2 (b)............................................ 20 

3. Vorticity Contours for Re = 50,0000: Comparison between 2D (TransSST) Spacing 1 a) vs. 3D (LES) Spacing 1 b)................................. 21 

4. Code Validation: Comparison of Trans-SST (2D) 1Lφ results to LES 

(3D) 1Lφ and Experimental 1Lφ.................................................................. 22 

5. Cp profiles for Re=25,000, LFSTI: Comparison between Trans-SST 

(2D) and Experimental data...................................................... 25 

6. Total Pressure Loss Coefficient for Re=25,000, LFSTI: Comparison 

between Trans-SST (2D) and Experimental Data............................. 25 

7. Cp profiles for Re=50,000, HFSTI: Comparison between Trans-SST 

(2D) and Experimental data......................................................... 26 

8. Total Pressure Loss Coefficient for Re=50,000, HFSTI: Comparison 

between Trans-SST (2D) and Experimental Data............................. 26 

9. Rod Wake Velocity Magnitude for Re=50,000, HFSTI: Comparison of 

Trans-SST (2D), 1Lφ to Experimental 1.6Lφ................................... 27 

10. Vorticity Contours for Re = 50,0000, HFSTI: a) 3D – Trans-SST with 

time step = .001 seconds, b) 3D – Trans-SST – time step = .001 – Qcriterion colored by Vorticity Contours c) 3D – LES – time step = .0001 

– Q-criterion colored by Vorticity Contours................................... 

29 

11. Rod Wake Velocity Magnitude for Re=25,000, LFSTI: Comparison of 

LES, 1Lφ to Experimental 1.6Lφ.................................................. 33 

12. Cp profiles for Re=25,000, LFSTI: Comparison between LES and 

Experimental data.................................................................. 33 

NASA/CR—2012-217417 YLLL
Figure Page

13. Total Pressure Loss Coefficient for Re=25,000, LFSTI: Comparison 

between LES and Experimental Data................................................. 34 

14. Comparison of Mean Cp and Cf on suction surface for Re=25,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp.................. 35 

15. Rod Wake Velocity Magnitude for Re=25,000, HFSTI: Comparison of 

LES, 1Lφ to Experimental 1.6Lφ................................................ 39 

16. Cp profiles for Re=25,000, HFSTI: Comparison between LES and 

Experimental data.................................................................. 39 

17. Total Pressure Loss Coefficient for Re=25,000, HFSTI: Comparison 

between LES and Experimental Data........................................... 40 

18. Comparison of Mean Cp and Cf on suction surface for Re=25,000, 

HFSTI: a) Contours of mean Cf b) Contours of mean Cp.................... 41 

19. Rod Wake Velocity Magnitude for Re=50,000, LFSTI: Comparison of 

LES, 1Lφ to Experimental 1.6Lφ.................................................. 49 

20. Cp profiles for Re=50,000, LFSTI: Comparison between LES and 

Experimental data.................................................................. 49 

21. Total Pressure Loss Coefficient for Re=50,000, LFSTI: Comparison 

between LES and Experimental Data........................................... 50 

22. Time averaged velocity profiles at six streamwise stations for 

Re=50,000, LFSTI: Comparison between CFD (LES) and Experimental 

data: a - Mean, b – RMS.......................................................... 51 

23. Comparison of Mean Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp.......................... 53 

24. Comparison of Instantaneous Cp and Cf on suction surface for 

Re=50,000, LFSTI: a) Contours of mean Cf b) Contours of mean Cp

c)Q-criterion, Cp Contours d)Q-criterion, x-velocity Contours............. 54 

25. Rod Wake Velocity Magnitude for Re=50,000, HFSTI: Comparison of 

LES, 1Lφ to Experimental 1.6Lφ................................................ 72 

26. Cp profiles for Re=50,000, HFSTI: Comparison between LES and 

Experimental data.................................................................. 72 

NASA/CR—2012-217417 L[
Figure Page

27. Total Pressure Loss Coefficient for Re=50,000, HFSTI: Comparison 

between LES and Experimental Data........................................... 73 

28. Time averaged velocity profiles at six streamwise stations for 

Re=50,000, HFSTI: Comparison between CFD (LES) and Experimental 

data: a - Mean, b – RMS.......................................................... 74

29. Comparison of Mean Cp and Cf on suction surface for Re=50,000, 

HFSTI: a) Contours of mean Cf b) Contours of mean Cp.................. 76 

30. Comparison of Instantaneous Cp and Cf on suction surface for 

Re=50,000, HFSTI: a) Contours of mean Cf b) Contours of mean Cp

c)Q-criterion, Cp Contours d)Q-criterion, x-velocity Contours............ 77 

31. Rod Wake Velocity Magnitude for Re=50,000, HFSTI: Comparison of 

LES, F=0.548 to LES, F=0.698................................................. 87 

32. Cp profiles for Re=50,000, HFSTI: Comparison between LES, F=0.548 

to LES, F=0.698.................................................................... 87 

33. Total Pressure Loss Coefficient for Re=50,000, HFSTI: Comparison 

between LES, F=0.548 to LES, F=0.698.......................................... 88 

34. Comparison of Mean Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.698: a) Contours of mean Cf b) Contours of mean Cp........ 89 

35. Comparison of Instantaneous Cp and Cf on suction surface for 

Re=50,000, HFSTI, F=0.698: a) Contours of mean Cf b) Contours of 

mean Cp c)Q-criterion, Cp Contours d)Q-criterion, x-velocity 

Contours............................................................................. 90 

36. Rod Wake Velocity Magnitude for Re=50,000, HFSTI: Comparison of 

LES, F=0.548 to LES, F=0.917.................................................. 98 

37. a. Cp profiles for Re=50,000, HFSTI case: Comparison between 

Experimental and LES, F=0.548 to LES, F=0.917............................ 98 

b. Cp profiles for Re=50,000, HFSTI: Comparison between LES, 

F=0.548, F=0.689 and F=0.917............................................. 99 

38. Total Pressure Loss Coefficient for Re=50,000, HFSTI: Comparison 

between LES, F=0.548 to LES, F=0.917............................................ 99 

39. Comparison of Mean Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.917: a) Contours of mean Cf b) Contours of mean Cp.......... 100

NASA/CR—2012-217417 [
Figure Page

40. Comparison of Instantaneous Cp and Cf on suction surface for 

Re=50,000, HFSTI, F=0.917: a) Contours of mean Cf b) Contours of 

mean Cp c)Q-criterion, Cp Contours d)Q-criterion, x-velocity 

Contours............................................................................ 101

NASA/CR—2012-217417 [L

NOMENCLATURE

Cp ( ) 2

T − ρU/PP2 e , pressure coefficient

Cx axial chord length

F fLj-te/Uave, dimensionless wake passing frequency 

f frequency 

HFSTI High Freestream Turbulence Intensity (4.9%) 

Lj-te length of adverse pressure gradient region on suction surface

LFSTI Low Freestream Turbulence Intensity (0.6%)

Ls suction surface length

Lφ blade spacing (pitch) 

P pressure

PS upstream static pressure

PT upstream stagnation pressure 

PTe downstream stagnation pressure 

Re UeLs/ν, exit Reynolds number 

s streamwise coordinate, distance from leading edge

T period of wake passing cycle

t time

TI background freestream turbulence intensity 

U local mean velocity

Uave average freestream velocity in adverse pressure gradient region

Ui inlet freestream velocity

Ue nominal exit freestream velocity, based on inviscid solution 

NASA/CR—2012-217417 [LLL
u′ rms fluctuating streamwise velocity

x axial distance from leading edge

φ coordinate along blade spacing, normal to axial chord 

ν kinematic viscosity

ρ density 

ψ (PT-PTe)/(PT-PS), total pressure loss coefficient

ζ Uicos(αi)/Urod = Uaxial/Urod, flow coefficient

NASA/CR—2012-217417 [LY
Chapter I 

Introduction 

The desire to reduce fuel costs and improve engine performance in the gas turbine 

industry has led many to do experimental and computational fluid dynamics (CFD) 

research on the effects of flow over the airfoils of the low-pressure turbine blades. These 

experiments have shown that separation of the flow can occur on the suction surface of 

these blades due to the presence of adverse pressure gradients. This separation can result 

in partial loss of lift and higher aerodynamic losses at high altitude cruise conditions and 

becomes increasingly more severe as the aft loading of the airfoils increases. 

The desire to reduce the airfoil count and thus make a more cost efficient engine 

outweighs the losses associated with increasing the loading of airfoils, thus studying and 

accurately predicting the size and severity of the separation associated with a given 

loading is required in order to make improved designs in these high lift airfoils. This has 

led many in the field of computational fluid dynamics to create models that match the 

experimental data of these high lift airfoils. However, much like the airfoils themselves, 

an efficient model being low in computational time is as desirable as an accurate one. 

This is because the flow can be modeled directly using a direct numerical simulation 

technique, however the grid size and resulting computational time associated with such 

models is far too expensive to be useful in industry. This has lead to a number of 

different turbulence models, which use approximations of the flow in different regions to 

model the flow rather than directly compute what is occurring, thus decreasing the 

computational costs. These models vary in success, especially since the flow over an 

airfoil is very complex. It is the goal of this report to show which turbulence models 

NASA/CR—2012-217417 1
accurately model available experimental data. Once a model is proven to provide 

accurate results, further insight to the physics of the flow over the airfoil is capable of 

being examined. In this report, a review of previous studies examining different laminar 

to turbulent transitions will be reviewed, along with the relevant computational studies of 

these flows, which have provided the base of this study. A detailed description of the 

experimental set up and the results that were used as the data to validate the 

computational models will be provided as well as a detailed description of the 

computational domain created to run these models. Finally an examination of the 

computational results will prove which turbulence models can provide accurate results 

and further insight into flow transitioning separation and suppression. 

