Comparison of Computational and Experimental Results for a Supercritical Airfoil

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https://ntrs.nasa.gov/search.jsp?R=19950010493 2019-01-22T03:08:01+00:00Z
NASA Technical Memorandum 4601
Comparison of Computational and
Experimental Results for a Supercritical Airfoil
Melissa B. Rivers and Richard A. Wahls
Langley Research Center • Hampton, Virginia
National Aeronautics and Space Administration
Langley Research Center • Hampton, Virginia 23681-0001
November 1994
This publication is available from the following sources:
NASA Center for AeroSpace Information National Technical Information Service (NTIS)
800 Elkridge Landing Road 5285 Port Royal Road
Linthieum Heights, MD 21090-2934 Springfield, VA 22161-2171
[phone] [phone]
Summary Unsteady flow in the form of an oscillating shock
was observed in the time-dependent surface pressure
A computational investigation was performed to
measurements on the stationary model. This shock
study the flow over a supercritical airfoil model.
movement, an unexpected result of this experimen-
Solutions were obtained for steady-state transonic
tal investigation, is either a naturally occurring, flow-
flow conditions using a thin-layer Navier-Stokes
physics-based phenomenon for the flow over the sta-
flow solver. The results from this computational
tionary airfoil or a result of the model vibrating on its
study were compared with time-averaged experimen-
mount in the tunnel. This phenomenon provided mo-
tal data obtained over a wide Reynolds number range
tivation for a computational investigation in which a
at transonic speeds in the Langley 0.3-Meter Tran-
thin-layer Navier-Stokcs flow solver is evaluated with
sonic Cryogenic Tunnel. Comparisons were made at
respect to the ability to model the experimentally
a nominal Mach number of 0.72 and at Reynolds
observed shock oscillations. The current investiga-
numbers ranging from 6 × 106 to 35 × 106.
tion, however, is limited to the evaluation of a thin-
Steady-state solutions showed the same trends as layer Navier-Stokes flow solver with respect to the
the experiment relative to shock movement as a func- prediction of steady-state Reynolds number effects.
tion of the Reynolds number; the amount of shock A similar computational study of this airfoil has pre-
movement, however, was overpredicted in the com- viously been performed by Whitlow and is discussed
putations. This study demonstrates that the com- in reference 5.
putational solutions can be significantly influenced In the present investigation, the primary objective
by the computational treatment of the trailing-edge was to assess the ability of the flow solver to predict
region of a blunt trailing-edge airfoil and the ne-
steady-state flow over a stationary supercritical air-
cessity of matching computational and experimental foil. Throughout the invcstigation, the effects of var-
flow conditions.
ious computational parameters on the agreement be-
tween computation and experiment were examined.
Introduction These parameters included grid trailing-edge spacing
and trailing-edge closure of the computational model.
The advent of cryogenic wind tunnels has enabled
simulation of full-scale flight Reynolds numbers with
Symbols
reasonably sized models at relatively low dynamic
pressures. Among the many uses of this test tech- a speed of sound
nology is the basic study of two-dimensional flow b airfoil span, in.
over airfoils as a function of both Mach number and
drag coefficient
Reynolds number. One such stu_ty, which was con-
ducted in the Langley 0.3-Meter Transonic Cryogenic Lift
Q
T_nnel (0.3-m TCT), is documented in reference 1 sectional lift coefficient, _, in-1
and the wind tunnel is described in reference 2. The
airfoil used in this test was a 14-percent-thick super- pressure coefficient, - ee
critical airfoil, designated as NASA SC(2)-0714,
which was developed at the NASA Langley Research
C airfoil chord, in.
