Vincent R. Capece

University of Kentucky, Lexington, Kentucky

Max F. Platzer

Naval Postgraduate School, Monterey, California

An Experimental and Computational

Investigation of Oscillating Airfoil

Unsteady Aerodynamics at Large

Mean Incidence

NASA/CR—2003-212199

March 2003

https://ntrs.nasa.gov/search.jsp?R=20030032464 2018-05-15T16:08:08+00:00Z
The NASA STI Program Office . . . in Profile

Since its founding, NASA has been dedicated to

the advancement of aeronautics and space

science. The NASA Scientific and Technical

Information (STI) Program Office plays a key part

in helping NASA maintain this important role.

The NASA STI Program Office is operated by

Langley Research Center, the Lead Center for

NASA’s scientific and technical information. The

NASA STI Program Office provides access to the

NASA STI Database, the largest collection of

aeronautical and space science STI in the world.

The Program Office is also NASA’s institutional

mechanism for disseminating the results of its

research and development activities. These results

are published by NASA in the NASA STI Report

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant

phase of research that present the results of

NASA programs and include extensive data

or theoretical analysis. Includes compilations

of significant scientific and technical data and

information deemed to be of continuing

reference value. NASA’s counterpart of peerreviewed formal professional papers but

has less stringent limitations on manuscript

length and extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies

that contain minimal annotation. Does not

contain extensive analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by

NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from

NASA programs, projects, and missions,

often concerned with subjects having

substantial public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific

and technical material pertinent to NASA’s

mission.

Specialized services that complement the STI

Program Office’s diverse offerings include

creating custom thesauri, building customized

databases, organizing and publishing research

results . . . even providing videos.

For more information about the NASA STI

Program Office, see the following:

• Access the NASA STI Program Home Page

at http://www.sti.nasa.gov

• E-mail your question via the Internet to

help@sti.nasa.gov

• Fax your question to the NASA Access

Help Desk at 301–621–0134

• Telephone the NASA Access Help Desk at

301–621–0390

• Write to:

 NASA Access Help Desk

 NASA Center for AeroSpace Information

 7121 Standard Drive

 Hanover, MD 21076
Vincent R. Capece

University of Kentucky, Lexington, Kentucky

Max F. Platzer

Naval Postgraduate School, Monterey, California

An Experimental and Computational

Investigation of Oscillating Airfoil

Unsteady Aerodynamics at Large

Mean Incidence

NASA/CR—2003-212199

March 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Grant NAG3–2613
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

This report contains preliminary

findings, subject to revision as

analysis proceeds.

The Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

Available electronically at http://gltrs.grc.nasa.gov
Contents

1 INTRODUCTION

2 PROGRAM OBJECTIVES

2.1 Overall Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2 Specific Objectives . . . ..........................

3 TECHNICAL APPROACH

3.1 Experimental Data .............................

3.2 Computational Models . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3 Cascade Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 PROGRAM STATUS AND RESULTS

4.1 Transition Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1.1 NACA 0012 Airfoil Test Case . . . . . . . . . . . . . . . . . . .

4.1.2 Numerical Models and Procedures . . . . . . . . . . . . . . . . .

4.1.3 Comparison of Turbulence Model and Flow Solver for 0 deg.

Angle-of-Attack . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1.4 Comparison of Thin-Layer and Full Navier-Stokes Solution . . .

4.1.5 Comparison of the Turbulence Models . . . . . . . . . . . . . .

4.1.6 Discretization of Convective Fluxes . . . . . . . . . . . . . . . .

4.1.7 Transitional Solution for 10 deg. Angle-of-Attack . . . . . . . .

4.1.8 Transitional Solution for 12 deg. Angle-of-Attack . . . . . . . .

4.1.9 Transitional Solution for 12 deg. Angle-of-Attack, SA Turbulence

Model . . . . . . . . . . . .....................

4.1.10 Transitional Solution for 12 deg. Angle-of-Attack, ROE Solver .

4.1.11 Summary . . . . ..........................

4.2 TURBO Modeling ................... ..........

4.2.1 Geometry and Grid Generation . . . . . . . . . . . . . . . . . .

4.2.2 Steady Flow Simulations......................

NASA/CR—2003-212199 iii

1

3

3

3

4

4

5

5

6

6

8

8

10

11

12

13

13

14

17

18

18

20

20

21

.......... .....................

1. INTRODUCTION

One of the major challenges in the design and development of fan, compressor, and

turbine airfoils for gas turbine engines is high cycle fatigue failures due to flutter and

aerodynamically induced forced vibrations. In order to predict flutter susceptibility

and forced vibration stress for gas turbine airfoils early in the design phase, accurate

unsteady aerodynamic models are required. While considerable progress has been made

in the development of unsteady aerodynamic models, accurate predictions of flutter and

forced vibration stress at all operating conditions have remained elusive.

The development of unsteady aerodynamic models to predict the unsteady aerodynamic loading acting on turbomachine airfoils is an area of fundamental research

interest. For flows at high incidence angles viscous effects dominate. In these cases the

Navier-Stokes equations need to be considered. Unsteady Reynolds Averaged NavierStokes (RANS) models (e.g., Weber and Platzer[1]; Swafford et al.[2]; Ekaterinaris and

Platzer[3]; Sidén[4]; and Wu et al.[5]) have been developed to accurately account for

viscous effects. For these Reynolds averaged equations turbulence models are needed for

the Reynolds stress terms. A transition model is also necessary, but in most cases the

transition location is specified at either the leading edge or the suction peak. Typically

the Baldwin and Lomax[6] algebraic turbulence model is used for solid surfaces with

turbulent wakes modeled using a turbulent wake model. Since the Reynolds numbers

in turbomachinery are large enough to guarantee the flow is turbulent, suitable transition and turbulence models are crucial for accurate prediction of steady and unsteady

separated flow.

It is generally agreed that a weakness in the CFD codes currently used for the development of high-performance turbomachinery airfoils is the treatment of transitional

boundary layers. The common computational approach of postulating a point transition from laminar to turbulent flow at either the leading edge or the suction peak is

usually acknowledged as being physically unrealistic, but this assumption is considered

to be conservative, and therefore acceptable. There are, however, many situations, especially under off-design conditions, where the assumption of point transition produces

large discrepancies between the computed and measured results. Stall resulting from

a laminar separation is such a case because the actual flow may exhibit a separation

NASA/CR—2003-212199 1
bubble that lengthens and ultimately bursts.

