AIAA 2001-2921 On the Use of Surface Porosity to Reduce Unsteady Lift Ana F. Tinetti, Jeffrey J. Kelly Virginia Polytechnic Institute and State University / VCES Hampton, VA Steven X. S. Bauer, Russell H. Thomas NASA Langley Research Center Hampton, VA 31st AIAA Fluid Dynamics Conference and Exhibit 11-14 June 2001 / Anaheim, CA For permission to copy or republish, contact the copyright owner named on the first page. For AIAA-held copyright, write to AIAA, Permissions Department, 1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344. https://ntrs.nasa.gov/search.jsp?R=20010055262 2019-08-09T14:24:43+00:00Z
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AIAA 2001-2921
On the Use of Surface Porosity to ReduceUnsteady Lift
Ana F.Tinetti, Jeffrey J. KellyVirginia Polytechnic Institute and State University / VCESHampton, VA
Steven X. S. Bauer, Russell H. Thomas
NASA Langley Research CenterHampton, VA
31st AIAA Fluid DynamicsConference and Exhibit
11-14 June 2001 / Anaheim, CA
For permission to copy or republish, contact the copyright owner named on the first page. For AIAA-held copyright,write to AIAA, Permissions Department, 1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344.
dependent, thin-layer approximation to the Reynolds-
Averagcd Navicr-Stokcs (RANg) equations using a
linitc volume formulation in generalized coordinates. It
uses upwind-biased spatial diffcrcncing with Roc's llux-
di/'t'crence splitting (FI)S) method J_' for the inviscid
terms, and central differences for the viscnus and heat
transfer terms. The code, which is second-order accurate
in space, is advanced in time with an implicit three-fac-
tor approximate factorization IAF) scheme. Temporal
subiterations with rnultigrid are used to recover time
accuracy lost as a result of the AF approach during
unsteady calculations. The pseudo-time subiteration ('i-
TS) method is used in the present work. In this option, a
pseudo-time term is added to the time-accurate Navier-
Stokes equations. This ext,a term is sub-iterated until
Suuctured Grid
The problem of trying to numerically simulate the acto-
dynamic environment within a turbofan is inherently
difficult. However. it can bc greatly simplilied by con-
sidering a system composed of a single rotor blade (or
any other suitable wake generator) transversely moving
past a single stator vane. Wake effects would still bc the
main cause of unsteadiness within such a system. Thick-
ness effects, although still present, would be small in
comparison to wake effects if the distance between the
rotor and the Slalor leading edge ix appn_ximatcly 4{)'/,
of the stator chord m. Circulation effects would be insig-
niticanl at this distance. Furthermore, three-dimensional
effects such as blade tip and cross-llow effects can bc
awfided if the system is made two-dimensional. Thus,
the computational setup chosen fur the study consists of
a single stator airfoil immersed in a frec llow lield, sub-
ject to the effects of a transversely moving wake. Sche-
matic representations of the grid, airfoil, and wake are
given in Figure 2.
The 9-zone. 2-1)grid contains approximately 2.39xl 05
points/plane, extending to 15c above and below the air-
full, 0.26c upstream and 2.5c downstream. Far licld
boundary conditions arc applied at the external faces of
the grid. interface boundary conditions arc applied at all
the internal faces, and viscous and porous surf:ace
boundary conditions arc applied at the airfoil surface.
The vertical extension of the grid, in conjunction with a
stretched distribution c_t points toward the tar lield, are
required in order to dissipate rcllcctions from thc bound-
reits. The majority of the grid points arc contained in
zones 1, 4. and 3, as is necessa,'y to ensure adequate
propagation of perturbation waves.
The chosen airfl_il was obtained from surface measurc-
ments taken at the mid-span of one of the stator vancs
composing the Pratt and Whitney Advanced I)ucted Pro-
poller high power fan model currently at NASA I,aRC I_.
l,eading and trailing edges wcrc not dclined. Thus, they
were created by carefully fitting circular arcs to the
given discrete points. Since the section would no hmgcr
function as part of a stator vane, its incidence had to be
3
American Institute of Aeronautics and Astronautics
adjustedin ordertoprecludeilowseparationoveritssurface.Resultsfromanangleofattacksweepindicatedthatthereexistsanarrowincidencerangewithinwhichtheflowwouldremainattachedovertheentireairfoilsurface.The mid-point of that range, 6", was selected.
05
0_
o;4
14
X_C
,Ja(or
samplingplane
! ,, i , i , i
IVa
average wake
I,,+iVk
4
L====,_
3
Figure 2.- Compulational grid.
Because a strong w_e was desired, a cylinder (not
shown) with a diameter of approximately 0.05c, and
located 0.41c upstream of the stator t+l'_ plane, was used
initially as a wake generator. Although a satisfactory
wake was obtained, its effect on stator lift was heavily
influenced by the w+rticity resulting from the Karman
vortex street chm'acteristic of ltow over blunt bodies.
The effect of the shed w)rtices manifested itself as oscil-
lations in c I with frequencies corresponding to Sn - 0.2.