Center and is discussed in detail in reference 3. This
airfoil had previously been tested in the 0.3-m TCT e total energy, nondimensionalized by poca_
to obtain steady-flow characteristics as part of the
G,H inviscid fluxes
Advanced 'Technology Airfoil Test (ATAT) program
described in reference 4. viscous fluxes
J transformation Jacobian
The experimental investigation described in ref-
erence 1, which was performed on a highly instru- L reference length, taken as chord c, in.
mented model of the SC(2)-0714 supercritical airfoil,
Moc free-stream Math number
obtained unsteady, time-dependent surface pressure
measurements on an oscillating supercritical airfoil NVr Prandtl number, taken to be 0.72
over a wide range of Reynolds numbers at transonic
P pressure, nondimensionalized by Pocfi_
speeds to supplement the previous steady-flow results
obtained for the nonoscillating (stationary) airfoil. Q conservation variable
During the course of the experiment, time-dependent
q total velocity, nondimensionalized by 5_c
data were also obtained for flow over the stationary
airfoil. heat flux terms
R Reynolds number Experimental Apparatus and Procedures
T temperature, °R
Wind Tunnel
t time, nondimensionalized by L/_oc
The experimental data used in this investigation
U, V contravariant velocities were obtained in the Langley 0.3-Meter Transonic
Cryogenic Tunnel (0.3-m TCT). The 0.3-m TCT is
U_ _3 velocities in x- and y-directions, a fan-driven, continuous-flow, transonic wind tun-
respectively, nondimensionalized by aoc nel with an 8- by 24-in. two-dimensional test sec-
tion. The tunnel uses cryogenic nitrogen gas as the
shear stress velocity, _w/Pw test medium and is capable of operating at temper-
atures from approximately 140°R to 589°R and at
x,y Cartesian coordinates, in.
stagnation pressures from approximately 1 to 6 atm
y+ wall similarity variable, u*y/uw with Mach number varying from approximately 0.20
to 0.90. (See ref. 2.) The ability to operate at cryo-
angle of attack, deg
genic temperatures combined with the pressure ca-
"7 ratio of specific heats, taken to be 1.4 pability of 6 atm provides a high Reynolds number
6 Kronecker delta capability at relatively low model loading. The floor
and ceiling of the test section were slotted to reduce
general curvilinear coordinates model blockage effects.
A coefficient of bulk viscosity Model
Iz coefficient of molecular viscosity
The airfoil used in this study is the NASA
I.] kinematic viscosity, in2/sec SC(2)-0714, which is a 14-percent-thick phase 2
supercritical airfoil with a design lift coefficient
P density, nondimensionalized by poc of 0.70 and a blunt trailing edge. (Scc sketch A.) The
design coordinates from reference 6 for this airfoil arc
Tw shear stress at wall, lb/in 2
listed in table 1. The model used in the 0.3-m TCT
Vx_xj viscous shear stress terms had a 6-in. chord, 8-in. span, and 0° sweep, and it
Abbreviations: was machined from maraging steel (fig. 1). A cavity
was machined in the underside of the airfoil model
CFD Computational Fluid Dynamics to provide the space necessary to house the pressure
Exp. experiment transducers (fig. 2). This cavity was closed by a cover
plate on which some lower surface transducers were
Ref. references
mounted. The gap between the end of the airfoil
and the fixed tunnel sidewall plate was sealed with
TE trailing edge
a sliding seal of felt. The position of the supports
Subscripts: was designed to locate the pitch axis at 35 percent
i, j, k tensor notation indices chord. (See ref. 1 for a further description of the
model details.)
l lower
t differentiation in time .4
.3
u upper
.2
un uncorrected
.1
w conditions at wall
y/cO
x, y differentiation in x- and y-directions,
--.l
respectively
--.2
c_ free-stream conditions
--.3
Superscripts:
-.40 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
quantity in generalized coordinates _c'
dimensional quantity Sketch A
Instrumentation number and angle of attack. These data points were
then time averaged by using the ensemble equation
Reference 1 also describes the instrumentation
utilized for the wind tunnel test. Forty-three pressure
7(t)= lim 1 N
transducers were mounted internally in the model, N-*c_ -N _-_ f(t)
and the location of the transducers is shown in fig- 1
ure 3. Because of space constraints, 40 of the trans-
ducers were mounted in receptacles connected by where f(t) is the averaged sample, f(t) is the in-
a short length (nominally 0.75 in.) of tubing to dividual sample, and N is the number of samples
the orifice. The remaining three transducers were (which varied from approximately 51 000 to 125 000,
mounted with the transducer head less than 0.1 in. depending on the available data). These averaged
below the surface of the wing. The tube-mounted data points were then integrated to produce the ex-
transducer orifices are located alternately in two perimental lift coefficient needed to make angle-of-
rows 0.25 in. on either side of the model midspan. attack corrections to the original data, as discussed
On the upper surface, the orifice distribution of the below.