The sensitivity of computed airfoil flows to the type of transition modeling used

in Reynolds-averaged Navier-Stokes calculations has been shown conclusively by van

Dyken, Ekaterinaris, Chandrasekhara and Platzer[7] in their studies of the dynamic stall

characteristics of NACA 0012 airfoils at a Reynolds number of 540,000. They showed

that the assumption of point transition to turbulence fails to predict the experimentally

measured separation bubbles near the airfoil leading edge, whereas a judiciously selected

transition onset location within the separation bubble together with a properly chosen

transition length succeeded in reproducing the separation bubble. Ekaterinaris and

Platzer[3] also showed that the application of the Baldwin-Barth turbulence model

(which allows for the incorporation of a transition region) enables the prediction of

the experimentally measured hysteresis loops of NACA 0012 and Sikorsky SC-A109

airfoils at high Reynolds numbers (greater than one million), whereas the assumption

of fully turbulent flow again fails to predict the correct dynamic stall loops. These

calculations were further improved by Sanz and Platzer[8] who used the new transition

model of Solomon, Walker and Gostelow[9], which accounts for the effect of adverse

pressure gradient and free-stream turbulence on transition. These calculations provided

further confirmation that the correct separation bubble behavior can be obtained only

if boundary layer transition is incorporated into the Navier-Stokes calculations. For a

more complete review of the state-of-the-art of the computational prediction of airfoil

dynamic stall we refer to Ekaterinaris and Platzer[10].

Hence, from the above discussion the it is evident additional work is necessary in the

area of transition and turbulence modeling for unsteady separated flow. The present

research project addresses this important fundamental issues for flows at large mean

incidence angles.

NASA/CR—2003-212199 2
2. PROGRAM OBJECTIVES

2.1. Overall Objectives

The overall objectives of this effort are listed below:

1. Develop a transition model suitable for unsteady separated flow and quantify the

effects of transition on airfoil steady and unsteady aerodynamics for attached and

separated flow using this model.

2. Evaluate the capability of current state-of-the-art unsteady aerodynamic models

to predict the oscillating airfoil response of compressor airfoils over a range of realistic reduced frequencies, Mach numbers, and loading levels through correlation

with benchmark data. This comprehensive evaluation will assess the assumptions

used in unsteady aerodynamic models. The results of this evaluation can be used

to direct improvement of current models and the development of future models.

The transition modeling effort will also make strides in improving predictions of

steady flow performance of fan and compressor blades at off-design conditions.

2.2. Specific Objectives

The following were the specific objectives for the first year of this research program.

1. Installation and verification of the operation of the parallel version of TURBO

on the NASA parallel computing network and on the SGI platforms of the Computer Laboratory of the Department of Aeronautics and Astronautics of the Naval

Postgraduate School.

2. Initiate steady flow simulations of the NASA/Pratt&Whitney airfoil, which has

been investigated experimentally in the NASA GRC Transonic Flutter Cascade.

3. Investigation of the influence of transition models and numerical procedures on

the prediction of separation bubbles.

NASA/CR—2003-212199 3
3. TECHNICAL APPROACH

The approach used to achieve the objectives listed above involves utilizing experiments

performed in the NASA-GRC 2D linear oscillating cascade to obtain fundamental unsteady aerodynamic data at high Mach numbers and large mean incidence angles for

cascade airfoils executing torsion mode oscillation around the midchord. These data will

be correlated with state-of-the-art computational models for oscillating airfoil unsteady

aerodynamics. Data will also be used from other appropriate experiments. Additionally,

a systematic study of the effect of transition modeling on the prediction of the unsteady

aerodynamics of typical high performance turbomachinery airfoils will be conducted.

The NASA/Pratt & Whitney airfoil cross-section will be used, which is representative of the airfoil section contour in the tip region of low aspect ratio fan blades.

In these experiments the unsteady pressure on the surface of the airfoils generated by

airfoil oscillation is measured using flush mounted pressure transducers. The unsteady

pressure is Fourier decomposed into harmonics with the first harmonic amplitude and

phase determined as a function of chordwise position along the airfoil in the form of a

pressure coefficient. In this form it can be directly correlated with the computational

models. Existing data ([11], [12])for this airfoil configuration is currently being used.

Additional experiments are also being conducted and this data will be used in the

future.

3.1. Experimental Data

The NASA Glenn Linear Oscillating Cascade facility combines a linear cascade

wind tunnel capable of inlet flow up to a Mach number of 1.15 with a high-speed airfoil

drive system. The drive system imparts torsional oscillations to the cascade airfoils at

specified interblade phase angles and realistic values of reduced frequency. Additional

facility details can be found in Buffum and Fleeter[13].

NASA/CR—2003-212199 4
3.2. Computational Models

Two different computational models will be utilized in this investigation, which are

discussed briefly below. Nonlinear unsteady aerodynamic models will be considered.

TURBO. This computational model analyzes three-dimensional steady and unsteady flow. It is capable of analyzing both inviscid (Euler) and viscous flows. In

addition, this computational model has been developed to compute the rotor-stator

interaction problem, plus the airfoils can oscillate. Phase lag boundary conditions are

used so that passages do not need to be stacked to satisfy periodicity, hence reducing

computational resources. Additionally, TURBO has the Baldwin-Lomax and k- turbulence models, but it does not have a transition model. However, a fixed transition

point (specified as a percent chord location on the suction surface) can be specified on

the airfoil.

NPS Code. This computational model analyzes quasi-three-dimensional steady

and unsteady flow. A variable stream surface thickness is used to account for threedimensional flow effects. A finite volume approach is used to solve the governing equations. Characteristic boundary conditions are used at the inlet and exit and the direct

store method is used at the periodic boundary. A mesh regeneration technique is

used for airfoil oscillation. Currently the Baldwin-Lomax turbulence model is used

in conjunction with the transition onset criterion introduced by Baldwin and Lomax.

Additional details can be found in Weber and Platzer[1].

3.3. Cascade Modeling

In 2D linear cascades only a finite number of airfoils are used. Typically nine are

used as in the NASA-GRC linear cascade. Due to the finite number of airfoils the

near side-wall airfoils do not behave aerodynamically like cascade airfoils. Additionally,

during oscillation of the airfoils propagating acoustic waves are found to reflect from the

side-walls. For this reason, as part of this research program the wind tunnel walls will

be modeled in TURBO. This will more accurately model the flow in the NASA-GRC

linear cascade.

NASA/CR—2003-212199 5
4. PROGRAM STATUS AND RESULTS

All of the previously noted specific objectives for the first year of this research program

have been successfully met.

4.1. Transition Modeling

The following discussion on transition modeling is from the paper by Sanz and Platzer[14].

Due to the importance of separated flow transition, significant experimental and

computational investigations have been performed especially in the last few years.

Mayle[15] gave an excellent overview of the research status on transition in turbomachinery in 1991. Hazarika and Hirsch[16] measured the Reynolds number effect on

separation bubbles, Walraevens and Cumpsty[17] investigated the effect of the leading edge shape, and Malkiel and Mayle[18] showed the turbulence development inside

a separation bubble. A very detailed study of separation bubbles was performed by

Hatman and Wang[19], [20], [21], [22] in 1998. They classified separation bubbles according to the status of the transition process and provided an empirical formulation

for separation bubble prediction. Lou and Hourmouziadis[23] performed experiments

on steady and periodic-unsteady boundary layers with separation bubbles. In a further

experimental study Yaras[24] showed the influence of the pressure-gradient history on

the location of the transition onset in a separation bubble. Also valuable databases

for further model development were provided by Volino and Hultgren[25] and Schreiber

et al.[26] who studied the influence of Reynolds number and inlet free-stream turbulence intensity on attached and separated flow transition. Even attempts to control

leading-edge separation bubbles by stationary bar wakes were investigated by Funazaki

et al.[27]. These expensive and detailed experimental studies are performed in order to

give more insight into the physics of separated flow transition and to provide the designer with correlations for the determination of the onset and length of the transition

process inside laminar separation bubbles.