NASA/CR—2012-217417 2
Chapter II 

Literature Review

 The transition from a laminar to a turbulent flow over the airfoil blade is

described by Langtry [2006]. Here it is described that there are several different 

transitions that can cause the flow to become turbulent. The first is a “Natural” transition 

that occurs when the freestream turbulence has a relatively low intensity that allows for 

the growth of Tollmien-Shlichting two-dimensional waves. In general it is assumed that 

the freestream turbulence intensity levels in real turbomachinery is rather high, thus the 

presence of this form of transition is only partially present. However, since there are the 

adverse pressure gradients that are created over these highly loaded airfoils, this form of 

transition will still be considered to play an effect over the airfoils in this study. The 

second form of transition is a result of the high freestream turbulence in the flow and is 

called “bypass transition.” This form of transition is a result of rapidly growing three 

dimensional instabilities, which disturb the boundary layer and cause the flow to become 

turbulent. The later form of transition is the type that is the main focus of this paper.

 Early experimental and computational studies of the flow over these high lift 

airfoils were performed by examining the airfoils by themselves in a wind tunnel with 

varying levels of freestream turbulence intensities applied to the upstream flows. 

However, it has become evident that the presence of the forward stages of stator blades in 

front of the rotor airfoil blades creates wake shedding vortices, which play a big role on 

the boundary layer of these rotor blades. The velocity deficit in these wakes cause flow 

outside of the wake to accelerate and impinge on the suction surface of stator blades 

NASA/CR—2012-217417 3
creating a sort of “negative jet” [Hodson and Howell, 2005]. The study of this wake and 

the wake induced transition associated with it has started to become the topic of study in 

a number of experimentals, however this type of flow has yet to be extensively modeled 

computationally due to the difficulties associated with creating these models, which will 

be explained in more detail below. 

 The creation of the impinging wake on a stator has been studied by Pluim et al. 

[2009] and it was shown that a circular rod provides a sufficient representation of the 

form of the true wake that comes off the rotor blade. Thus experimental data is collected 

by passing a line of circular rods upstream of a cascade of airfoils with data collected by 

hot wire anemometers over the suction side of these airfoils. Many experiments have 

been run analyzing the wake/blade interaction effects; see Bons et al. [2008] and Pluim et 

al. [2009], however in this study direct experimental data was provided from Volino 

[2010]. Thus it was these experiments that the focus of this computational study will be 

based on. 

 In Volino [2010] the study of the effect of different rod to blade spacings was 

studied. The data behind the results of this experiment was available for this report and 

thus these cases are the basis of what this report attempted to numerically model. The 

details of the experimental domain and results are given in more detail below. 

Numerical studies of the wake and its subsequent interaction with an airfoil was 

studied in Sakar [2009]. In this study, the wake was created via a circular rod in its own 

computational domain and then interpolated into a domain containing the airfoil. The 

analysis of a circular wake generating rod and its effect on a downstream airfoil was 

examined for a Reynolds number of 78,000 (based on the axial chord and the inlet 

NASA/CR—2012-217417 4
velocity). The airfoil used is T106 [Stieger et al., 2003] with flow coefficient (ζ ) of 0.83 

and reduced blade passing frequency of 0.68. The wake was originally generated in both 

a 2D and 3D simulation using URANS and LES turbulence models respectively. These 

results were then interpolated into a 3D airfoil geometry and the effects of the 

wake/airfoil interaction were studied in LES. It was shown that the wakes produced in 

LES and interpolated into the airfoil domain produced smaller scale eddies and thus 

produced more accurate predictions of separation flow control than the 2D wakes. 

 Suzen and Huang [2005] numerically studied unsteady wake/blade interactions in 

LPT PAK-B flows using an intermittency transport equation. They followed experiments 

of Kaszeta et al. [2001, 2002] and Stieger [2002]. In that study predictions of the flow 

with the Intermittency Transport model were in a good agreement with experimental data 

for pressure coefficient. Differences in velocity predictions in the separated region were 

attributed to the inability of hot wire anemometry, used in experiment, to measure

negative velocities. The observation was made that high wake passing frequency resulted 

in suppression of the separation zone due to higher turbulence levels generated in the 

wake.

 Rodi [2006] conducted DNS and LES studies of the flow past turbine blades with 

incoming wakes. Reynolds number based on axial chord and inlet velocity was 51,800 in 

the low Re case and 148,000 in the high Re case. In both cases DNS and LES showed 

similar results for the pressure coefficient, which were in a reasonable agreement with 

experimental data. Some disagreement in pressure coefficient near the leading edge on 

the suction side was attributed to the difference in the inlet flow angle and 

compressibility effects of the flow, which was modeled as incompressible. In the high Re 

NASA/CR—2012-217417 5
case, where the flow was attached, LES predicted transition a little later compared to 

DNS and therefore it was concluded that LES is not a good tool for predicting this type of 

flow. However, it is necessary to mention that DNS required 10 times longer to compute, 

compared to LES and it cost the author several months of calculations on a 

supercomputer. 

Ladreau [2005] took an Unsteady Reynolds Averaging Navier Stokes (URANS) 

turbulence model and applied it to a moving wake generating rod and airfoil blade 

geometry. Here it was shown that the URANS models were very sensitive to the grid 

size and the time step size of the calculation. The results showed that with too coarse of 

size of either one of these results in the wake structure, with vortex shedding, not 

developing due to the small length scale of the circular wake generating rod as compared 

to the blade. 

NASA/CR—2012-217417 6
Chapter III

Experimental Facility and Measurements

The experimental data used for comparison in this study came from experiments 

by Volino [2010] on a very highly loaded LPT airfoil L1A. This airfoil was designed at 

the Air Force Research Laboratory (AFRL) and is available on a limited basis from Clark 

[2007]. The L1A is aft loaded which makes the boundary layer more prone to separation 

[Bons et al., 2008, Ibrahim et al., 2008 and Volino et al., 2008]. As described in Volino 

[2010], experiments were conducted in a closed loop wind tunnel with a seven blade 

linear cascade as shown in Fig. 1 with the dimensions shown in Table 1. The streamwise 

component of the turbulence intensity was 0.6% with the integral length scale of 6.3 cm. 

A tailboard, shown on Fig. 1, was used to ensure the correct flow angle from the cascade 

with periodicity at high Reynolds numbers. At low Reynolds numbers the periodicity was 

not as good because large separation was present and due to suppression of the separation 

on the blades closest to the tailboard. 

The wake generator includes a chain near each endwall of the cascade that passes 

0.54Cx upstream of the leading edges of the cascade blades. The chain links have hollow 

pins, through which the wake generator rods are attached. The diameter of each rod is 4 

mm. Tests were run with average distances between rods of 136 mm, 221 mm, and 272 

mm, which correspond to 1Lφ, 1.6Lφ and 2Lφ, where Lφ is the blade spacing in the 

cascade. These ratios of rod to blade spacing are in the range expected for vane to rotor 

blade spacing in an engine. This wake was initially examined to determine if the wake 

shedding produced similar velocity and RMS profiles to that from an airfoil. These 

NASA/CR—2012-217417 7
results were compared against downstream profiles from airfoil designs with and without 

vortex generator jets showing similar profiles, thus proving the circular rod to be a 

sufficient simulator of an upstream wake generator. Flow coefficients were varied from 

0.35 to 1.4 and wake spacing was varied from 1 to 2 blade spacings, resulting in 

dimensionless wake passing frequencies F=fLj-te/Uave (f is the frequency, Lj-te is the length 

of the adverse pressure gradient region on the suction surface of the airfoils, and Uave is 

the average freestream velocity) ranging from 0.14 to 0.56. 

For most tests, the rods were driven at a velocity of 1.18 times the cascade inlet 

velocity, Ui. This gives a flow coefficient, ζ =Uicos( αi)/Urod=0.7, where αi is the inlet 

flow angle. This is also in the expected range for an engine. 

Fig. 1a. Schematic of the linear cascade

Rod

NASA/CR—2012-217417 8
Table I: Cascade parameters

Axial Chord, 

Cx

[mm]

True 

Chord 

[mm]

Pitch,

Lφ

[mm]

Span

[mm]

Suction 

side, Ls

[mm]

Inlet 

flow 

angle

Exit 

flow 

angle

134 146 136 724 203 35° 60°

The results of this experiment showed that flow over an L1A airfoil is separated 

without reattachment for Re = 25,000 and 50,000 (based on the suction surface length 

and the nominal exit velocity from the cascade) [Ibrahim et al., 2008 and Volino et al., 

2008]. Volino [2010] observed that in the presence of the wakes passing with high 

frequencies separation on this airfoil was largely suppressed for Re = 25,000 and 50,000. 

At lower frequencies the boundary layer separated between wakes. 

NASA/CR—2012-217417 9
Chapter IV

Numerical Models and Domain

 The numerical simulations were conducted utilizing the finite-volume code 

ANSYS FLUENT [2009]. Cases were run at different Reynolds numbers, wake passing 

frequencies, and free stream turbulence intensity levels. Table 2 shows a summary of all 

CFD conducted in this study. 

The computational domain was based off of Ibrahim et al. [2010, however the grid 

was then sub-divided into three cell-zone domains, a stationary inlet zone, a moving via a 

sliding, periodically repeating translational zone with the circular wake generating rod in 

it, and a stationary zone with the airfoil and rest of the downstream domain in it. The 

mesh generated around the rod was refined until it showed a wake that was produced and 

did not dissipate as it propagated downstream. The interaction between the interface 

zones was set up so the conditions periodically repeated themselves allowing for the 

wake to carry between zones even as the interfaces became unaligned. The inlet and 

outlet conditions varied based on Reynolds’ number and the freestream turbulence 

intensity of the flow and the boundaries on each face of the grid were set up as periodic in 

order to simulate a full blade and a full cascade. For the two dimensional cases this 

assumed no variation in the z direction, which will prove to cause modeling issues. 

For the two dimensional cases, a URANS calculation utilizing the Transition-SST 

turbulence model of Menter et al. [2006] was used. The three dimensional computational 

domain was used for both the same URANS calculations and LES calculations. The 

number of passages used varied based on a two dimensional or three dimensional domain 

NASA/CR—2012-217417 10
and will be explained further below (see Table 1. for cascade parameters). A uniform 

velocity inflow condition is specified 1.9 Cx upstream of the blade leading edge in the 

flow direction. The inlet flow angle is set to 33o based on an inviscid calculation of the 

full cascade used in the experiment [Ibrahim et al., 2008]. This angle agrees with the 

experimentally measured inlet angle to within the experiment uncertainty. The exit 

boundary is located 3.8 Cx downstream of the trailing edges in the flow direction. The 

boundary conditions on the sides of the passage are periodic. 