25 transducers results in an orifice every 2 percent
In reference 1, experimental data for selected test
chord from the leading edge to x/c = 0.10, then ev-
conditions were corrected for wall effects; these cor-
ery 4 percent chord to x/c = 0.70, and finally ev-
rections took the form of an upwash correction to the
ery 5 percent chord to x/c = 0.95. The distribution
angle of attack and a blockage correction to the Mach
of the 15 tube-mounted transducer orifices on the
number. The blockage corrections are presented in
lower surface is every 2 percent chord from the lead-
tabular form in reference 8 and are used in this CFD
ing edge to x/c = 0.06, and then every 10 percent
study; the corrections in reference 8 are based on the
chord from x/c = 0.10 to 0.90. Extra orifices are lo-
theory of reference 9. The upwash corrections de-
cated at x/c = 0.45, 0.55, and 0.85, as described in
reference 1. scribed in reference 10 (sometimes referred to as the
"Barnwell-Davis-Moore correction") adjust this the-
The transducers were miniature, high-sensitivity, ory with experimental data. The wall-induced down-
piezoresistive, differential dynamic pressure trans- wash immediately over the model in the 0.3-m TCT
ducers with a full-scale range of 10 psid with a quoted is given in reference 1 as
accuracy of +1 percent of full-scale output. The
model angle of attack was measured by an onboard Aa -Qc 180
accelerometer package. 8(1 + j)h r
The parameters necessary to make the correction
Data Set
are chord (c = 6 in.), tunnel semiheight (h = 12 in.),
Test points were taken for this model primarily at and j, where j = aK/h (with a denoting a slot
a free-stream Mach number of 0.72, which had pre- spacing (4 in.) and K denoting a semiempirical
viously been shown (ref. 7) to be the drag rise Mach constant (3.2), which is a function of the slot width
number, and at Reynolds numbers from 6 x 106 (0.2 in.) and the slot spacing). The values of Cl were
to 35 x 106. The boundary-layer transition was not found by integrating the time-averaged experimental
fixed (through the use of grit, for example) during pressure data and are listed in table 2. The original
this experiment and all calculations in this Compu- (uncorrected) and corrected Mach number and angle-
of-attack values are also listed in table 2. Some CFD
tational Fluid Dynamics (CFD) study were made by
results were computed by using the corrected flow
assuming fully turbulent flow.
conditions, whereas others were computed by using
The model angle-of-attack and pressure data the uncorrected flow conditions.
used for this comparison were recorded directly
onto analog tapes and subsequently digitized at Computational Method
5000 samples/sec. The surface pressure data were
The computational method used in this study
then integrated to obtain the normal-force coeffi-
cient, which was assumed to be equal to the lift needed to have both a viscous modeling capability
coefficient in reference 1 because of the small-angle for the current Reynolds number effect study and
a time-accurate capability for the projected follow-
approximation.