These empirical correlations are welcomed by design engineers, because despite the

significant advances in numerical methods and computational power CFD codes still

have deficiencies in the prediction of turbulent flow phenomena and boundary layer

NASA/CR—2003-212199 6
transition. The various transition models developed for attached as well as separatedflow transition are incorporated into two- and three-dimensional Navier-Stokes solvers

in order to improve the prediction of turbomachinery flow. These models use an intermittency function as defined by Emmons[28] to modify either the turbulent viscosity

(as is generally done) or the turbulence production term of the turbulence model (e.g.

[29]). Different ways to consider transition are chosen by Suzen et al.[30] who developed a transport equation for the intermittency and Steelant and Dick[31] who use a

separate solver for laminar and turbulent components blending the solutions based on

the intermittency.

Design engineers and numerical researchers apply their modified Navier-Stokes codes

to various measured flow cases to study the validity and sensitivity of the transition

models and to obtain confidence in their simulations. Besides many numerical investigations of cases with attached-flow transition, also numerical predictions of laminar

separation bubbles are performed. Platzer and collaborators (e.g. [7], [32], [3], [8])

were among the first who used such an approach to predict laminar separation bubbles

on airfoils. In 1998 Sanz and Platzer [33] studied a laminar separation bubble on a

controlled-diffusion compressor cascade comparing different transition models. Most of

them gave reasonable results, but the need for further improvements was shown. The

same test case was also studied by Hobson and Weber[34], using two different flow

solvers in addition to a transition model. It turned out that transition modeling improved the results for one flow solver, whereas the best results were obtained with the

second solver using a "pure" turbulence model. Also a detailed comparison of different

transition models was published by Müller et al.[35] and Thermann et al.[36]. They

showed that transition modeling was the key to predict observed laminar separation

bubbles, although the results for some of the transition models deviated significantly

from the measurements.

Most researchers investigate the quality of transition models by implementing them

into the same Navier-Stokes code in a certain way. In contrast to this, Chernobrovkin

and Lakshminarayana [29] studied different ways of implementing the transition model,

as well as the influence of the numerical scheme (i.e., form of differential approximation)

on the transition prediction. They concluded that the potential error associated with

the solver could significantly change the separation bubble thickness and length. The

same objective is pursued by this work. It is not the influence of the transition model

which is studied, but the influence of the flow solver itself (numerical discretization,

constant vs. local time step, turbulence modelling, etc.) on the prediction of laminar

separation bubbles.

NASA/CR—2003-212199 7
4.1.1. NACA 0012 Airfoil Test Case

In this investigation numerical results were compared with the measurements of the flow

over a NACA 0012 airfoil obtained by Chandrasekhara et al.[37] at the NASA Ames Research Center in 1992. The measurements were obtained for steady flow at fixed anglesof-attack and for an oscillatory motion of the airfoil, α (t) = 10 deg +2 deg sin (ωt), with

a reduced frequency k = 0.05. Point diffraction interferometry (PDI) was used to obtain

the pressure distribution along the airfoil. Here the steady flow for a free-stream Mach

number of 0.3 and a Reynolds number of 540,000 based on the airfoil chord length will

be investigated for two different flow angles.

At 10 deg. angle-of-attack a laminar separation bubble is formed close to the leading

edge. At 12 deg. angle-of-attack the flow is fully stalled. This flow was already investigated by the Sanz and Platzer ([8]), implementing the transition model of Solomon

et al.[9] into an upwind-biased Navier-Stokes code, showing not only the importance of

transition modeling but also the limited reliability.

4.1.2. Numerical Models and Procedures

Two different flow solvers were applied in this investigation. The first one (OSH) is

based on the thin-layer approximation of the compressible Reynolds-averaged NavierStokes equations. Time iteration is accomplished by an implicit scheme based on a

Newton procedure and applying local time stepping. The Euler fluxes are discretized using a second-order or third-order TVD-upwind, node-centered scheme based on Osher’s

approximate Riemann solver. The eddy viscosity can either be modeled by the BaldwinLomax[6] (BL), the one-equation Baldwin-Barth[38] (BB), or the one-equation SpalartAllmaras[39] (SA) turbulence model.

Transition is modeled in a one-dimensional way by determining an intermittency

function γ (x) as a streamwise function along the blade profile. Because the grid lines are

nearly perpendicular to the blade surface within the boundary layer, the intermittency

along the normal grid lines is set to the value on the blade surface.

Two transition models are implemented into this code. In the first transition model

which was developed by Solomon et al.[9] (SWG), the transition onset location is set

and the transition length is calculated based on the correlations for turbulent spot

generation, spot propagation and spot spreading as functions of the pressure gradient

parameter λθ. Although this model has been derived for attached flows, it is being used

quite widely also to predict laminar separation bubbles and was therefore considered

in this investigation. But in separated-flow regions high negative values of the pressure

gradient parameter can occur which are beyond the limits for which experimental data

exist. This does not pose a problem for the spot propagation and spot spreading,

NASA/CR—2003-212199 8
because their correlations approach a maximum, which is close to the value at the

laminar separation limit of λθ = −0.12. On the other hand the spot generation rate

can increase to infinity for high negative values of λθ, so that it is limited to a value

which proved to predict instantaneous transition (for more details see [8]).

For the second transition model (SIM) transition is modeled by setting the transition onset and the transition length, and assuming an exponential function according to

Narashimha[40]. This approach was chosen because it allows a very basic investigation

of the influence of transition modeling on the numerical solution.

The second flow solver (ROE) was developed by Gehrer[41] and is a full NavierStokes code. Time iteration is accomplished by an implicit procedure similar to the

one used for OSH. The Euler fluxes are similarly discretized by a third-order accurate,

TVD-upwind, approximate Riemann solver, but in this case it is cell-centered and

uses Roe’s method. The eddy viscosity is determined by the Baldwin-Lomax[6] (BL)

model or the one-equation model of Spalart and Allmaras[39] (SA) in this investigation.

Transition is modeled by the SIM model.

For both codes the viscous fluxes are evaluated by central differencing in a similar

way. Transition is included by modifying the turbulent viscosity using the intermittency

function γ (x):

μturb,ef f = γμturb

For the comparison of the different numerical results the pressure distribution and

the skin friction along the airfoil are used. The pressure distribution allows comparison

with the measurement data and the skin friction is a very sensible parameter which

also shows the extent of separation zones on the airfoil by negative values. Only the

flow on the suction side of the airfoil is investigated, because the flow on the pressure

side is fully attached. The influence of the different simulations on the pressure surface

flow behavior is negligible. Convergence is controlled by checking the skin friction

distribution along the blade suction surface. Convergence for the oscillating results is

controlled by monitoring the lift coefficient over time.