Convergence was established when: 1) residuals reduced to a value 10-5, 2) no change 

was observed in any field results, and 3) the mass imbalance was less than 0.01 %. 

For the 2-D cases, a two-channel domain was designed, having an entire airfoil in the 

middle, with two rods spaced equally one blade spacing apart as seen in Fig 1b with the 

details of this grid given in Table II. In the 3-D simulations, with rod to blade spacing of 

1 a single airfoil with half a channel spacing above and below was used. Periodic 

boundary conditions were applied to simulate the entire cascade (Fig. 1b.) and in order to 

save on computational time. Adding multiple rods to a single domain (in the 2D cases) 

did not increase the mesh size significantly nor computational time, therefore two blade 

passages with two rods were used, however for the 3D domain one full blade passage 

(half a blade passage above and below an airfoil) was simulated to keep the mesh size at 

a minimum. 

Table III summarizes cases examined in this paper, with the same cases also studied 

experimentally by Volino, [2010] indicated. A combination of variation in Re (25,000, 

and 50,000), free stream turbulence intensities (LFSTI and HFST) and turbulence 

modeling approach (URANS-Transition-SST and LES) was considered to match 

NASA/CR—2012-217417 11
experimental data. Additional cases with increased rod speeds, and thus increased wake 

passing frequency values (F) were studied to examine what effect having a more frequent 

wake passing over the blade would cause. 

NASA/CR—2012-217417 12
Table II: Grid Refinement Parameters

Grid # Size 

(Cells)

Number of 

grids in z 

direction

y+ ∆z+ ∆x+ 

1 

(2-D)

60,600 NA 0.132 NA < 28

2*

(2-D)

122,000 NA 0.115 NA < 10

3

(2-D)

200,000 NA 0.113 NA < 4

4*

(3-D)

1.7 

million

32 0.117 <1 < 18

*Grid Used in Computations. 

 Details of Grid 4

Number of cells (million) 1.7

Number of nodes on the suction surface 292

Number of nodes on the pressure surface 240

Number of nodes in span direction 32

y+ 0.117

∆z+ < 1

∆x+ < 18

Distance from inlet boundary to the leading edge 3.8 Cx

Distance from the trailing edge to the outlet 

boundary 

1.9 Cx

NASA/CR—2012-217417 13
Inlet

Periodic

Periodic

Wall

Outlet

Wall

a) b)

Sliding Mesh

Inlet

Outlet

Wall

Periodic

Periodic

c)

Fig 1b. Schematic of Computational Domains and mesh: a) 2D Domain b) Refined 

Rod Mesh c) 3D Computational Domain

NASA/CR—2012-217417 14
Table III. CFD Test matrix

Case Re

Free Stream 

Turbulence 

Intensity

Dimensionless 

Frequency, 

F

Turbulence 

Model 

1 25,000

LFSTI*

0.513

Trans-SST (2D)

2 50,000 0.548

3

25,000 

LFSTI*

0.513 

LES

4 HFSTI*

5

50,000 

LFSTI*

0.548 

6 HFSTI*

7

HFSTI

0.698

8 0.917

 *Experimental data available from Volino [2010]. 

TURBULENCE MODELS

LES with Dynamic Kinetic Energy Subgrid-Scale model

The governing equations employed for LES are obtained by filtering the timedependent Navier-Stokes equations in either Fourier (wave-number) space or 

configuration (physical) space. The filtering process effectively filters out eddies whose 

scales are smaller than the filter width or grid spacing used in the computations. The 

resulting equations thus govern the dynamics of large eddies. The subgrid-scale stresses 

resulting from the filtering operation are unknown, and require modeling. The subgridscale turbulence models in Fluent employ the Boussinesq hypothesis as in the RANS 

models. 

NASA/CR—2012-217417 15
The dynamic subgrid-scale kinetic energy model, used in the present study, is 

based on the model proposed by Kim and Menon [1997]. In this model a separate 

transport equation is solved for subgrid-scale kinetic energy. The model constants are 

determined dynamically. The details of the implementation of this model in ANSYS 

FLUENT and its validation are given by Kim [2004]. 

Transition-SST (4 equation) model of Menter [2006] 

A correlation-based transition model was proposed by Menter et al. [2006]. This 

model is based on two transport equations. The intermittency transport equation is used 

to trigger the transition onset. The transport equation for the transition momentum 

thickness Reynolds number (Reθt) is used to capture non-local effects of freestream 

turbulence intensity and pressure gradient at the boundary layer edge. Outside the 

boundary layer the transport variable was forced to follow the value of Reθt given by 

correlations. Those two equations were coupled with the shear stress transport turbulence 

model (SST). This model is available in ANSYS FLUENT V-13 as Transition-SST (4 

equation) turbulence model.

NASA/CR—2012-217417 16
Chapter V 

Results and Discussion

 As further validation of the computational domain, the initial cases run were those 

that a direct comparison with the experimental data provided by Volino [2010] was 

possible. In all cases, the data will be presented first with the time average statistical data 

to show how consistent the model is overall. For the cases that proved exceptionally 

accurate, further analysis and instantaneous data is examined to help better understand 

the wake interaction over the suction side surface of the airfoil. Using this comparison 

with the experimental data to validate the accuracy of the results, further cases where 

simulated to see how changing the rod speed, and thus the wake passing frequency, 

would then effect the separation and reattachment of the boundary layer. For all the 

cases presented, a discussion of the results will be given with all the figures associated 

with the given case presented at the end of each section. 

 For each case plots of the rod wake velocity profile, Cp, and Total Pressure Loss 

are compared directly with experimental data for a rod to blade spacing of 1. For the 

cases which showed exceptional consistency with the experimental data, plots of six 

streamwise velocity profiles are compared against data for rod to blade spacings of 1.6 

and 2. Thus, the CFD results will be analyzed versus the trend of the experimental data, 

but a direct comparison is not possible. 

 In computing the Cp plots, the plots were created to match the experimental data, 

thus: 

(where Uave is the mean freestream velocity between blades.)

NASA/CR—2012-217417 17
However, when creating the contours of Cp, Ansys Fluent utilizes the equation: 

Thus, the contour color values are in reverse of the typical, where blue represents the 

suction peak and positive values and red is zero to negative. 

Further analysis of the wake passing through the cascade passage is done by 

plotting the second invariant of the velocity gradient tensor, Q-Criterion, iso-surfaces on 

a mid-z plane, colored by x-velocities in one and Cp values in another plot. This is done 

to capture the turbulence and vortex shedding of the wake since the definition of QCriterion is:

 

where, , and 

A two dimensional mesh was first generated to establish a grid that was refined 

enough to capture the wake vortex shedding and allow for the wake to proceed through 

the entire blade passage. Figure 2 shows that the initial mesh would capture the 

shedding, but the wake would quickly dissipate downstream. Therefore a finer mesh was 

created, allowing for not only the vortex shedding to be captured, but then to continue 

onward toward the blade passage. A further refinement was then made (not pictured) to 

see if the results would be improved, however, the results remained consistent with the 

initial refinement, thus any additional refinements only added computational time without 

adding any extra benefit. Once this two dimensional grid proved effective, it was used as 

the base for the projection into the three dimensional grid domain.

NASA/CR—2012-217417 18
 It has been shown by Sakar [2009] and Ladreau[2005] that a two dimensional 

domain would capture the wake effects on a separated boundary layer. However due to 

the lack of ability to capture the three dimensionality of a wake vortex and the small scale 

eddies associated with them, as shown in Figure 3, the effects of the wake only show the 

proper trends, but the overall magnitude and shape of the wake impinging on a boundary 

layer are not consistent. The 2D results under-predict the suction peak value by about 

15% and has the peak location 4% too far downstream. It also predicts reattachment to 

occur about 6% further upstream than the experimental data shows, thus predicting 

overall a smaller, less intense separation bubble. The three dimensional domain with the 

LES turbulence model is much more consistent as show in Figure 4, which validates the 

reason for this domain and turbulence model. It predicts a suction peak value less than 

2% less than the experimental and has nearly the same reattachment point. The size and 

intensity of the separation bubble is also very consistent with the experimental data, as 

well as the trailing edge values. 

 However, the two dimensional results did show some good promise with the 

Unsteady Reynolds Averaging Navier Stokes (URANS) code. The overall trend was 

accurate and the results will be further discussed some since the computational time for 

these cases were on order of 90% faster. 

NASA/CR—2012-217417 19
a)

b)

Fig. 2 Rod Wake Velocity Magnitude Contours for Re 50,000: Comparison between 

a) Grid 1 and b) Grid 2. 

NASA/CR—2012-217417 20
a) 

b) 

Fig. 3 Vorticity Contours for Re = 50,0000: Comparison between a) 2D (Trans-SST) 

Spacing 1 versus b) 3D (LES) Spacing 1 

5,500

3,850

1,920

825

0 

NASA/CR—2012-217417 21
Fig. 4 Code Validation: Comparison of Trans-SST (2D) 1Lφ results with LES (3D) 

1Lφ and Experimental Data 1Lφ. 

NASA/CR—2012-217417 22
2D Results

The Re=25,000, LFSTI Cp values found in Figure 5 shows that the overall shape 

and trend of the pressure distribution over the suction side of the airfoil is accurately 

predicted, the magnitude of these values is where the discrepancies lie. This can be 

associated with the formation of the wake from the rod which will be discussed further 

below, since the pressure side values, which are not as affected by the wake, match the 

experimental data nearly exactly and are on order with the no-wake CFD results. 

The total pressure loss values (Figure 6) for the Re=25,000, LFSTI case predict 

less of a pressure drop, ∆ ψ= 0.7 as compared to a 0.8 pressure loss shown in the 

experiment. This can be attributed to the smaller Cp values and separation bubble size 

prediction on the suction surface. These values are also shifted due to the lack of ability 

of the periodic boundary conditions of the CFD model to take into account the tailboard 

of the experimental domain, as seen and described in Kartuzova [2010]. 