on studies of the experimentally observed unsteady
Specific data points used for the present CFD flow. Based on these requirements, the state-of-the-
study were selected according to the desired Mach art Navier-Stokes flow solver known as CFL3D was
3
chosen.(Seeref. 11.) AlthoughCFL3Dis three-
The equations are nondimensionalized by the free-
dimensionaalndtheoreticallycapableofsolvingthe
stream density (Poe) and speed of sound (5_). The
fullNavier-Stokeesquationsit, isusedhereinitstwo-
shear stress and heat flux terms are defined in tensor
dimensionalt,hin-layerNavier-Stokems ode. The
notation as
thin-layerapproximationismadewhentheviscous
termsassociatewdithderivativetsangenttothebody
areconsiderednegligible. The equationscanbe
written in conservationformby usinggeneralized
coordinateass(seeref.12)
i'M°c#] 0a2 (10)
.R_N_r(_- 1} Oxi
0--/-_ _ + 0¢ - 0 (1)
P_ / (11)
where
Moo = :--
aco
(2) In equation (5), the term bx_ is defined in indicial
notation as
bxi ---- UjTxix j = qx i (12)
The hypothesis of Stokes, that is, )_= -2/3p, is used
for bulk viscosity in equation (9), and Sutherland's
1 pUu + rlxp law,
= -J pVv + _yp I (3)
(13)
1
(e + p)U -- _tP J
is used for molecular viscosity, with :Foc denoting
the free-stream temperature (460°R), and _denoting
I pVu + ¢_p Sutherland's constant (198.6°R).
= J [ p+VCyp l.lpVv (4) An implicit, upwind-biased, finite-volume method
described by Rumsey in reference 13 is used to solve
(e + p)V- _tPJ
equation (1). All viscous terms are centrally dif-
0 ferenced, and implicit cross-derivative terms are ne-
glected in this formulation. The algorithm is accu-
1 ¢_-_x+ ¢_,,-xy (5) rate to first order in time and to second order in
space. Implicit spatial derivatives of the convective
and pressure terms are first-order accurate. Because
_xbz + @by the present investigation is an upwind method, no
additional artificial dissipation is necessary, and no
U = rlxi_ + rlyv + nt (6) dissipation parameters exist to be adjusted. For the
/
V = Cxu + Cyv + Ct entirety of this study, flux-difference splitting (that
is, Roe's scheme as described in reference 14) was em-
ployed. The two-layer algebraic eddy viscosity model
p=(7-1)[e-O.bp(u 2 +v2)] (7)
of Baldwin and Lomax described in reference 15 was
where _ is the coordinate along the body and _ is the used throughout the investigation. Additionally, a
coordinate normal to the body. The mesh velocity limited number of solutions were obtained using the
is represented by the terms _t and _t. Both terms one-half-equation turbulence model of Johnson and
are zero for flow over a nonmoving (stationary) grid. King (ref. 16) and the one-equation turbulence model
The vector Q represents the density, momentum, and of Baldwin and Barth (ref. 17).
total energy per unit volume. The Jacobian of the Boundary conditions are applied explicitly.
transformation (J) is defined as No-slip adiabatic wall conditions and zero
pressure-gradient conditions are applied on the body
J - 007'¢) (8) to give
0(x,y) u = v = 0 (143)
- 4
Op Oa2 grid. These three grids were run at a Mach num-
-- - 0 (14b)
a_ a_ ber of 0.72, an angle of attack of 2°, and a chord
Reynolds number of 35 x 106. Computed lift and
where a2 is proportional to the fluid temperature. In
drag coefficients are plotted in figures 9 and 10, re-
the far field, the subsonic free-stream boundary con-
spectively, as a function of the inverse of the mesh
ditions are determined through a characteristic anal-
size (where the mesh size is equal to the total num-
ysis normal to the boundary and a point vortex rep-
ber of grid points). The lift and drag coefficients
resentation is included for induced velocities on the
have been linearly extrapolated to values of 1.0056
outer boundary. Details can be found in reference 18
and 0.0147, respectively, for a mesh of infinite den-
by Thomas and Salas.
sity. On the finest mesh, the lift coefficient is pre-
dicted to within 1.8 percent of the extrapolated value
Results and Discussion
on an infinite mesh; the drag coefficient is predicted
to within 10.3 percent. Based on these results, the
Grid
257 x 65 C-mesh with 193 points on the airfoil sur-
As shown in sketch A, the NASA SC(2)-0714 face was judged to be of sufficient density, and it was
airfoil has a blunt trailing edge. The trailing-edge used throughout the remainder of the investigation.