The numerical investigation requires a verification to ensure grid independence.

Three C-grids (181 x 81, 257 x 65 and 271 x 91, the last one with twice as many grid

points in streamwise direction on the suction side) were utilized. Fig. 4.1 shows a grid

detail of the region close to the leading edge, where laminar separation is predicted.

The maximum distance between the surface and the first grid point varies between

y+ = 1.2 ∼ 1.4 and y+ = 1.0 for OSH. (For ROE it was about half the value because

of the cell-centered scheme.) Numerical predictions with these grids were very close to

each other and the reported computational results are based mainly on the finest grid.

NASA/CR—2003-212199 9
Figure 4.1: Leading edge region illustrating grid resolution where laminar boundary

layer separation is predicted (271x91 nodes)

4.1.3. Comparison of Turbulence Model and Flow Solver for 0 deg. Angleof-Attack

To demonstrate that both codes give similar results for a simple attached-flow test case,

the skin friction on the suction side of the NACA 0012 airfoil is shown for an angle-ofattack of 0 deg. in Fig. 4.2. Results are compared for all available turbulence models

for both numerical codes. The different codes give very similar results when using the

same turbulence model, but the influence of the turbulence models on the predicted

skin friction coefficient is remarkable (as is generally known).

The BL solutions are nearly identical; the small differences in the SA results can

be explained by slightly different implementations of the different code developers. A

comparison of the "fully turbulent" BL, BB and SA solutions shows that they differ

in the front part of the airfoil. However, downstream of about 30 % chord length

all solutions with the different turbulence models achieve the same values of the skin

friction coefficient. The BB model is derived from the k −  model and has the feature

of an inherent laminar-to-turbulent transition as shown by the minimum skin friction

at 10% chord length. In summary, Fig. 4.2 shows that both codes give similar results

for this simple flow with the differences mainly caused by the turbulence models.

NASA/CR—2003-212199 10
Figure 4.2: Skin friction distribution for different flow solvers and turbulence models

for 0 deg. angle-of-attack

4.1.4. Comparison of Thin-Layer and Full Navier-Stokes Solution

For high Reynolds numbers wall shear layers for attached flows are of limited size with

the gradients transverse to the main flow direction dominating the viscous stresses.

Therefore for these flows a thin-shear-layer approximation is often used neglecting all

derivatives in "flow direction" appearing in the turbulent and viscous shear terms. This

simplification is also supported by the fact, that, generally, the computational grids are

made dense only in the direction normal to the walls, so that the neglected derivative

terms are computed with lower accuracy compared to the normal derivatives. But for

separated flows with high gradients in the flow direction the question arises whether

the thin-layer approximation is still valid for commonly used grids.

Therefore two cases are investigated for an angle-of-attack of 12 deg., one with

attached flow and one with highly separated flow. The ROE code was used with the

SA turbulence model and transition modeling was applied for the second case (SIM,

transition from 5% to 5.1% chord length). The same solver control parameters, like

CFL number, number of time steps, etc., and both the 257 x 65 and 271 x 91 grids were

used. The skin friction distribution does not show any significant differences for both

the attached and the highly separated flow with two separation zones in the forward

20% chord length of the airfoil (see Fig. 4.3). Therefore, it can be concluded that the

thin-layer approximation does not influence the accuracy of the numerical solution for

NASA/CR—2003-212199 11
Figure 4.3: Airfoil suction surface skin friction distribution for the ROE solver with SA

turbulence model for 12 deg. angle-of-attack

these high Reynolds number flows.

4.1.5. Comparison of the Turbulence Models

The OSH code is used to compare the BB and SA turbulence model for the flow

around the NACA 0012 airfoil at 12 deg. angle-of-attack. As shown in Fig. 4.2, the

BB model predicts some kind of transition close to the leading edge. At 12 deg. this

leads to the BB prediction of a leading edge separation bubble of about 2% chord length

on the suction side, whereas the flow computed by the SA model is fully attached (Fig.

4.4). This separation bubble can also be seen in the pressure distribution in Fig. 4.5.

Generally, the skin friction distribution predicted by both models differs remarkably

along the whole airfoil suction side. On the pressure side both solutions show a similar

skin friction distribution. The zero skin friction value on the pressure side indicates the

location of the stagnation point. The BB yields a smaller value between 10 and 34%

chord length explained by the inherent transitional feature of this model (see above).

This result indicates that the implementation of a given transition model into different

turbulence models will lead to different results, so that the correct computation of

sensible boundary-layer phenomena like laminar separation bubbles seems to need the

right combination of turbulence and transition modeling.

NASA/CR—2003-212199 12
Figure 4.4: Skin friction distribution along the airfoil for the the OSH solver with no

transition for 12 deg. angle-of-attack

4.1.6. Discretization of Convective Fluxes

The Roe and Osher codes both use an approximate Riemann solver. The discretization

scheme is third-order accurate for both codes, but the ROE code uses a TVD scheme.

For this investigation the SA turbulence model is used, a transition model is not applied.

For an angle-of-attack of 12 deg. (Fig. 4.6) the ROE solver predicts a smaller skin

friction in the forward section of the airfoil with a difference of about 25% at 10% chord

length and this difference increases towards the leading edge. Both results approach

each other near the trailing edge of the airfoil. The onset of the trailing edge separation

is predicted at the same location by both codes.

4.1.7. Transitional Solution for 10 deg. Angle-of-Attack

To show the influence of transition modeling on the numerical solution, the flow for an

angle-of-attack of 10 deg. is calculated, using the OSH code with the BB turbulence

model and the SWG transition model. Fig. 4.7 shows the resulting pressure distribution for different transition onset locations. Similar to the investigation of Sanz and

Platzer[8] it can be seen that moving the transition onset location downstream results

in a longer separation zone indicated by the flat pressure profile and a smaller suction

peak. Fully stalled flow can be "achieved" by delaying the transition onset even more.

NASA/CR—2003-212199 13
Figure 4.5: Airfoil pressure distribution for the OSH code with no transition for 12 deg.

angle-of-attack

This result agrees with the expectations of the influence of transition on flow separation.

The experimental data allows the location of the separation zone to be quantified.

Comparing its onset and extent with the numerical solutions, the result for xt/c = 4.5%

agrees best with the experiment. The calculated skin friction distribution shows two

separation bubbles within the measured zone of separation indicated by the occurrence

of a short region of positive skin friction (e.g. see Fig. 4.3). This local maximum of

the skin friction coefficient within the separation zone is caused by the rapid pressure

increase at the end of the flat pressure region shown in Fig. 4.7.