In order to eliminate these unwanted oscillations, an
avcrage prolile was obtained from several temporal sam-
pies of the wake generated by the rod as it approached
and passed the stator. This average wake, which has a
33';+ velocity defect at the plane of the stator LE. repre-
sented tremendous savings in computing time. since the
zones dcfining the rod would no longer bc neccssm'y.
The average wake, now a user input, is delined at the
sampling plane (face j l of zone 5.0.15c downstream of
the original rod) using a velocity distribution boundary
condition. Through the use of dynamic patched interfac-
ing, this wake is displaced a distance of approximately
4c, from face kl to face kmax of zone 5. by a downward
translation of zones 5, 8 and 9. At the end of the speci-
fied traverse, the algorithm translates the moving blocks
and their solution back to their original position.
To minimize numerical dissipation as the wake traverses
the stator Ilow field, the axial distance between the plane
of the wake and the stator I+E is kept as small as possi-
ble. and the cell size ratio between the zones defining
the wake and the stator does not exceed 3:1 during the
entire wake traverse. A translational speed (V) of 78c/s,
corresponding to an angular velocity of 500 rpm and a
mid-span radius of 1.5c, was chosen for the wake. The
entire wake traverse requires 2232 time steps. The given
translational speed, traversed distance, and free stream
Math number (0.166) guarantee that, at any given time,
the stator is subject to the passage of a single wake only.
Results and Discussion
Effect of Moving Wake on Airfoil Surface Pressure
The effect of the moving wake on the llowlield anound
the stator leading edge is sequentially dcpictcd in Fig-
arcs 3a through 3d. Corresponding surfacc pressure
coefficient distributions are presented in Figure 4. In
general, the pressure on the convex surface c,t+ a stator
vane (or rotor blade) is relatively low, and the pressure
on the concave side is relatively high. For this reason,
the convex and concave surfaces are usually called the
suction and pressure sides, respectively, of the stator.
The process described here is common in turbomachin-
cry llows m'_H,,.eo.
At the start of the traverse, t = 0.0 seconds (Figure 3a),
the wake is located approximately 2c above the statur.
This relative placement precludes any signilicant intcr-
action between the two. The associated surface pressure
distribution is as would be expected for the airfoil
immersed in a free stream at the chosen incidence. Note
from Figure 4 that surface pressure is minimum at the
409+: chord location, coincident with the point of maxi-
mum airfoil thickness. The recomprcssion of the surface
pressure downstream of the maximum thickness loca-
tion indicates that the flow remains attached over the
entire airfoil surface. Close examination of the llow past
the TE revealed that the "blip" in the % distributionsresults from a combination of airfoil incidcnce and TE
geometry, and is not an indication of llow separation.
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American Institute of Aeronautics and Astronautics
The p_finl _1 maximum pressure is h_caled at the Sial(H
I,E. Because of the airfoil positive incidence, a point ol
local minimum pressure, a direct consequence of h_cal
llow expansion, is located on the suction (leew_u'd) sideat ×/c ~ 0.003.
The flow around the stator remains virtually unaffected
by the moving wake until approximately t = 0.0176 s
{Figure 3h). After this time, the close proximity of the
wake to the stator I,E causes a gradual decrease in the
local flow incidence. At time t = 0.0229 s, the wake
intersects the stalor I,E (Figure 3c) causing a large
reduction in ACp that extends over 90'_ of the airfoil,
The change in relative wind incidence shifts the stagna-
Iron poJnl from the origin {x/c = ,,/c = 0) to the suctitm
side of the airfoil, and the point of local minimum pres-
sure from the suction side to the pressure _windward)
side. In the immediate vicinity of the wake. as il passed
over the airfoil, the velocity was seen to decrease and
then increase on the suction side, and, conversely, to
increase and then decrease on the pressure side, As a
consequence, the pressure rises and then falls on the
suction side, and falls and then rises on the pressure
side. This behavior is clearly seen in lhe surface Cp dis-
tributions of Figure 4. The process is then reverted as the
wake moves past the statler airfoil (Figure 3d).
0015
OO_
O OO5
go
-0005
-001
-0015-1 , I ,, I , I0 1 2 -0 01 0 001
x/c x/c
_ch
025024023
022021020
'31£01831Z316
015014Q13012
0 I{,
009008007006005
00,1003002
001,3 O0
h_ ( = 0,0!76 s0015
001
o OO5
_o
0.005
001
0015-1 I I , I ,0 1 2 401 0 001
_c x/c
Figure 3.- Math Nulnher contours for solid stator. M_ = O.166. Re = 1.125x I(I*',c* = 6°. V = 78c/see.
Medium grid level.
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American Institute of Aeronautics and Astronautics
1 ,
c) I = (I.0229 s0015
I I i,
0 I 2
x/c
d) t = 0.(1264 s
001
0 O0
001
0015
001
O0
0005
0
-0.005
-001
, I , I I
0 1 2
x/c
0015
t"igure 3= Concluded.
O01 0 001
x/c
-001 0 001
x/c
01601.5
-1 5
-05
1
15
gt
t
i'EI
l=oos
t - 00176 s
t - 0 0229 s
1 = 0 0264 s
, tI
I , I I I , I
0.25 0,5 0.75 1
x/c
Figure 4= Surface pressure coefficient distribution for solid