thickness is 0.7 percent chord. The trailing edge was
closed to facilitate the use of a single block grid, Computational Test Conditions
rather than rigorously modeling the blunt trailing All computations were made for comparison with
edge with a multiblock grid; the closing of a blunt experimental data obtained at an uncorrected Mach
trailing edge for this purpose is a common practice number of 0.72. Reynolds numbers ranged from
and is often used successfully. (See ref. 19.) In 6x 106 to 35 x 106 and angle of attack ranged
this study, the trailing edge was initially closed by from 0° to 2.5°. As discussed previously, Mach num-
averaging the upper and lower surface trailing-edge ber and angle-of-attack corrections based on data in
points (fig. 4). As discussed below, initial results references 8 and 10 were evaluated and applied dur-
with this closure prompted other methods of closure ing the course of this study; some solutions presented
to be examined; all the methods were within the below are computed at the uncorrected test condi-
framework of a single block grid. tions and others are computed at the corrected con-
A 257 x 65 C-mesh with 193 points on the airfoil ditions. All computations were made by assuming
fully turbulent flow.
was generated by using the CRIDGEN grid genera-
tion package. (See ref. 20.) The normal cell spacing
at the surface was fixed at 1 x 10-6 chord based on Modeling Study
the resolution requirements for turbulent flow at a The initial phase of this activity involved a
chord Reynolds number of 35 x 106. The y+ values modeling study in which the surface smoothness,
in the cells adjacent to the surface were on the order trailing-edge closure, Mach number and angle-of-
of 1; representative values of y+ are shown in fig- attack corrections, and trailing-edge grid spacing
ure 5 for low and higtl Reynolds numbers. As part of were investigated to assess each effect prior to a de-
the airfoil closure study, the trailing-edge spacing was tailed analysis. Because of the preliminary nature of
varied from 0.0005 to 0.012 chord. Trailing-edge grid this modeling study, the majority of the solutions
spacing as used herein is defined as the minimum cell in this section are not satisfactory; they serve in
size tangent to and on the surface at the trailing edge. an academic sense showing the progression toward a
The far-field boundaries were fixed at a distance of satisfactory surface definition used for further study.
20 chords from the surface. Several solutions were
Wiggle. An initial solution, shown in figure 11,
obtained at a far-field boundary of 10 chords from
had a trailing-edge closure in which the upper and
the surface; comparisons of solutions for the two far-
lower surface trailing-edge points were averaged to
field boundary lengths showed negligible differences.
a single closure point. The trailing-edge grid spac-
Figures 6, 7, and 8 show a global, near-field, and
ing for this case is 0.008; as previously described,
close-up view, respectively, of a typical grid used in
trailing-edge grid spacing as used herein is defined as
this study.
the minimum cell size tangent to and on the surface
In addition to the baseline grid described above, at the trailing edge. Flow conditions used for this
two coarser grids of 129 x 33 and 65 x 17 were used solution were the uncorrected Mach number of 0.72,
to study the effects of grid density. These two coarser an uncorrected angle of attack of 2°, and a Reynolds
grids were constructed by eliminating every other number of 35 x 106. Several aspects of this solu-
point in each coordinate direction on the next finer tion are of note. The first item is the oscillation
5
ontheuppersurfacepressureplateau.Asdiscussed
in large part due to the experimental Mach number
in the followingparagraph,this effectwascaused
and angle-of-attack corrections not being taken into
byanonsmoothsurfacecurvature
d2y/dx 2 resulting account in the initial computations; therefore, cor-
from the discrete-point geometry definition reported rections for Mach number and angle of attack were
in reference 6. determined and compiled in table 2, as described
previously, and have been applied for further com-
This upper surface pressure oscillation was elim-
putations. The corrected Mach number and angle
inated by smoothing the surface (defined in ref. 6)
of attack for the case shown in figure 15 are 0.7055
with a b-spline routine. Figures 12 and 13 show the
and 0.5202 °, respectively. Significant improvement
changes in the slope and curvature, respectively, be-
on the agreement between computational and exper-
tween the original and smoothed airfoil definitions.