4.1.8. Transitional Solution for 12 deg. Angle-of-Attack

A more difficult test case is the flow around the NACA 0012 airfoil at 12 deg. angle-ofattack, because here the flow is very close to stall and small changes in the transition

onset location can significantly change the flow situation. The same flow solver (OSH

with BB and SWG) is used as previously. Besides a time iteration with local time

stepping as convergence acceleration (as applied in the previous investigations), an "unsteady" simulation with a constant time step is also used. The influence of a variation

of the transition onset location as well as of the iteration procedure on the pressure

distribution is shown in Figs. 4.8a,b,c.

At a transition onset location of xt/c = 2.0% there is no difference between the

NASA/CR—2003-212199 14
Figure 4.6: Airfoil suction surface skin friction for SA model with no transition model

for 12 deg. angle-of-attack

steady and unsteady solutions; both solutions converge to the same skin friction distribution. The pressure curve shows a flat region, succeeded by a small peak, before a

rapid pressure decrease indicates the end of the separation bubble at x/c = 2.6% (see

also Fig. 4.9). The end of transition is predicted at x/c = 2.2% by the SWG model.

Moving the transition onset location gradually downstream, at first the computed

results change as expected. The zone of separation becomes longer (till x/c = 3.2%), the

leading edge suction peak decreases. But also differences between steady and unsteady

solutions can be observed. Whereas the unsteady solution computed with a constant

time step converges towards a constant lift value for xt/c = 2.3%, the steady solution

starts oscillating with periodic fluctuations of the lift. The observed amplitude in lift

oscillation is about 10%. The pressure distributions for minimum and maximum lift

are shown.

By reducing the Courant number for the steady solution, the amplitude and frequency of the oscillations increase, indicating that the solution achieved is quite arbitrary. The reason for this behavior can be partly found in the transition modeling. The

SWG model uses boundary layer parameters such as the momentum thickness for the

determination of the transition length. Performing a computation with variable local

time steps leads to quite arbitrary boundary layer profiles when the flow is separated.

The computed transition length varies considerably during the iteration process thus

NASA/CR—2003-212199 15
Figure 4.7: Airfoil pressure distribution for the OSH solver with BB turbulence model

for 10 deg. angle-of-attack

leading to the strong oscillations observed in the steady solution. Using a fixed transition length (see Fig. 4.12), these oscillations are again encountered, but only if the

transition onset is moved farther downstream.

Moving the transition onset farther downstream to xt/c = 2.6% (Fig. 4.8b) causes

pressure oscillations in the unsteady solution. However, in contrast to the steady solution, these unsteady oscillations are independent of the time-step size, suggesting

physical flow oscillations of the separation zone. Despite this behavior all solutions

are similar with similar length of the flat pressure region as well as similar skin friction distribution (see Fig. 4.9). All the results (xt/c = 2.0% to xt/c = 2.6%) show

the same separation onset and similar skin friction values in the separation zone with

a small maximum. The reattachment location moves downstream to x/c = 3.7% for

xt/c = 2.6%.

For a transition onset location xt/c = 2.8% (Fig. 4.8c) the unsteady solution shows

a dramatic reduction of the suction peak caused by fully stalled flow. The solution

oscillates, but the pressure distribution is smooth and there is still a short flat region

as a consequence of the transition modelling. The skin friction distribution is quite

different as shown in Fig. 4.9. The flow separates later because of the reduced suction

peak, and the laminar separation bubble is relatively short. The flow separates again at

23% chord length, reattaches at mid chord, and separates close to the trailing edge. This

NASA/CR—2003-212199 16
can be explained by a shedding of the leading edge separation bubble and downstream

transport of the vortex (see [33]). The steady solution for xt/c = 2.8% as well as the

different solutions for xt/c = 3.0% are unstable, as evidenced by the large bandwidth

of the solution or the oscillations in the pressure curve.

In summary it can be said that short laminar separation bubbles can be computed

using a steady as well as an unsteady time iteration. But increasing the laminar separation zones by delaying the transition onset yields the following type of solution:

• Convergent steady or unsteady solutions with no oscillations over time (e.g. for

xt/c = 2.0%).

• Unsteady solutions with physical oscillations over time (e.g. for xt/c = 2.6%).

• Steady solutions with nonphysical oscillations over time (e.g. for xt/c = 2.6%).

The mean pressure distribution is nearly the same, but the flow details in the

separation zone are only predicted by the unsteady solver.

• Unstable oscillatory solutions (e.g. for xt/c = 3.0%).

Finally, no solution shows the measured flat pressure distribution along the whole

suction surface. But looking at the sparse experimental data in the separated zone

(besides the leading edge region there are only two more data points on the suction

side) it is doubtful if the applied PIV measurement method was sensitive enough to

resolve the small pressure variations as shown for example by the unsteady solution

for xt/c = 2.8%. Besides, it must be emphasized that the investigated flow case at

12 deg. is very sensitive to changes in the angle-of-attack. Therefore, for 12.5 deg.

angle-of-attack full stall was already predicted for xt/c = 2.6%.

4.1.9. Transitional Solution for 12 deg. Angle-of-Attack, SA Turbulence

Model

In Fig. 4.4 it has been shown that different turbulent flow solutions are obtained

with the BB and SA turbulence models. In Figs. 4.10 and 4.11 the differences are

investigated for transitional flow, using the OSH solver with local time stepping and the

SWG transition model. The pressure distribution shows similar results for xt/c = 2.0%,

but differs for xt/c = 2.6%, where the SA solution is already unstable, as indicated by

the oscillations in the pressure profile.

The comparison of the skin friction distribution between the SA and BB solution

for xt/c = 2.0% shows similar values for the separation bubble, but after transition the

BB solution gives lower values. This corresponds to the behavior of the fully turbulent

NASA/CR—2003-212199 17
solution in Fig. 4.4. The lower skin friction and thus lower turbulent viscosity can

also be the reason for the full separation of the BB solution, shown by a negative skin

friction along most of the blade length.

Use of the SWG model causes the transition length calculated inside the separation

zone to become relatively long due to the variation of the boundary layer parameters.

If instead a short constant transition length of 1% chord length is assumed (SIM

transition model), the computed flow remains stable for a wider range of transition

onset locations (see Fig. 4.12). The steady solution converges to a constant value up to

xt/c = 3.0%, for xt/c = 4.0% the solution starts to oscillate between two stable results.

4.1.10. Transitional Solution for 12 deg. Angle-of-Attack, ROE Solver

As a next step the same flow situation was investigated with the ROE solver. The SA

turbulence model is applied together with the SIM transition model. The transition

onset is varied and the transition length is set to 1%. The resulting pressure and skin

friction distribution are shown in Figs. 4.13 and 4.14. Moving the transition onset

downstream has a similar effect as found for the SWG solutions shown before. The

suction peak decreases and the length of the separation zone increases. The "steady"

solution converges to a constant value even for xt/c = 4.0%. For xt/c = 5.0% the

solution oscillates with nonphysical wiggles occurring in the pressure distribution. The

result closest to the experimental data is the nonphysical solution obtained for xt/c =

6.0%.