As for to Re=50,000 LFSTI, the experimental data show (Figure 7) an increase in 

the suction peak Cp value of about 2%, however the CFD does not predict much of a 

difference from Re=25,000. This leads to a greater discrepancy between the 

experimental and CFD results, translating to a greater difference in prediction of the total 

pressure loss profile (Figure 8). Again the pressure side Cp values match experimental 

data nearly exactly, and as well, like Re=25,000, the same periodicity of the domain error 

seems to shift the total pressure loss.

In examining the further detail of the rod wake velocity profile, a very smooth 

velocity profile that has a symmetric profile about the middle of the wake can be seen in 

Figure 9. The experimental data available was for a rod of the same size and shape 

NASA/CR—2012-217417 23
(circular) however it was simulated at a rod to blade spacing of 1.6, and the speed at 

which it moved at was also different. These differences would be seen mostly in the 

wake width, not the magnitude since both cases had the same Reynolds number flow 

value. Therefore the smoothness of the wake profile can be associated with the lack of 

three-dimensionality of the wake structure and this lack in three dimensionality in the 

wake profile would also be the main cause of the difference in magnitude of the pressure 

profiles on the suction surface seen in Figure 7. 

 These two dimensional simulations provided good enough results to have the 

confidence to project this mesh in the z-direction and create the three dimensional 

domain. It also should be noted that the Reynolds numbers (25,000 and 50,000) along 

with the LFSTI levels associated with these cases are cases that have been historically 

noted difficult to simulate. Therefore, further two dimensional studies using the TransSST turbulence model with a higher freestream turbulence and a higher Reynolds number 

may prove this model to be more accurate. 

NASA/CR—2012-217417 24
Fig.5 Cp profiles for Re=25,000, LFSTI: Comparison between Trans-SST (2D) and 

Experimental data

Fig. 6 Total Pressure Loss Coefficient for Re=25,000, LFSTI: Comparison between 

Trans-SST (2D) and Experimental Data.

NASA/CR—2012-217417 25
Fig. 7 Cp profiles for Re=50,000, HFSTI: Comparison between Trans-SST (2D) and 

Experimental data

Fig. 8 Total Pressure Loss Coefficient for Re=50,000, HFSTI: Comparison between 

Trans-SST (2D) and Experimental Data

NASA/CR—2012-217417 26
Fig. 9 Rod Wake Velocity Magnitude for Re=50,000, HFSTI: Comparison of TransSST (2D), 1Lφ to Experimental 1.6Lφ

NASA/CR—2012-217417 27
3D Results

Initially the idea was to take the 3D projection of the 2D mesh and keep the same 

URANS turbulence model to provide further insight into the difference of switching from 

a 2D mesh to a 3D one. However, when the cases were run with the same time step size 

as our 2D cases, ∆t = .001, the 3D mesh was unable to capture the vortex shedding off of 

the rod, as seen in Fig. 10a and 10b. As mentioned, in the study of Ladreau [2008], it 

was found that URANS turbulence models need a sufficiently fine mesh and time step in 

order to produce wake shedding due to the small length scale of the rod in the 

computational domain. Therefore, the need to switch to a time step of ∆t=.0001(s)

eliminated most of the computational cost savings benefit of a 3D URANS turbulence 

model, thus the 3D cases were subsequently all run using the LES turbulence model with 

a ∆t of .0001(s). This proved to show a much better defined wake, with vortex shedding 

and wake structures taking a three dimensionality. In Figure 10b, an attempt to display 

vortex shedding from the Trans-SST model showed that little to no vorticity was 

produced and that which was produced was uniform in the z-direction. However, by 

plotting the Q-criterion values colored by vorticity for the LES turbulence model, one can 

see that the formation of the wake structures vary across the span-wise direction as well 

as does the magnitude of vorticity. This three dimensionality will play a major role in the 

interaction of the wake with the suction surface. 

 

NASA/CR—2012-217417 28
a) b)

c)

Fig. 10 Vorticity Contours for Re = 50,0000, HFSTI: a) 3D – Trans-SST with time 

step = .001 seconds, b) 3D – Trans-SST – time step = .001 – Q-criterion colored by 

Vorticity Contours c) 3D – LES – time step = .0001 – Q-criterion colored by 

Vorticity Contours 

NASA/CR—2012-217417 29
Re=25,000 

LFSTI, F=0.513 

 In a 3D domain, the rod wake velocity profile seen in Figure 11 shows a wake 

that has a much less smooth structure to it, yet is still symmetric across the width. The 

magnitude of the wake matches the trend of the experimental data slightly better, as does 

the width and shape of the wake. The peak velocity outside of the wake is considerably 

higher, which is the same for all the wake profiles produced and may be attributed to the 

difference of taking a time averaged of a line in a computational domain and taking the 

time averaged results of a single probe point and using the rod speed and cycle time to 

determine the pitch location of the averaged values. With that said, the wake structure is 

deemed sufficiently consistent to proceed.

The fact that the wake shows a profile closer to that which is expected leads to a 

more consistent Cp prediction with the experimental data, however the CFD predictions 

still have areas where the consistency with the experimental data lacks. The suction peak 

is seen to be predicted slightly downstream from that of the experimental and is larger in 

magnitude. Then as flow proceeds downstream, the point of separation seems to occur 

earlier than it should as well as reattachment. The magnitude of the pressure bubble is 

greater and shorter than what the experimental data show. As the flow approaches the 

trailing edge, the pressure magnitude is underpredicted and seems to be forming another 

plateau as if to start to form another separated region, near the trailing edge, that is not 

evident in the experimental data. 

The total pressure loss shown in Figure 13 has a peak that is proportional to the f 

the experimental data, however the shape is quite different. There seems to exist the same 

NASA/CR—2012-217417 30
shift associated with the periodic domain and the sharp decline from the peak to 

minimum is associated with the sharp decline in the Cp curve as the flow reaches the 

trailing edge. The difference in the peak value can be also correlated to the over 

prediction of the size of the separation bubble indicted by the size of the plateau of the Cp 

curve.

 In Figure 14a one can see the contour plots of the time averaged mean skin 

friction coefficient (Cf) values along with the mean contours associated with the Cp 

profile over the suction surface of the airfoil. This along with the data plots of these 

values in the graph above them can lead to further insight in the separation, transition, 

and reattachment locations. As previously referenced, the separation region has 

traditionally been associated with a “plateau” of the Cp values on the suction surface of 

an airfoil. Here one can see that even before the flow gets to the suction peak, the skin 

friction starts to drop steadily. Slightly after the suction peak, where the Cp values show 

the start of a plateau, there is a slight inflection in the decreasing Cf values. This point 

shows where the flow starts to become separated, with full separation reached when Cf

hits zero and thus no flow is attached to the surface. Coming out of the separation point 

there is another inflection at about .63Ls, which indicates an increase in the rate of 

change of Cf growth and thus the start of transition. At about .65Ls, where the end of the 

Cp plateau occurs there is again another inflection point to the Cf plot indicating 

reattachment. Now since this point is predicted too far upstream of the experimental 

point of reattachment, and the fact that the data fails to be consistent with the flow over 

the rest of the airfoil, the fact that this point is not the peak, but continues to rise in Cf

value, indicates part of the error in this prediction. Better results will be shown in the 

NASA/CR—2012-217417 31
case of Re=50,000. However, in speaking to what is shown, the same trend of a peak in 

Cf, followed by a decrease, inflection point, and zero point coincides with the Cp 

prediction of a plateau forming on the trailing edge. 

NASA/CR—2012-217417 32
Fig 11 Rod Wake Velocity Magnitude for Re=25,000, LFSTI: Comparison of LES, 

1Lφ to Experiment 1.6Lφ

Fig. 12 Cp profiles for Re=25,000, LFSTI: Comparison between LES and 

Experimental data

NASA/CR—2012-217417 33
Fig. 13 Total Pressure Loss Coefficient for Re=25,000, LFSTI: Comparison between 

LES and Experimental Data 

NASA/CR—2012-217417 34
a) b)

Fig. 14 Comparison of Mean Cp and Cf on suction surface for Re=25,000, LFSTI: a) 

Contours of mean Cf b) Contours of mean Cp 

Separation

Transition

Reattachment

NASA/CR—2012-217417 35
Re=25,000 

HFSTI, F=0.513 

In changing the free stream turbulence level from low to high, the experimental 

data showed that the magnitude of the peak Cp value would decrease; however its 

location along with the location of the separation and reattachment points all remained 

basically the same, thus giving an overall shape to the curve nearly identical to the low 

turbulence case The CFD results once again do an insufficient job of capturing these 

details.

In figure 15, the rod wake profile for the Re=25,000 HFSTI case is nearly 

identical to the profile for the LFSTI. This is to be expected since the wake shape should 

be highly dependent on the flow over the cylinder, or on the Reynolds’ number, which is 

seen here. The wake does appear to be slightly wider, but the magnitude is the same. 

This does not translate though into similar to experiment Cp results.

 In Figure 16, one can see that the predicted peak magnitude of Cp decreased from 

the LFSTI case, as did the experimental, but the proportion with which it decreased is 

less, thus causing the already over-predicted peak value to be even larger for the HFSTI 

case. The point of the peak did remain the same, which is expected from the 

experimental data. Moving downstream, the experimental data shows a very well defined 

drop in Cp, with a plateau, or prediction of a separation bubble, and then reattachment. 

The CFD results show a much slower decrease from the Cp maximum, with only a slight, 

small plateau and then quick reattachment. After reattachment the results remain below 

NASA/CR—2012-217417 36
the experimental data, however this time it does not incorrectly show the formation of 

another separation bubble at the trailing edge. 

 The fact that the separation bubble predicted by the CFD is very small, and the 

fact the pressure drops steaper near the trailing edge, leads to a total pressure loss 

prediction that is smaller in amplitude than the experimental and has a quicker drop 

(Figure 17). The same effect, shown earlier in Figure 6,of a shift in the profile due to the 

periodic boundary conditions in once again also present. 