imental results is shown in figure 18. These compu-
The change in the surface definition was small; the
tational runs were consistent with the original runs;
most significant surface changes occurred near the
only the Mach number and angle-of-attack values
leading edge (fig. 14). The smoothed grid is de-
changed. The shock location, lower surface pres-
fined by the same number of points as the original
sures, and pressure plateau agree much better with
geometry. This smoothed geometry had a major im-
these corrections applied; the trailing-edge region,
pact on the computational results, as shown in fig-
however, appears to need further refinement.
ure 15. These computational results were obtained
in the same manner as the previous results with the Trailing-edge spacing. Trailing-edge grid spac-
only change being the geometry itself. The pre- ing was next examined. Figure 19 compares the origi-
viously computed pressure oscillations on the pres- nal geometry definition (table 1) with a series of com-
sure plateau were eliminated by using this modified putational surfaces (grid) generated for trailing-cdgc
surface definition. spacings from 0.0005 to 0.012; these grids maintained
a constant leading-edge spacing (tangent to and on
Trailing-edge closure. A second item concern- the surface) of 0.005 and number of points on the sur-
ing the solution in figures 11 and 15 is the spike in face. In effect, as the trailing-edge spacing changed,
the pressure distribution at the trailing edge. In an the change propagated over the entire chord. Note
attempt to improve the pressure distribution near that the global effect of the change on the grid was
the trailing edge, various other methods of closing small and that the resolution in the area of the shock
the trailing edge were tried. These methods included was not degraded. Figure 19 shows that the smaller
splining the last 10 percent chord to close at the aver- trailing-edge grid spacing tended to round off the
aged trailing-edge point, extending the trailing edge discontinuity, whereas the larger trailing-edge grid
until the upper and lower surfaces connected, trans- spacings maintained a sharper corner. The computa-
lating the lower surface trailing-edge point to the up- tional results are shown in figure 20. The 0.004-chord
per surface trailing-edge point, and translating the spacing was chosen, although not optimized, and was
upper surface trailing-edge point to the lower surface used during the remainder of the study.
trailing-edge point (fig. 16). Several of these meth-
ods can result in surface discontinuities, but such ap- Computational Results
proaches have previously been applied successfully
This section describes computed Reynolds num-
(ref. 19). Figure 17 shows the computational results
using the last method of trailing-edge closure with ber effects for a stationary (nonoscillating) airfoil
a trailing-edge spacing of 0.008 chord. This closure assuming steady flow; all solutions have been com-
puted with the Baldwin-Lomax turbulence model
was judged to be the best among the four methods
described above because the solution obtained from (ref. 15). Comparisons of Reynolds number effects
using this trailing-edge closure resulted in the best with angle of attack are shown in figures 21-23.
minimization of the trailing-edge spike. As discussed The Reynolds number range for this set of data is
from 6 x 106 to 35 × 106. The corrected Mach num-
below, trailing-edge grid spacing also affects the re-
sults with different trailing-edge closures as it relates ber and angle of attack (from table 2) were used
to the resolution of the flow around the upper surface for each Reynolds number, and all cases were com-
discontinuity. puted using the same grid, which had a trailing-
edge spacing of 0.004 chord, a leading-edge spac-
Mach number and angle-of-attack correc- ing of 0.005 chord, and a normal cell spacing of
tions. A third item of note relates to the general 1× 10-6 chord. As shown in figure 5, y+ val-
lack of agreement between experiment and CFD re- ues ranged from approximately 0.5 for the Reynolds
sults. The discrepancies between experimental data number case of 6 × 106 chord to 1.5 for the Reynolds
and computational data seen in figures 11 and 15 are number case of 35 x 106 chord; because of this small
effecton the turbulentboundary-layerresolution assumedto becorrect;thesecorrectionsimproved
(i.e.,laminarsublayerc)losetothesurfacet,hesame comparisonsb,ut modificationstothesecorrections
gridwasusedforallReynoldsnumbers.Figure21 mayhaveimprovedcomparisonfsurther. Steady-
showstheReynoldsnumbereffectsforaMachnum- statesolutionsshowedthesametrendsastheexper-
berof0.72andanangleofattackof1°;appropriate imentrelativeto shockmovemenatsa functionof
Machnumberandangle-of-attacckorrections(listed theReynoldsnumber;howevers,hocklocationwas
intable2)havebeenappliedindeterminingthecon- predictedfartherupstreame,speciallyforthelower
ditionsto obtainthe computationaslolutions.At Reynoldsnumberconditions.