Comparing the ROE solutions with the OSH solutions for the same turbulence and

the same transition model, there is close agreement for xt/c = 2.0% and 3.0%. Also

for xt/c = 4.0% the ROE solution is between the two extremes as predicted by OSH.

The skin friction distribution also agrees well for both solution algorithms. Both solvers

predict the same size of the separation zone, but the absolute size of the skin friction

differs, as was also seen before. The location of the separation onset at the trailing

edge are also similar, i.e. x/c = 82% for xt/c = 2.0%, x/c = 67% for xt/c = 3.0% and

x/c = 45% for xt/c = 4.0%, respectively.

4.1.11. Summary

Turbulence models in general are not able to predict laminar-to-turbulent transition

correctly. Therefore, transition modeling has to be applied in addition to turbulence

modeling in order to predict phenomena that mainly depend on transition, like boundary layer separation, skin friction or heat transfer. In this work numerical investigations

were carried out to get some insight into the interaction of transition modeling, turbulence modeling and the numerical flow solver for the calculation of laminar separation

NASA/CR—2003-212199 18
bubbles.

The following conclusions can be drawn from the results described above:

1. The occurrence and size of predicted separation bubbles are influenced by the

application of transition models. Most transition models derived for attached

flows can only be used in a limited range for separated-flow transition, because

they tend to become unstable. The reason is the difficult evaluation of the required boundary layer parameters which can lead to unrealistically long transition

lengths. Therefore, models for separated-flow transition which predict the transition onset and length as function of the flow conditions at the separation onset

are more suitable.

2. Using a thin-layer or full Navier-Stokes code does not change the results for commonly used computational grids.

3. The numerical scheme used also influences the result. Chernobrovkin and Lakshminarayana [29] showed that the level of artificial dissipation in their centraldifferencing code can change the solution considerably. In this study different

upwind schemes gave qualitatively similar results, but significant quantitative

differences.

4. The computation of long laminar separation bubbles tends to lead to oscillations

over time. If local time stepping is used these oscillations occur earlier, so that

constant time stepping should be applied if the solution oscillates over time.

5. If the laminar or transitional zone is set too long, the solution shows very strong

oscillations caused by shedding and reforming of the separation bubbles. These

strong oscillations seem to be nonphysical.

6. Because different turbulence models predict different boundary layer flow, statements about the applicability of different transition models can only be made for

combinations of transition and turbulence models. Beyond that, this investigation also shows an additional influence of the flow solver (numerical discretization

scheme), so that the applicability can only be verified for the combination of

numerical scheme, turbulence model and transition model.

Clearly, many factors influence the prediction of laminar separation bubbles. To

ensure a more reliable prediction, more experience has to be obtained about the interaction of these factors. Further computations shall be carried out which have to include

comparisons with experimental flow field data inside the separation bubbles.

NASA/CR—2003-212199 19
Table 4.1: Airfoil and cascade parameters

Chord, C 8.89 cm

Maximum thickness, tmax 0.048 C

Location of maximum thickness, xmax 0.625 C

Camber angle, θ* -9.5◦

Number of airfoils 9

Stagger angle 60◦

Solidity, C/s 1.52

Pitching axis, (xpitch/C, ypitch/C) (0.5, -0.017)

4.2. TURBO Modeling

The geometry and grid generation techniques used for the NASA/P&W airfoil modeling

in TURBO will be presented in this section.

4.2.1. Geometry and Grid Generation

This airfoil has a cross-section typical of the tip section of advanced low aspect ratio

fan blades. The steady and unsteady aerodynamic surface pressure distributions were

quantified in a cascade experimentally by Buffum et al.[11],[12]. Fig. 4.15 and Table

4.1 present the cascade geometry. This figure also depicts the geometry and flow angle

definitions.

The NASA/Pratt&Whitney airfoil is being tested in the GRC Transonic Flutter

Cascade (TFC). This is a linear cascade consisting of nine airfoils. To model this

situation for TURBO the input geometry needs to be at a large radius. For this

investigation the hub radius was set at 41.346 chord lengths with a hub-to-tip radius

ratio of 0.98. The solidity at mid-span was taken to match the geometry tested in the

cascade.

Simulations were conducted with the extruded cross-section in order to assess the

influence that the fillet radii have on the flow field. Fig. 4.16 presents the extruded

section. Note that two shafts have been placed on the airfoil at mid-chord. These shafts

are not to scale. They are shown merely to indicate the location of the pitching axis

of the airfoil. A three dimensional model with one airfoil in a pie-shaped section is

presented in Fig. 4.17.

A series of passage-centered sheared H-grids were used to describe the airfoil surfaces. Grids generated by TCGRID, which was developed by Chima. Due to the high

stagger angle there is a great deal of shearing that is apparent in the grids in the leading

and trailing edge regions.

NASA/CR—2003-212199 20
The sheared H-mesh primarily used in this study has the dimensions of 162 points in

the axial direction 55 in the pitchwise direction, and 49 points in the radial direction.

There are 100 axial grid points on each airfoil surface. The far field computational

boundaries were 2.5 chords upstream of the leading edge and 2.5 chords downstream of

the leading edge. The first point off the airfoil surface yields y+ values less than 2 for

the attached flow viscous simulations considered in this study.

The grid discussed above was established through a series of initial grid studies

using TURBO. Fig. 4.18 presents an overall view of the grid. The grid leading edge

region is illustrated in Fig 4.19. The high resolution of the mesh is apparent.

For parallel computations the grid was subdivided into blocks using GUMBO.

The simulations presented below were performed using a 12 block grid, which is presented in Fig. 4.20.

4.2.2. Steady Flow Simulations

Results will be presented for the NASA/P&W airfoil for 0 deg. and 10 deg. of chordal

incidence (α) at an inlet Mach number (M) of 0.5. These incidence angles are based on

the cascade inlet angles relative to the airfoil chord-line (see Figure 4.15); upstream flow

angle measurements were not made. All data-computation correlations are referenced

by the experimental value of the chordal incidence angle and inlet Mach number. The

cascade inlet flow angle was varied until the best match was found between the steady

chordwise pressure coefficient data (−Cp (x)=(Pin − P) /ρV 2

in), and the predictions. In

the present investigation the k −  model is used with the flow fully turbulent starting

at the leading edge.

The resulting airfoil surface pressure distributions for M = 0.5, α = 0 deg.,

Re = 0.9 · 106 are shown in Fig. 4.21. The cascade inlet flow angle was varied until

the best match was found between the steady chordwise pressure coefficient data and

the predictions. This resulted in a 1.0 deg. chordal incidence angle giving the best

correlation between the experimental data and the steady flow solver.

For this case there was a very thin region of separated flow that was predicted

as can be seen from the region of reversed flow presented in Fig. 4.22, which shows the

velocity vectors along the suction surface leading edge.