In an attempt to determine the locations of predicted separation, transition and 

reattachment, the Cp profile is difficult to use due to its small, non-dominate bubble 

plateau. However, when looking at the Cf curve inf Figure 18, the same points of 

inflection as seen in the LFSTI case are present and indicated in Fig. 18. Once again, 

from the Cf peak, a steady decrease is observed through the suction peak, then at about 

.54Ls, there is an inflection coinciding with the beginning of a slight plateau to the Cp 

profile. Then, after Cf hits zero, it quickly increases to another inflection indicating 

transition and then reattachment can be seen by a peak in the Cf. Upon examining the 

contours, it can be seen that this separation bubble is not even indicated across the span 

of the airfoil, thus resulting in more of a local, less defined separation as compared to a 

full separation bubble Again, the trend of another Cf zero point with inflections around it 

is not seen, nor is the formation of a plateau on the trailing edge. 

 These results give a good indication of what to look for in the data to come, 

however, as stated, they do not correlate very well with the experimental data results. 

From the literature review it was found that low Reynolds number flows have been 

deemed difficult to model, thus the fact that the trends are predicted correctly is 

NASA/CR—2012-217417 37
sufficient, but it is not surprising that the Re=25,000 results are less than exact. An 

attempt to run a finer mesh was run and did not show any significant improvement in 

results. A finer time-step may prove more effective however the computational costs 

would have to increase, rendering using a turbulence model and not a direct numerical 

simulation useless. 

NASA/CR—2012-217417 38
Fig 15 Rod Wake Velocity Magnitude for Re=25,000, HFSTI: Comparison of LES, 

1Lφ to Experimental 1.6Lφ

Fig. 16 Cp profiles for Re=25,000, HFSTI: Comparison between LES and 

Experimental data

NASA/CR—2012-217417 39
Fig. 17 Total Pressure Loss Coefficient for Re=25,000, HFSTI: Comparison between 

LES and Experimental Data 

NASA/CR—2012-217417 40
a) b)

Fig. 18 Comparison of Mean Cp and Cf on suction surface for Re=25,000, HFSTI: a) 

Contours of mean Cf b) Contours of mean Cp 

Separation

Transition

Reattachment

NASA/CR—2012-217417 41
Re=50000 

The Reynolds 50,000 cases proved to be the most consistent with the 

experimental results and the wake passing over the airfoil will be examined in greater 

detail. Data were available for HFSTI and LFSTI inlet conditions for a wake passing 

frequency, F, of 0.548. After confirming that the CFD results for these cases were 

sufficiently accurate, additional cases where the rod speed was increased to create a 

greater wake passing frequency were simulated. The desire was to see if when a wake 

was nearly always impinging on the airfoil could separation be eliminated completely. 

The two cases that were run were a case that represented a 25% increase in rod speed, 

resulting in an F = 0.689. The second was run based off the time it took for the wake 

effects to be eliminated from the base Re=50,000 cases with a rod speed of 2.63 m/s. 

This resulted in a 40% increase in rod speed and a wake passing frequency of .917 from 

the base, F=0.548 case, or an additional 33% increase from F=.689. 

NASA/CR—2012-217417 42
Re=50,0000 

LFSTI, F=0.548 

 The wake produced by the Re=50,000 LFSTI case shows in Figure 14 a 

wake that has nearly the same shape and magnitude as displayed in the 

experimental data, which was an initial indication that the Re=50,000 results will 

produce results much more consistent with the experimental data. The width of 

the wake is slightly larger than the experimental rod to blade spacing of 1.6 data, 

however it is consistent to the width of all the other CFD rod to blade spacing of 1 

results. 

The result of this wake profile provide Cp values that were in very good 

agreement with the experimental data. In Figure 20 it can be seen that the CFD 

results predict a suction peak that is slightly under-predicted in magnitude and 

slightly downstream. This slight under-prediction persists until reattachment and 

may be a result of a wake that is greater in magnitude than what the experimental 

data would show. The prediction of the location of separation, the size of the 

bubble, and the location of reattachment are all very consistent though with the 

experimental data. The flow over the trailing edge of the airfoil also matches the 

data in both location and magnitude. 

The consistency of the Cp profiles leads to similar results in the total 

pressure loss data, Figure 21. Here the magnitudes of the peak and trough of the 

CFD are under-predicted compared to the experimental data. This is a result of 

the fact that the Cp values show an under-prediction in the pressure bubble size. 

The shape of the total pressure loss coefficient profile though shows a much more 

NASA/CR—2012-217417 43
consistent result, especially compared to the Re=25,000 results. This is due to the 

fact that as the flow passes over the airfoil, even though the magnitudes vary 

slightly, the shape and location of different separation and reattachment events is 

very well matched.

 In Figure 22 suction surface velocity profiles from six streamwise 

locations are shown. The CFD data for a rod to blade spacing of 1 is compared 

against the available experimental data for cases with rod to blade spacings of 1.6 

and 2. Therefore a direct match in these profiles is not expected but it will be 

analyzed based on what is seen as the trend of the data as the rod to blade spacing

is reduced from 2 to 1.6. In figure 22a, the mean velocity profiles are plotted with 

experimental data in dots and the CFD result in a solid line. The results show that 

even though the experimental data does not vary much from rod to blade spacing 

of 2 to 1.6, there does seem to be the trend of the magnitude of the U/Ue profiles 

to grow as spacing is reduced. The CFD models the shape of the velocity profiles 

very well, however it does not show a greater magnitude than the experimental 

data until station 5. This is consistent with the fact that the pressure magnitudes 

over that span is also less than the experimental data until the trailing edge, this

shows consistent matching and thus also shows a consistent trend in velocity 

magnitude at those stations. In figure 22b, the turbulence, or u’/Ue, profiles are 

plotted for the same six locations. Here again, the results become more consistent 

with the experimental data trends toward the trailing edge where better matching 

is observed. Overall, the shape and trend seem to be consistent, however the 

magnitude seems to be amplified a bit too much with what the experimental data 

NASA/CR—2012-217417 44
trend shows. However, these results are believed to be in good agreement with 

the data with some of the error due in part to the inability of an anemometer to 

resolve the difference between attached and reversed flow.

With the Cp results showing very consistent trends with the experimental 

data, looking at the Cp vs Cf plot in Figure 23 will allow for more confidence in 

observing what happens to the skin friction as flow proceeds down an airfoil. 

Here one can see that the skin fiction reaches a peak before the suction peak of the 

airfoil. The subsequent decline in Cf is very consistent and smooth as flow moves 

past the suction peak and down the aft side of the airfoil. At about .53Ls, right as 

the Cp is starting to show the plateau of separation bubble there is a slight 

inflection in the skin friction plot, leveling out slightly and having the decrease in 

Cf taking a less negative slope. This continues until Cf hits zero and thus full 

separation has occurred. While still in the separation bubble, the skin friction 

increases at a slow rate, staying near zero, until at about .63Ls there is an initial 

sharp increase in Cf signaling the start of transition. This increase continues until 

.65Ls where the rate of increase changes and grows even greater signaling the 

start of reattached flow. By the Cf peak at .68Ls the flow is fully reattached and 

continues on that way to the trailing edge. As the flow approaches the trailing 

edge it stay attached due to the presence of turbulence in this region evident by 

the fluctuations in Cf from .75Ls to the end. 

 Figure 24-1 through 24-14 represents instantaneous plots and contours of a 

wake passing over the airfoil. Each separate plot represents a 10% time step of a 

full cycle, even though there is greater than one cycle shown so the full effect of 

NASA/CR—2012-217417 45
the wake can be seen. An instantaneous plot of Cp and Cf values are shown at the 

top with the corresponding contours of these values over the suction surface 

shown beneath. Then continuing clockwise, beneath the Cp suction surface 

contour is another contour plot of Cp values at mid-z span with iso-surfaces of qcriterion also displayed at that instant to show where the wake is currently located 

and how it is affecting the boundary layer on the suction surface. Finally the last 

contour is the x-velocity contours at mid-z span with iso-surfaces of Q-criterion 

for that instant also plotted to give an idea of the magnitude and direction of the 

flow.

 Figure 24-1 starts as a wake is passing through a passage to show the regrowth of the suction peak. Here there is evidence of the last parts of the wake to 

hit the suction surface (before entirely hitting the pressure side) moving its way 

up the forward part of the airfoil. The suction peak has been rolled up into three 

separate peaks, as described in Hodson and Howell [2005], along with their 

prediction of a calm zone seen following the high turbulence fluctuations in the Cf

values. Moving from Figure 24-1 to 24-2 the suction peak of the airfoil continues 

to be suppressed as is the peak skin friction that is seen before the peak. The 

rolled up separation bubble is compressed and increases in magnitude as does the 

magnitude of Cf in this region. Again trailing behind these amplified values of Cf

is a low Cf, calm region. From the contours of Cf, it can be seen that the aft side 

of the suction surface is fully turbulent, with spots of zero skin friction present 

where the separation bubble is being rolled downstream. 

NASA/CR—2012-217417 46
 By Figure 24-3, or within 10% of the suction peak hitting its lowest 

magnitude, the peak begins to reform with a subsequent Cf peak preceding it. 

From the q-criterion and Cf plot, it is evident that turbulent wake structures are 

still making their way up the forward side of the airfoil, however their presence 

seems to play little effect on the growth of the suction peak. The rolled up 

separation bubble that is making its way down the aft portion of the airfoil 

continues to be compressed and grow in magnitude along with the Cf values; the 

calm region still trails.

 By Figure 24-4, the suction bubble has completely separated from the 

surface causing high levels of turbulence to shed off the trailing edge of the 

airfoil. At this point, where the separation bubble stops drawing the wake 

towards the surface, the Cf values show less of a turbulent peak and the entire 

calmed region starts to decrease to zero, with some local values of zero Cf already 

present. This shows that immediately after the wake influence on the surface 

ends, the start of formation of another separation bubble begins. 

From this point to Figure 24-6, the suction peak continues to grow as does 

the presence of another separation bubble. The turbulent structures on the forward 

part of the airfoil have all moved beyond the suction peak and the flow in this area 

seem to be completely laminar, having no fluctuations present in the Cf plots. By 

Figure 24-7, the contours of Cf on the suction surface show a point of zero Cf, or 

separation, that is no longer just a point, but covers the whole span and by Figure 

24-8 and 24-9 a more definite zero Cf band is formed over the suction surface 

with the separation plateau present in the Cp plot. In figure 24-10, the wake 

NASA/CR—2012-217417 47
begins to collapse in on the suction peak, putting a shear stress on the separation 

bubble, pushing it downstream. The Cp plot still shows separation in the flow 

with an abrupt reattachment point.