this lowangleof attack,Reynoldsnumbereffects
aredifficulttodiscernforboththeexperimentaalnd
NASALangleRyesearCchenter
computationadlata.
HamptoVn,A23681-0001
Figure22showstheReynoldsnumbereffectsfor Septemb2e7r,1994
aMachnumberof0.72andanangleofattackof2°,
References
againwiththeappropriateMachnumberandangle-
of-attackcorrectionsapplied. TheReynoldsnum- 1.HessR,oberWt .;SeideDl,avidA.;Igoe,WilliamB.;
berrangefor thissetofdatais alsofrom6x 106 andLawingP,ierceL.: TransonUicnsteadPyressure
to35x 106.TheMachnumberandangle-of-attack MeasuremeonnatsSupercriticAairlfoilatHighReynolds
Numbers.
correctionswereagaindifferentfor eachReynolds J. Aircr., vol. 26, July 1989, pp. 605-614.
number,andallthesecaseswereagaincomputedby
2. Ray, E. J.; Ladson, C. L.; Adcock, J. B.; Lawing, P. L.;
usingthesamegrid. At this angleof attack,the and Hall, R. M.: Review of Design and Operational Char-
shockmovesaft astheReynoldsnumberincreases acteristics of the 0.3-Meter Transonic Cryogenic Tunnel.
forboththeexperimentadlataandcomputational NASA TM-80123, 1979.
solutions.Althoughtheexperimenat ndcomputa-
3. Harris, Charles D.: Aerodynamic Characteristics of a
tionshowthesametrend(directionofshockmove-
14-Percent- Thick NASA Supercritical Airfoil Designed for
ment),theresultsindicatethattheshock-movement a Normal-Force Coefficient of 0.7. NASA TM X-72712,
dependenctoytheReynoldnsumberwaslargerfrom 1975.
computationadlatathanfromexperimentadlata.
4. Jenkins, Renaldo V.; Hill, Acquilla S.; and Ray,
Figure23showstheReynoldsnumbereffectsfor Edward J.: Aerodynamic Performance and Pressure Dis-
aMachnumberof0.72andanangleofattackof2.5°, tributions for a NASA SC(2)-0714 Airfoil Tested in the
Langley 0.3-Meter Transonic Cryogenic Tunnel. NASA
againwith appropriateMachnumberandangle-
TM-4044, 1988.
of-attackcorrectionsapplied. TheReynoldsnum-
berrangefor this angleof attackis from6x 106 5. Whitlow, Woodrow, Jr.: Application of Unsteady Aero-
to30x 106.Atthisangleofattack,aftmovemenotf dynamic Methods for Transonic Aeroelastic Analysis.
theshockastheReynoldsnumberincreaseissagain NASA TM-100665, 1988.
observedforboththeexperimentadlataandcom- 6. Harris, Charles D.: NASA Supercritical Airfoils--A
putationalsolutions.Howevers,imilartotheprevi- Matrix of Family-Related Airfoils. NASA TP-2969, 1990.
ousresults(seefig.22),theshocklocationappears
7. Jenkins, Renaldo V.: NASA SC(2)-0714 Airfoil Data
to havebeenpredictedfartherupstreamcompared Corrected for Sidewall Boundary-Layer Effects in the
withtheexperimentadlata,especiallyforthelower Langley 0.3-Meter Transonic Cryogenic Tunnel. NASA
Reynoldsnumberconditions. TP-2890, 1989.