Increasing the incidence angle to 10 deg., Re = 0.9 · 106 changes the behavior

of the cascade so that now there is flow separation off the leading edge of the airfoil

upper surface and a net pressure rise across the cascade. Flow visualization at midspan

in the cascade indicated the flow was separated from the leading edge to about 40%

of chord[12]. Fig. 4.23 presents the results for 7.5 deg. chordal incidence angle. This

shows that the angle-of-attack needs to be increased further. This work is in progress.

NASA/CR—2003-212199 21
Figure 4.8: Airfoil pressure distribution for the OSH solver with BB turbulence model

for 12 deg. angle-of-attack

NASA/CR—2003-212199 22
Figure 4.9: Airfoil skin friction distribution for the OSH solver and BB turbulence

model for 12 deg. angle-of-attack

Figure 4.10: Airfoil pressure distribution for the OSH solver for 12 deg. angle-of-attack

NASA/CR—2003-212199 23
Figure 4.11: Airfoil skin friction distribution for the OSH solver for 12 deg. angle-ofattack

Figure 4.12: Airfoil pressure distribution for the OSH solver with SA turbulence model

for 12 deg. angle-of-attack

NASA/CR—2003-212199 24
Figure 4.13: Airfoil pressure distribution for the SA turbulence model for 12 deg. angleof-attack

Figure 4.14: Airfoil skin friction distribution for the SA turbulence model for 12 deg.

angle-of-attack

NASA/CR—2003-212199 25
Figure 4.15: Airfoil and cascade geometry

Figure 4.16: Extruded section of NASA/Pratt&Whitney airfoil

NASA/CR—2003-212199 26
Figure 4.17: Three-dimensional model of the NASA/Pratt&Whitney airfoil

Flow

Figure 4.18: Periodic passage of NASA/Pratt&Whitney airfoil.

NASA/CR—2003-212199 27
Figure 4.19: Suction surface grid in the leading edge region

Figure 4.20: Overall view of 12 block grid.

NASA/CR—2003-212199 28
Figure 4.21: Steady chordwise pressure distribution for 0 deg. chordal incidence angle

NASA/CR—2003-212199 29
Figure 4.22: Velocity vectors in the leading edge region of the suction surface at 0 deg.

chordal incidence angle

NASA/CR—2003-212199 30
Figure 4.23: Chordwise distribution of the steady pressure coefficient for 7.5 deg.

chordal incidence angle

NASA/CR—2003-212199 31
Bibliography

[1] Weber, S. and Platzer, M.F., (2000), "A Navier-Stokes Analysis of the Stall Flutter

Characteristics of the Buffum Cascade", ASME Paper 2000-GT-385.

[2] Swafford, T.W., Loe, D.H., Huff, D.L., Huddleston, D.H., and Reddy, T.S.R., 1994,

"The Evolution of NPHASE: Euler/Navier-Stokes Computations of Unsteady TwoDimensional Cascade Flow Fields," AIAA Paper No. AIAA-94-1834.

[3] Ekaterinaris, J.A. and Platzer, M.F., 1996, "Numerical Investigation of Stall Flutter," ASME Journal of Turbomachinery, Vol. 118, pp. 197-203.

[4] Sidén, L.D.G., 1991, "Numerical Simulation of Unsteady Viscous Compressible

Flows Applied to Blade flutter Analysis," ASME 91-GT-203.

[5] Wu, J., Huff, D.L., and Sankar, L.N., 1989, "Evaluation of Three Turbulence

Models for the Prediction of Steady and Unsteady Airloads," NASA Technical

Memorandum 101413.

[6] Baldwin, B.S. and Lomax, H., 1978, "Thin Layer Approximation and Algebraic

Model for Separated Turbulent Flows," AIAA Paper No. 78-257.

[7] van Dyken, R.D., Ekaterinaris, J.A., Chandrasekhara, M.S., and Platzer, M.F.,

1996, "Analysis of Compressible Light Dynamic Stall Flow at Transitional

Reynolds Numbers", AIAA Journal, Vol. 34, No. 7, pp. 1420-1427.

[8] Sanz, W. and Platzer, M.F., 1998, "On the Navier-Stokes Calculations of Separation Bubbles with a New Transition Model," ASME Journal of Turbomachinery,

Vol. 120, pp. 36-42.

[9] Solomon, W.J., Walker, G.J., and Gostelow, J.P., 1996, "Transition Length Prediction for Flows With Rapidly Changing Pressure Gradients", ASME Journal of

Turbomachinery, Vol. 113, pp. 744-751.

[10] Ekaterinaris, J.A. and Platzer, M.F., 1997, "Computational Prediction of Airfoil

Dynamic Stall," Progress in Aerospace Sciences, Vol. 33, No. 11/12, pp. 759-846.

NASA/CR—2003-212199 32
[11] Buffum, D.H., Capece, V.R., King, A.J. and EL-Aini, Y.M., "Experimental Investigation of Unsteady Flows at Large Incidence Angles in a Linear Oscillating

Cascade," AIAA Paper No. 96-2823.

[12] Buffum, D.H., Capece, V.R., King, A.J. and EL-Aini, Y.M., "Oscillating Cascade Aerodynamics at Large Mean Incidence," ASME Journal of Turbomachinery,

Vol.120, No. 1, January 1998, pp. 122-131.

[13] Buffum, D.H. and Fleeter, S., 1990, "Aerodynamics of a Linear Oscillating Cascade," NASA Technical Memorandum 10350.

[14] Sanz, W. and Platzer, M.F., 2002, "On the Numerical Difficulties in Calculating

Laminar Separation Bubbles," ASME Paper No. GT-2002-30235.

[15] Mayle, R. E., 1991„ "The Role of Laminar-Turbulent Transition in Gas Turbine

Engines", ASME Journal of Turbomachinery, Vol. 113, pp. 509-537.

[16] Hazarika, B.K., and Hirsch, C., 1996, "Effect of Reynolds Number on a Leading

Edge Separation Bubble", ASME Paper No. 96-GT-410.

[17] Walraevens, R.E., and Cumpsty, N.A., 1995, "Leading Edge Separation Bubbles

on Turbomachinery Blades", ASME Journal of Turbomachinery, Vol. 117, pp. 115-

125.

[18] Maikiel, E., and Mayle, R.E., 1996, "Transition in a separation bubble", ASME

Journal of Turbomachinery, Vol. 118, pp. 752-759.

[19] Hatman, A., and Wang, T., 1998, "Separated-Flow Transition, Part 1 - Experimental Methodology and Mode Classification", ASME Paper No. 98-GT-461

[20] Hatman, A., and Wang, T., 1998, "Separated-Flow Transition, Part 2 - Experimental Results", ASME Paper No. 98-GT-462.

[21] Hatman, A., and Wang, T., 1998, "Separated-Flow Transition, Part 3 - Primary

Modes and Vortex Dynamics", ASME Paper No. 98-GT-463.

[22] Hatman, A., and Wang, T., 1998, "A Prediction Model for Separated-Flow Transition", ASME Paper No. 98-GT-237.

[23] Lou, W., and Hourmouziadis, J., 2000, "Separation Bubbles Under Steady and

Periodic-Unsteady Main Flow Conditions", ASME Paper No. 2000-GT-0270.