 Figures 24-11 thru 24-14 show the same things as Figure 24-1 thru 4. 

They are included to help visualize the full wake/blade interaction. 

In this Re=50,000, LFSTI flow, the CFD results are shown to be in very good 

agreement with the experimental data. The magnitudes of both the mean Cp values and 

total pressure loss are slightly under-predicted, however, the shape and trend of the data 

matches the experimental data. In looking at the instantaneous plots, many of the trends 

that were evident in the time averaged plots were seen. A peak in the skin friction was 

seen slightly upstream of the suction peak, separated flow is marked by zero skin friction 

coefficient, and reattachment is seen near a subsequent inflection or near peak of Cf. The 

inflections seen that indicated the start of separation and the point of transition are not 

always prevalent, but this could be as much associated with a small magnitude in change 

which could be too difficult to pick up on the given plots. Ultimately, the flow is seen to 

separate and grow a prevalent separation bubble between wakes.

NASA/CR—2012-217417 48
Fig. 19 Rod Wake Velocity Magnitude for Re=50,000, LFSTI: Comparison of LES, 

1Lφ to Experimental 1.6Lφ

Fig. 20 Cp profiles for Re=50,000, LFSTI: Comparison between LES and 

Experimental data

NASA/CR—2012-217417 49
Fig. 21 Total Pressure Loss Coefficient for Re=50,000, LFSTI: Comparison between 

LES and Experimental Data

NASA/CR—2012-217417 50
a) 

Fig. 22 Time averaged velocity profiles at six streamwise stations for Re=50,000, 

LFSTI: Comparison between CFD (LES) and Experimental data: a - Mean, b - 

RMS

NASA/CR—2012-217417 51
b)

Fig. 22 Time averaged velocity profiles at six streamwise stations for Re=50,000, 

LFSTI: Comparison between CFD (LES) and Experimental data: a - Mean, b - 

RMS

NASA/CR—2012-217417 52
 a) b)

Fig. 23 Comparison of Mean Cp and Cf on suction surface for Re=50,000, LFSTI: a) 

Contours of mean Cf b) Contours of mean Cp 

Separation

Transition

Reattachment

NASA/CR—2012-217417 53
 a) b)

d) c)

Fig. 24-1 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp Contours 

d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 54
a) b)

d) c)

Fig. 24-2 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp Contours 

d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 55
 

Fig. 24-3 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp Contours 

d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 56
a) b)

d) c)

Fig. 24-4 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp Contours 

d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 57
a) b)

d) c)

Fig. 24-5 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp Contours 

d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 58
a) b)

d) c)

Fig. 24-6 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp Contours 

d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 59
a) b)

d) c)

Fig. 24-7 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp Contours 

d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 60
a) b)

d) c)

Fig. 24-8 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp Contours 

d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 61
a) b)

d) c)

Fig. 24-9 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp Contours 

d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 62
a) b)

d) c)

Fig. 24-10 Comparison of Instantaneous Cp and Cf on suction surface for 

Re=50,000, LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, 

Cp Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 63
a) b)

d) c)

Fig. 24-11 Comparison of Instantaneous Cp and Cf on suction surface for 

Re=50,000, LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, 

Cp Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 64
a) b)

d) c) 

Fig. 24-12 Comparison of Instantaneous Cp and Cf on suction surface for 

Re=50,000, LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, 

Cp Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 65
a) b)

d) c)

Fig. 24-13 Comparison of Instantaneous Cp and Cf on suction surface for 

Re=50,000, LFST: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, 

Cp Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 66
a) b)

d) c)

Fig. 24-14 Comparison of Instantaneous Cp and Cf on suction surface for 

Re=50,000, LFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, 

Cp Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 67
Re=50,000, F=0.548 

HFSTI

 In switching to Re=50,000 HFSTI inlet flow conditions, like switching from 

Re=25000, LFSTI to HFSTI, the wake profile (Figure 25) does not change very much. In 

this HFSTI case, the wake deficit is predicted to be slightly lower than the LFSTI case, 

and the wake is predicted to be slightly wider. However, the overall trend and shape of 

the wake matches the profiles seen in all the cases thus far. 

The experimental data showed very little change in the data as far as magnitudes 

and locations of the suction peak, separation, and reattachment points. However, in 

switching the CFD model to a HFSTI inlet flow, the result is that instead of slightly 

under-predicting the magnitude of Cp, it slightly over-predicts these values. However 

this over-prediction is very slight at the suction peak, separation and reattachment point, 

and the prediction of the locations of these events is nearly identical to the experimental 

data. The over-prediction on the leading edge is consistent with that was seen in the 

LFSTI which under-predicted the values from leading edge until reattachment, however 

the LFSTI had very good matching at the trailing edge, where in this HFSTI case it overpredicts these magnitudes all the way through the airfoil suction surface. This is also 

seen to be the trend on the pressure side, which when switching from LFSTI to HFSTI in 

the Re=25,000 cases, the ability to predict the pressure distribution on the pressure side 

surface also decreased. These effects show a trend that the high freestream turbulence 

that is imposed at the inlet of the domain will help in showing the interaction of this 

turbulence with the boundary layer over a suction peak and separation bubble, however it 

also seems to show more interaction with the areas of laminar flow, thus causing the 

NASA/CR—2012-217417 68
discrepancies in these regions. For this paper, the interaction of the flow with the 

boundary layer is the focus of the results, thus the reason for HFSTI inlet conditions used 

for the remainder of the cases.

When looking at the total pressure loss coefficient in Figure 27, the slightly overpredicted pressure leads to a slight over-prediction in the magnitude of the loss, however 

the amplitude of the curve varies by less than 10%. This consistent matching is also seen 

in Figures 28a and 28b which show velocity profiles and u’ profiles respectively. The 

profiles themselves are very consistent with the trend the data shows as rod to blade 

spacing is reduced and show the same similar shape as does the LFSTI case. 

 When looking at the Cp and Cf values plotted on the same graph, as seen in 

Figure 29, the same trend of an inflection in the Cf downward slope is seen at the point 

where the separation bubble plateau begins. The Cf values then slowly decline to zero 

with a small length near zero slightly downstream from the zero point, then a sharp 

increase in Cf occurs which indicates the start of transition. Right before the Cf reaches a 

subsequent peak, the plateau in Cp ends, showing where reattachment occurs. In the 

previous plots, this point was seen as an additional inflection point, however since in this 

case the peak Cf is so close to the reattachment point it is just seen as more of a rounding 

off of the curve up to the peak. The upstream trends of a peak in Cf just before the 

suction peak, and the trailing edge trends of a steady amount of turbulence noted by 

fluctuations in the Cf along with attached flow through the end are the same as seen 

previously. 

Since the HFSTI flow has the same mean flow properties and seems to model the 

data with similar consistency as the LFSTI case, the instantaneous plots below represent 

NASA/CR—2012-217417 69
20% advancements in time per cycle rather than the 10% plots shown for LFSTI since 

most of the details shown are consistent between the two.

With that said, Figure 30-1 shows a wake just reaching the leading edge of the 

airfoil, without any wake effect present over most of the suction side, with an exception 

for the very trailing edge. A clear suction peak is present, along with a small plateau in 

the Cp values before a reattachment is seen at .6Ls. This plateau is associated with near 

zero Cf values, with a zero Cf point. At about .58Ls a sharp increase is seen in Cf and 

right before its peak at .61Ls, reattachment is observed. Looking at the contours, this 

separation bubble is present across the entire span of the airfoil. 

In Figure 30-2 the wake can be seen affecting the upstream portion of the airfoil 

surface along with starting to collapse down and compress the suction peak. This 

collapsing effect also puts a shear force over the suction peak and separation bubble, 

pushing it farther downstream, however the wake has yet to impinge enough into the 

boundary layer to suppress the separation. This is evident to have happened by Figure 

30-3, which shows the pressure bubble being rolled up and compressed down the aft 

portion of the airfoil. The pressure bubble still shows some attachment to the surface on 

the contour Cp plots, which results in a turbulent spike in the Cf values in that region. 

Trailing behind this turbulent peak is the expected calmed zone, which, though near zero 

Cf, is suppressant to separation. The wake has moved far enough downstream for the 

suction peak to start its re-growth as well as the re-growth Cf peak. 

In Figure 30-4, it can be seen that even though the suction bubble only has a faint 

attachment to the surface still (looking at the surface Cp contours), it still has enough of 

an effect to cause a spike in the Cp and Cf values at that point. Since this turbulent peak 

NASA/CR—2012-217417 70
is still evident, the calmed zone remains attached to the surface. This area is close to 

becoming separated by Figure 30-5, however there seems to be enough turbulence on the 

trailing edge to keep the flow from separating. This is evident by the lack of any dark 

blue contours on the surface, along with the fact that the Cf graph never hits zero nor is 

any sort of plateau evident in the Cp plot. It is clear that flow does separate eventually 

though because in Figure 30-6, as the next wake is starting to impinge on the surface, the 

suction peak again in compressed in magnitude and the separation bubble is sheared 

downstream, as seen in Figure 30-1. 

It can be seen that in switching from LFSTI to HFSTI that the experimental 

differences are minimal for a Re=50,000 flow, as is predicted in CFD. There is a slight 

change in the prediction of the magnitude of the pressure profile over the suction surface, 

however, with this change in magnitude also results in excellent prediction of the suction 

peak value as well as the location of separation and reattachment. In looking at the 

instantaneous plots, further insight into the effect of the suction bubble and its affect on 

the suction surface as it is rolled off the trailing edge of the airfoil is shown. It can be 

seen that as long as the pressure bubble exists on the surface, a turbulent spike is also 

present, followed by a calm region, that though close to zero Cf, it near separates from the 

surface.