8. Jenkins, Renaldo V.; and Adcock, Jerry B.: Tables for
Concluding Remarks
Correcting Airfoil Data Obtained in the Langley 0.3-Meter
Thepurposeofthisstudywastodeterminethe Transonic Cryogenic Tunnel for Sidewall Boundary Layer
capabilityof a state-of-the-artu,pwind,thin-layer Effects. NASA TM-87723, 1986.
Navier-Stokefslow solverto predictsteady-state 9. Sewall, William G.: The Effects of Sidewall Bound-
Reynoldsnumbereffectsfor flow over a two- ary Layers in Two-Dimensional Subsonic and Transonic
dimensionaslupercriticaalirfoil.Thestudydemon- Wind Tunnels. AIAA J., vol. 20, no. 9, Sept. 1982,
stratedthat thecomputationaslolutionscouldbe pp. 1253 1256.
significantlyinfluencedbythecomputationatlreat- 10. Barnwell, Richard W.: Design and Performance Evalua-
mentofthetrailing-edgeregionofablunttrailing- tion of Slotted Walls for Two-Dimensional Wind Tunnels.
edgeairfoil. Thestudyalsodemonstratedthene- NASA TM-78648, 1978.
cessityofmatchingcomputationaalndexperimental
11. Thomas, J. L.: Navier-Stokes Computations of Vortical
flowconditions.Machnumberandangle-of-attack
Flows Over Low Aspect Ratio Wings. AIAA-87-0207,
correctiontsakenfrompreviousdocumentatiownere Jan. 1987.
7
12. Rumsey, Christopher L.; and Anderson, W. Kyle: Para- 16. Johnson, D. A:; and King, L. S.: A Mathematically Simple
metric Study of Grid Size, Time Step and Turbu- Turbulence Closure Model for Attached and Separated
lence Modeling on Navier-Stokes Computations Over Turbulent Boundary Layers. AIAA J., vol. 23, no. 11,
Airfoils. Validation of Computational Fluid Dynamics. Nov. 1985, pp. 1684-1692.
Volume 1--Symposium Papers and Round Table Discus-
17. Baldwin, Barrett S.; and Barth, Timothy J.: A One-
sion, AGARD-CP-437-VOL-1, Dec. 1988. (Available from
Equation Turbulence Transport Model for High Reynolds
DTIC as AD-A211 893.)
Number Wall-Bounded Flows. NASA TM-102847, 1990.
13. Rumsey, C. L.: Time-Dependent Navier-Stokes Compu- 18. Thomas, James L.; and Salas, M. D.: Far-Field Boundary
tations of Separated Flows Over Airfoils. AIAA-85-1684, Conditions for Transonic Lifting Solutions to the Euler
July 1985. Equations. AIAA-85-0020, Jan. 1985.
19. Londenberg, W. K.: Turbulence Model Evaluation for the
14. Roe, P. L.: Approximate Riemann Solvers, Parameter
Prediction of Flows Over a Supercritical Airfoil With De-
Vectors, and Difference Schemes. J. Comput. Phys.,
flected Aileron at High Reynolds Number. AIAA-93-0191,
vol. 43, no. 2, Oct. 1981, pp. 357-372.
Jan. 1993.
15. Baldwin, Barrett; and Lomax, Harvard: Thin-Layer Ap- 20. Steinbrenner, John P.; and Chawner, John R.: The
proximation and Algebraic Model for Separated Turbulent GRIDGEN Version 8 Multiple Block Grid Generation
Flows. AIAA-78-257, Jan. 1978. Software. MDA Engineering Report 92-01, 1992.
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