NASA/CR—2003-212199 33
[24] Yaras, M.I., 2001, "Measurements of the Effect of Pressure Gradient History on

Separation Bubble Transition", ASME Paper 2001-GT-0193.

[25] Volino, R.J., and Hultgren, L.S., 2000, "Measurements in separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions", ASME

Paper No. 0260.

[26] Schreiber, H.-A., Steinert, W., and KQsters, B., 2000, "Effects of Reynolds number and Free-Stream Turbulence on Boundary Layer Transition in a Compressor

Cascade", ASME Paper No. 2000-GT-0263.

[27] Funazaki, K., Harada, Y., and Takahashi, E., 2000, "Control of Separation Bubble

on a Blade Leading Edge By a Stationary Bar Wake", ASME Paper No. 2000-GT267.

[28] Emmons, H.W., 1951, "The Laminar-Turbulent Transition in a Boundary Layer -

Part I", J. of Aerospace Science, 018(7), pp. 490-498.

[29] Chemobrovkin, A. and Lakshminarayana, B., 1999, "Turbulence Modeling and

Computation of Viscous Transitional Flows for Low Pressure Turbines", ASME

Journal of Fluids Engineering, Vol. 121, pp. 824-833.

[30] Suzen, Y.B., Huang, P.G., Hultgren, L.S., and Ashpis, D.E., 2001, "Prediction of

Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil

Conditions Using an Intermittency Transport Equation", AIAA Paper 2001-0446.

[31] Steelant, J., and Dick, E., 2001, "Modelling of Laminar-Turbulent Transition for

High Freestream Turbulence", ASME Journal of Fluids Engineering, Vol. 123, pp.

22-30.

[32] Ekaterinaris, J.A., Chandrasekhara, M.S. and Platzer, M.F., 1995, "Analysis of

Low Reynolds Number Airfoil Flows", Journal of Aircraft, Vol. 32, No. 3, pp.

625-630.

[33] Sanz, W., and Platzer, M.F., 1997, "On the Calculation of Laminar Separation

Bubbles Using Different Transition Models", ASME Paper 97-GT-453.

[34] Hobson, G.V., and Weber, S., 2000, "Prediction of a Laminar Separation Bubble

Over a Controlled-Diffusion Compressor Blade", ASME Paper No. 2000-GT-277.

[35] Müller, M., Gallus, H.E., and Niehuis, R., 2000, "A Study on Models to Simulate

Boundary Layer Transition in Turbomachinery Flows", ASME Paper No. 2000-

GT-274.

NASA/CR—2003-212199 34
[36] Thermann, H., Müller, M., and Niehuis, R., 2001, "Numerical Simulation of the

Boundary Layer Transition in Turbomachinery Flows", ASME Paper No. 2001-

GT-0475.

[37] Chandrasekhara, M.S., Carr, L.W., and Ekaterinaris, J.A., 1992, "Interferometric

and Computational Studies of an Oscillating Airfoil Compressible Dynamic Stall

Field", Proc. 5th Asian Conference of Fluid Dynamics, Vol. 2, pp. 1047-1050.

[38] Baldwin, B.S., and Barth, T.J., 1990, "A One-Equation Turbulence Transport

Model for High Reynolds Number Wall-Bounded Flows", NASA TM 102847.

[39] Spalart, P.R., and Allmaras, S.R., 1994, "A One Equation Turbulence Model for

Aerodynamic Flows", La Recherche Aerospatiale, No. 1, pp. 5-21.

[40] Narasimha, R., 1985, "The Laminar-Turbulent Transition Zone in the Boundary

Layer", Progress in Aerospace Science, Vol. 22, pp. 29-80.

[41] Gehrer,A. and Jericha, J., 1999, "External Heat-Transfer Predictions in a Highly

Loaded Transonic Linear Turbine Guide Vane Cascade Using an Upwind Biased

Navier-Stokes Solver," ASME Journal of Turbomachinery, Vol. 121, pp. 525-531.

NASA/CR—2003-212199 35
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

REPORT DOCUMENTATION PAGE

2. REPORT DATE

19. SECURITY CLASSIFICATION

 OF ABSTRACT

18. SECURITY CLASSIFICATION

 OF THIS PAGE

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Form Approved

OMB No. 0704-0188

12b. DISTRIBUTION CODE

8. PERFORMING ORGANIZATION

 REPORT NUMBER

5. FUNDING NUMBERS

3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

6. AUTHOR(S)

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS

17. SECURITY CLASSIFICATION

 OF REPORT

16. PRICE CODE

15. NUMBER OF PAGES

20. LIMITATION OF ABSTRACT

Unclassified Unclassified

Annual Contractor Report

Unclassified

1. AGENCY USE ONLY (Leave blank)

10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546–0001

Available electronically at http://gltrs.grc.nasa.gov

March 2003

NASA CR—2003-212199

E–13802

WU–708–87–23–00

NAG3–2613

42

An Experimental and Computational Investigation of Oscillating Airfoil

Unsteady Aerodynamics at Large Mean Incidence

Vincent R. Capece and Max F. Platzer

Turbomachinery; Flutter; Forced vibrations; Aeroelasticity; Gas turbine; Unsteady

aerodynamics; Large mean incidence

Unclassified -Unlimited

Subject Category: 07 Distribution: Nonstandard

University of Kentucky

500 S. Limestone St.

Lexington, Kentucky 40506–0003

Project Manager, George Stefko, Structures and Acoustics Division, NASA Glenn Research Center, organization

code 5930, 216–433–2587.

A major challenge in the design and development of turbomachine airfoils for gas turbine engines is high cycle fatigue failures due

to flutter and aerodynamically induced forced vibrations. In order to predict the aeroelastic response of gas turbine airfoils early in

the design phase, accurate unsteady aerodynamic models are required. However, accurate predictions of flutter and forced vibration

stress at all operating conditions have remained elusive. The overall objectives of this research program are to develop a transition

model suitable for unsteady separated flow and quantify the effects of transition on airfoil steady and unsteady aerodynamics for

attached and separated flow using this model. Furthermore, the capability of current state-of-the-art unsteady aerodynamic models

to predict the oscillating airfoil response of compressor airfoils over a range of realistic reduced frequencies, Mach numbers, and

loading levels will be evaluated through correlation with benchmark data. This comprehensive evaluation will assess the assumptions used in unsteady aerodynamic models. The results of this evaluation can be used to direct improvement of current models and

the development of future models. The transition modeling effort will also make strides in improving predictions of steady flow

performance of fan and compressor blades at off-design conditions. This report summarizes the progress and results obtained in the

first year of this program. These include: installation and verification of the operation of the parallel version of TURBO; the grid

generation and initiation of steady flow simulations of the NASA/Pratt&Whitney airfoil at a Mach number of 0.5 and chordal

incidence angles of 0 and 10 deg.; and the investigation of the prediction of laminar separation bubbles on a NACA 0012 airfoil.