NASA/CR—2012-217417 71
Fig 25 Rod Wake Velocity Magnitude for Re=50,000, HFSTI: Comparison of LES, 

1Lφ to Experimental 1.6Lφ

Fig. 26 Cp profiles for Re=50,000, HFSTI: Comparison between LES and 

Experimental data

NASA/CR—2012-217417 72
Fig. 27 Total Pressure Loss Coefficient for Re=50,000, HFSTI: Comparison between 

LES and Experimental Data

NASA/CR—2012-217417 73
a) 

Fig. 28 Time averaged velocity profiles at six streamwise stations for Re=50,000, 

HFSTI: Comparison between CFD (LES) and Experimental data: a - Mean, b - 

RMS

NASA/CR—2012-217417 74
b)

Fig. 28 Time averaged velocity profiles at six streamwise stations for Re=50,000, 

HFSTI: Comparison between CFD (LES) and Experimental data: a - Mean, b - 

RMS

NASA/CR—2012-217417 75
a) b)

Fig. 29 Comparison of Mean Cp and Cf on suction surface for Re=50,000, HFSTI: a) 

Contours of mean Cf b) Contours of mean Cp 

Separation

Transition

Reattachment

NASA/CR—2012-217417 76
a) b)

d) c)

Fig. 30-1 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 77
a) b)

d) c)

Fig. 30-2 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 78
a) b)

d) c)

Fig. 30-3 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 79
a) b)

d) c) 

Fig. 30-4 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 80
a) b)

d) c)

Fig. 30-5 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 81
a) b)

d) c)

Fig. 30-6 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 82
a) b)

d) c)

Fig. 30-7 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 83
Re50,000 HFSTI 

F = 0.698 

The initial analysis of increasing the rod speed, and thus the wake passing 

frequency, F, was chosen for an arbitrary increase in rod speed of 25%. This produces a 

wake passing frequency of F=0.698 and the effect of these results will be compared 

against the Re=50,000, HFSTI CFD results. The inlet conditions for these cases match 

the Re=50,000 HFSTI case since it was felt it did a better job at predicting the location of 

the significant events over the suction surface, like separation and reattachment. 

The first thing to analyze is to make sure that the wake being produced at this 

speed is still consistent with the rest of the results seen so it can be determined that a 

realistic wake effect is being observed on the suction surface. In looking at Figure 31, the 

rod wake velocity profile is very consistent with the Re=50,000, F=0.548 wake that was 

produced in the previous section. The magnitude of this wake is seen to be slightly less 

than the base case, but the width seems to be just about the same size.

 In looking at the mean Cp plot comparison on Figure 32 it is evident that 

increasing the wake passing frequency has nearly eliminated the separation plateau 

bubble over the suction surface. Not only has this increase in the amount of turbulence in 

the cascade passage allow for greater suppression of the separation bubble, it also has 

computationally produced results nearly the same as the experimental data. On the 

leading edge up to the suction peak and towards the trailing edge of the airfoil, this 

Re=50,000, HFSTI case actually models the experimental Re=50,000 case with a wake 

passing frequency of F=0.548 better than does the results for the CFD model of this case 

shown in the previous section. This shows that the mean effect of the wake in these 

NASA/CR—2012-217417 84
regions is to drive down these predicted magnitudes, since the Re=50,000, HFSTI case 

with F=0.548 had less of a wake presence and over-predicted the magnitudes on these 

surfaces. 

 In Figure 34 there is a better indication of the severity of the separation that 

occurs on the suction surface and where reattachment takes place. Due to the reduction 

in the separation bubble to nearly no separation at all, the amount of total pressure loss 

seen in Figure 33 is reduced by about 60 percent from the experimental data loss of .7Ψ. 

It is seen from the mean Cf plot that the same characteristics of an inflection in the Cf

curve occurs where the Cp plot tends to level out some. The Cf values then decrease until 

it does finally hit zero, indicating that separation is still present on the suction surface of 

this blade, even if the plateau of a suction bubble is not very well defined. The following 

transition and reattachment happen shortly after the Cf zero point, which along with the 

contours of Cf, indicate that the separation is more a local event over the surface and not a 

long separation bubble. 

 In analyzing the instantaneous plots, Figure 35-1 shows a wake approaching the 

passage as another is just making its way past the suction peak. The Cp magnitude at the 

suction peak had been suppressed by the wake and is already starting to reform even 

though the previous suction bubble is not even half way down the aft side of the suction 

surface. The wake has rolled up and compressed this bubble to form the three Cp peaks 

expected, and the Cf shows high levels of turbulence in this region as well. Trailing 

behind this turbulent peak is the calmed region, which remains attached to the surface 

even though it has a minimal Cf. 

NASA/CR—2012-217417 85
 By Figure 3, or 50 percent of a cycle, even though the overall amount of time that 

has passed is much less than in the F=0.548 case, the suction peak has reformed and the 

previous suction bubble has been completely rolled off the suction surface. This results 

in the calmed region detaching from the surface, even though a high level of turbulence 

still exists on the aft portion of the airfoil. Looking at the Cf contours it can be seen that 

these points of separation do not span the entire width of the blade, forming a very 

defined zero band that is present in a long separation bubble. This fact along with the 

fact that the Cp plot doesn’t show the presence of a plateau indicates that these separation 

bubbles are very short and local bubbles over the surface. However by Figure 4, the zero 

band is more defined across the width, and even though the wake has begun to collapse 

upon the suction peak, the same form of a separation bubble being sheared downstream is 

present.

Therefore, even though the wake passing frequency was increased and the mean 

Cp plot barely indicates a separation of flow over the suction surface, it is clear that as a 

wake passes over the aft portion of the airfoil and rolls the suction bubble off the surface, 

the flow does start to experience small separated zones which eventual form into a 

separation bubble before the arrival of the next wake. 

NASA/CR—2012-217417 86
Fig. 31 Rod Wake Velocity Magnitude for Re=50,000, HFSTI: Comparison of LES, 

F=0.548 to LES, F=0.698. 

Fig. 32 Cp profiles for Re=50,000, HFSTI: Comparison between LES, F=0.548 to 

LES, F=0.698. 

NASA/CR—2012-217417 87
Fig. 33 Total Pressure Loss Coefficient for Re=50,000, HFSTI: Comparison between 

LES, F=0.548 to LES, F=0.698. 

NASA/CR—2012-217417 88
 

Fig. 34 Comparison of Mean Cp and Cf on suction surface for Re=50,000, HFSTI, 

F=0.698: a) Contours of mean Cf b) Contours of mean Cp. 

Separation

Transition

Reattachment

NASA/CR—2012-217417 89
a) b)

d) c)

Fig. 35-1 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.698: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours

NASA/CR—2012-217417 90
a) b)

d) c) 

Fig. 35-2 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.698: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 91
a) b)

d) c)

Fig. 35-3 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.698: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 92
a) b)

d) c)

Fig. 35-4 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.698: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 93
a) b)

d) c)

Fig. 35-5 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.698: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 94
Re50,000, HFSTI 

F=0.917 

The final case run was to increase the rod speed about another 33% percent on top 

of the wake passing frequency of F=0.689. The results did not show much of a variation 

as one can see in Figure 37b. The rod wake velocity profile took the same shape that had 

been seen in the previous cases, and has nearly the same width and magnitude as the rod 

passing frequency of F=0.698. This identical profile gives a good explanation of why the 

rest of the data between these two cases is also very similar.

 In Figure 37a, the mean Cp profiles seem to match the experimental data for 

F=0.548 at the suction peak and after reattachment, however this case does not match the 

leading edge or pressure side quite as well as the F=0.689 case. The differences between 

all three of these cases can be seen clearly in Figure 37b. Here, it is evident that 

increasing the rod passing frequency from F=0.548 to F=0.689 played a significant role 

in reducing the separation bubble, however a further increase in rod speed only created 

the slightest of difference between F=0.689 and F=0.917. Again, this similar Cp profile 

lead to a similar prediction in the reduction of the total pressure loss coefficient seen in 

Figure 38. 

The biggest discrepancy between the F=0.689 case and the F=0.917 case comes in 

the mean Cf plot. In the F=0.689 plot, once the Cf hit a zero point it had a noticeable 

increase, with an associated “reattachment peak” downstream after. However here in the 

F=0.917 case, the Cf value hits zero and then stays right near zero for the majority of the 

downstream portion of the surface. This makes trying to find a transition zone out of the 

separated point near impossible to dictate, and like in the F=0.689 case, since the Cp plot 

NASA/CR—2012-217417 95
only shows the slightest inflection towards a plateau and then again towards a 

reattachment, says that these separated zones must be very small and local. This is also 

indicated by the Cf contour plots. 

In looking through the instantaneous plots, this constant near zero Cf value over 

the aft portion of the suction surface becomes evident. From Figure 40-1, one can see a 

wake on the forward portion of the airfoil as the previous wake is just making it off the 

trailing edged. The suction peak is well defined as is the proceeding Cf peak. However, 

downstream of the peak there is a large area where the Cf values stay near and hit zero. 

These areas do not form a well defined band across the width of the blade which is 

evident when a full separation bubble is present, thus these areas of zero Cf are much 

more local instances. 

 In Figure 40-2, one can once again see a rolled up suction bubble being 

compressed and moved down the suction surface. The associated turbulent peak and 

calmed region are also evident. It is in this calmed region over the suction peak and in 

the turbulent peak that the Cf values ever really get much above the zero line. Again, 

Figure 40-3 shows that as the suction bubble separates from the suction surface, the 

calmed region starts to have points that show detachment from the surface. Right before 

another wake reaches the suction peak, the most prominent zero Cf band across the 

suction surface can been seen in Figure 40-4. This band is also accompanied by a slight 

inflection towards a plateau in the Cp plot, thus indicating a slightly large separated 

region. Right before another wake approaches the peak in Figure 40-6, this is also evident 

with an even stronger presence of a plateau and a large region of Cf values at or near 

NASA/CR—2012-217417 96
zero. This shows that a separation bubble still does have a chance to form even at these 

high wake passing frequencies. 

In these higher wake passing frequency cases, one thing that is noticeable is that 

with a strong formation of a suction peak bubble, the wake seems to make its way up the 

suction surface much more as compared to having the wake in the free stream collapse 

down on the suction peak. This could be a reason why further increasing the rod speed 

did not show much difference in the results. Nevertheless, these increased rod speeds did 

suppress a bubble growth for the majority of a wake cycle, with only a small fraction of 

time where separation seemed present right as another wake arrived at the suction peak.

NASA/CR—2012-217417 97
Fig 36 Rod Wake Velocity Magnitude for Re=50,000, HFSTI: Comparison of LES, 

F=0.548 to LES, F=0.917. 

Fig. 37a Cp profiles for Re=50,000, HFSTI: Comparison between Experimental and

LES, F=0.548 to LES, F=0.917. 

NASA/CR—2012-217417 98
Fig. 37b Cp profiles for Re=50,000, HFSTI: Comparison between LES, F=0.548, 

F=0.689 and F=0.917. 

Fig. 38 Total Pressure Loss Coefficient for Re=50,000, HFSTI: Comparison between 

LES, F=0.548 to LES, F=0.917. 

NASA/CR—2012-217417 99
a) b)

Fig. 39 Comparison of Mean Cp and Cf on suction surface for Re=50,000, HFSTI, 

F=0.917: a) Contours of mean Cf b) Contours of mean Cp.

Separation

Reattachment

NASA/CR—2012-217417 100
a) b)

d) c)

Fig. 40-1 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.917: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 101
a) b)

d) c)

Fig. 40-2 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.917: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 102
a) b)

d) c)

Fig. 40-3 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.917: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 103
a) b)

d) c)

Fig. 40-4 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.917: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 104
a) b)

d) c) 

Fig. 40-5 Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, 

HFSTI, F=0.917: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

-.5 .457 2.42 4.38 6 2.8 2.45 1.765 .25 0

NASA/CR—2012-217417 105
a) b)

d) c)

Fig. 40-6 

Comparison of Instantaneous Cp and Cf on suction surface for Re=50,000, HFSTI, 

F=0.917: a) Contours of mean Cf b) Contours of mean Cp c)Q-criterion, Cp 

Contours d)Q-criterion, x-velocity Contours 

NASA/CR—2012-217417 106
Conclusion

In simulating a wake/blade interaction in the same computational domain, the first 

challenge was to create a mesh that was fine enough to capture the wake vortex shedding 

off of a wake generating rod and propagate it downstream to the airfoil. Once this 

geometry was established in 2D, it was then projected in the z-direction to create the 3D 

domain. 

Overall the 2D URANS results showed the proper trend of interaction between 

the wake and the suction surface of the airfoil with the mean coefficient of pressure 

profiles (Cp) indicating a reattachment after separation. These trends were only 

marginally accurate in comparison to the experimental data for both Re=25,000 and 

Re=50,000 cases since the predicted magnitude of the Cp profile and the location of 

reattachment were not very consistent with the experimental data. This was mainly 

attributed to the lack of ability to take into account the three dimensionality of a wake 

structure and its subsequent interaction with the boundary layer. Thus the mesh was then 

projected into a 3D domain and the same URANS (Trans-SST) model was run at the 

same time step as in the 2D cases. These 3D URANS cases were unable to capture any 

wake vortex shedding off of the rod, which had been seen in cases run by Ladreau 

[2005]. It was determined that in order to capture the wake, the time step size would 

have to be reduced to levels associated with a LES turbulence, thus the remainder of the 

cases were run using LES since the computational cost savings of using a URANS model 

with a larger time step were diminished.

 In the Re=25,000, 3D cases the results showed better matching in the predicted 

magnitude of the mean Cp profile over the suction surface, however the predicted 

NASA/CR—2012-217417 107
magnitude of the separation bubble and its location of reattachment still lacked in 

consistency with the experimental data. Switching from a low freestream turbulence 

intensity model (LFSTI) to a high (HFSTI), showed marginal improvements, however 

overall the results were still consistently inaccurate. This lack of ability to properly 

predict turbulent flow in low Reynolds’ number flow has been noted in the past, thus the 

remainder of the cases were run at Re=50,000.

 These Re=50,000 cases showed excellent consistency in both magnitude and 

predicted location of separation and reattachment in the mean Cp profiles. The predicted 

total pressure loss still varied slightly from the experimental data, however this was to be 

expected to the fact the computational domain is set up as a repeating periodic domain, 

thus not taking into account the effects of the endwalls and tailboard of the actual 

experimental domain. Due to the exceptional prediction in mean results, the 

instantaneous profiles of Cp and Cf were examined to see the affect the wake has over the 

suction surface as it passes through the cascade passage.

These instantaneous results showed that as a wake reaches the suction peak of the 

suction surface, it collapses down, compressing the peak Cp value of the suction bubble, 

eventually rolling it up into three defined peaks. These peaks first experience a shear, 

stretching effect and eventually beginning to roll down the aft side of the suction surface, 

remaining attached to the surface and being further compressed and increasing in Cp 

magnitude. The correlating effect on the Cf values over these events show that as the 

suction bubble in broken down and compressed, the three defined suction peaks are 

associated with defined peaks in the Cf values, thus showing a high amount of turbulence 

in this region. Trailing behind this turbulent peak is the predicted calmed region 

NASA/CR—2012-217417 108
described by Hodson and Howell [2005]. This calmed region remains near zero in Cf

value, but shows resistance to separation as long as the suction bubble being remains 

attached to the surface. As this bubble is eventually rolled off of the surface, the calmed 

regions shows an immediate location of separation with a zero Cf value. This spotted 

separation grows and eventually spans across the width of the suction surface as the Cp 

values start to show a defined separation bubble, indicated by a “plateau” in the Cp 

profile. Also indicated by the Cf profile is that where separation is indicated to start, an 

inflection in the decreasing Cf values is also indicated, leveling out the curve as it 

approaches, hits, and recovers from a zero Cf value. As it starts to increase out of this 

zero value, another inflection incurs in the curve slightly before reattachment is indicated 

on the Cp values. This inflection shows a start of a sharp increase in Cf and indicates the 

start of transition in the boundary layer. Reattachment occurs just before another peak in 

the Cf values, which then shows turbulence in the flow as it stays attached to the trailing 

edge.

Finally, Re=50,000 cases were simulated with an increase in the rod speed and 

thus increasing the wake passing frequency to see what additional affect this would have 

on the suction surface. Initially about a 25% increase in rod speed significantly reduced 

the separation bubble to near nonexistent in the mean Cp values, however a slight 

indication of one still was present. Increase the rod speed an additional 25% on top of 

this showed little effect. These results showed that even with an increase in the wake 

passing frequency and an increase in turbulence in the cascade passage, any amount of 

time in between wakes was enough for the suction peak to re-grow to its peak magnitude, 

and some separation to occur. 

NASA/CR—2012-217417 109
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Clark J.P., 2007 

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Aerofoils in Low-Pressure Turbine,” Annual Review of Fluid Mechanics, 37, pp. 71-98. 

Ibrahim, M.B., Kartuzova, O. and Volino, R.J., 2008, “Experimental and Computational 

Investigations of Separation and Transition on a Highly Loaded Low Pressure Turbine 

Airfoil: Part 1 – Low Freestream Turbulence Intensity”, ASME Paper IMECE2008-

68879. 

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Simulations For Highly Loaded Low Pressure Turbine Airfoil (L1a) Using Pulsed Vortex 

Generator Jets”, ASME Paper GT2010-23015. 

NASA/CR—2012-217417 110
Kaszeta, R. W., Simon, T. W., and Ashpis, D. E., 2001, “Experimental Investigation of 

Transition to Turbulence as Affected by Passing Wakes,” Proceedings of ASME Turbo 

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Ladreau, S., 2005, “Unsteady RANS modeling of wake-blade interaction: computational 

requirements and limitations.” Computers and Fluids 34. 3-21.

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NASA/CR—2012-217417 112
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NASA/CR—2012-217417 113
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4. TITLE AND SUBTITLE

CFD Simulations for the Effect of Unsteady Wakes on the Boundary Layer of a Highly 

Loaded Low Pressure Turbine Airfoil (L1A) 

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13. SUPPLEMENTARY NOTES

This report was submitted as a thesis in partial fulfillment of the requirements for the degree Master of Science to the Cleveland State 

University, Department of Mechanical Engineering, Cleveland, Ohio, May 2010. Grant technical monitors, Anthony J. Strazisar, Office of 

the Chief Scientist, Glenn Research Center, organization code ASOO, James D. Heidmann, Aeropropulsion Division, Glenn Research 

Center, organization code RTTO, David E. Ashpis, Aeropropulsion Division, Glenn Research Center, organization code RTTO, 

ashpis@nasa.gov 

14. ABSTRACT

This report is the third part of a three-part final report of research performed under an NRA cooperative Agreement contract. The first part 

was published as NASA/CR-2012-217415. The second part was published as NASA/CR-2012-217416. The study of the very high lift lowpressure turbine airfoil L1A in the presence of unsteady wakes was performed computationally and compared against experimental results. 

The experiments were conducted in a low speed wind tunnel under high (4.9%) and then low (0.6%) freestream turbulence intensity for 

Reynolds number equal to 25,000 and 50,000. The experimental and computational data have shown that in cases without wakes, the

boundary layer separated without reattachment. The CFD was done with LES and URANS utilizing the finite-volume code ANSYS Fluent 

(ANSYS, Inc.) under the same freestream turbulence and Reynolds number conditions as the experiment but only at a rod to blade spacing 

of 1. With wakes, separation was largely suppressed, particularly if the wake passing frequency was sufficiently high. This was validated in 

the 3D CFD efforts by comparing the experimental results for the pressure coefficients and velocity profiles, which were reasonable for all 

cases examined. The 2D CFD efforts failed to capture the three dimensionality effects of the wake and thus were less consistent with the 

experimental data. The effect of the freestream turbulence intensity levels also showed a little more consistency with the experimental data 

at higher intensities when compared with the low intensity cases. Additional cases with higher wake passing frequencies which were not run 

experimentally were simulated. The results showed that an initial 25% increase from the experimental wake passing greatly reduced the size 

of the separation bubble, nearly completely suppressing it.

15. SUBJECT TERMS

Gas turbines; Turbomachinery; Turbine; Low pressure turbine; Turbulence; Flow control; Synthetic jets; CFD; LES; Turbulence 

models; Wakes; Separation; Vortex generated jets 

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