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OCR for page 314
Hydrofoil Turbulent Boundary Layer Separation
at Hiah Reynolds Numbers
D BouTgoyne, S. Ceccio, D Dowling (University of Michigan, USA)
W. Brewer, S. Jessup, J. Park (Naval Surface Warfare Center, Carderock Division, USA)
R Pankajakshan (Mississippi State University, USA)
One of the mam hyd oacoustic noise sources
from fully submerged li ting so faces is file un teady
separated turbulent flow neat file so face's hailmg
edge Hat produces pressure tract ations on file
su face md unsteady oscillato y flow in the neat
wake However, the t rbulent flow character tics
near boundary layer sepmation are largely
undocumented at the high Rey olds numbers typical
of mmy hyd ody amic Implications This paper
describes results fiom file Or t phase of m
experimental ego t to identify md measure file
dominmt flow features neat the tmiling edge of a
hyd foil at chordbased Reynolds numbed
mproachmg 108 The experiments are conducted at
the US Navy's Large Cavitation Ch mnel with a tw -
dimensional test-section- pmnmg hyd of oil (2 I m
chord, 3 Om par I atflow peedsfiom 0 5 to 16 m/s
The foil section is a modified NACA 16 wish a flat
pressure side md m mti-smgmg trading edge The
results presented here cover file flu t phase of
experiments md emphasi e LDV measured mem
flow velocities md turbulence statistics from the
sepamtmg boundary layer flow near the hyd foil's
tmiling edge at Rey olds mmmbers fiom 6 to 60
million
INTRODUCTION
The flow at the hailing edge of liflmg
su faces has received considerable attention md has
been inw stigated by m my ho hers Desigmers of
ship propulsory md conhol surfaces have ex mined
flow over tw -dimensional hyd foils md al foils m
order to understmd how modification of the hailmg
edge geomet y rllnence. the produ tion of lifl md
d ag as well as the creation of flow generated noise
(Blake 1966) Similarly, researchers have attempted
to compute bodh the flow held End file noise it
generates TV mg et al 1996, A ah hahi et al 1999)
1
Unfortunately highly controlled test data at
operational scales is essentially non-exi tent Thus,
sea dials of actual hardware have beat the only
mems of validating scaling laws or computational
models of propeller pe lo m mce M my impo t mt
flow phenomena are Rey olds number dependent
between model md f 11 scale Contt oiled tests over a
wide rmge of Reynolds numbed cat result m
improw d scaling mles
A example of a Reynolds mmmber
dependmt flow is Hat ovens the trading edge of a
hyd foil Intere tingly, relatively small
modifications to the hailing edge geomet y c m lead
to sub trivial cb.r. es in file hyd odynamic md
hyd acoustic pe to mmce of a hyd of oil (Blake
1966) The Implication of a chamfer or k uckle to file
tmiling edge of the hyd of oil cm mcrease file
t msv~sse thickness of file wake md consequently
modify file bedding of large-scale vo ticity fiom file
tmiling edge This, m tm, c m sub t mtially ch mge
the manumit de md spect m of the acoustic energy
generated near the trading edge The tmiling edge
flow neat file hyd of oil is trongly related to the wall-
bounded shear flow on the suction md pressme
sides These boundary layer flow separate md
ultimately combine togedher to to m the wake The
complexity of t rbulent boundary layers separation
on either flat or coved so faces is sub tantial
(Simpson 1969) Thus, signiEcmt charges m
Reynolds number may lead to fmmdamental
modification of file 7hdmg edge boundary laser
(e pecially on file suction side of file foil) md near-
wake flow
Typical wind md water t nnel te ts of
hyd foils c m achieve chordbased Reynolds
numbers of up to 10 or so However, f 11 scale
Reynolds numbers achieved on the liflmg su faces
associated wish navy vessels easily exceed 107
Consequently, ex mmation offLeseflow ~~ dead able
at the highest Reynolds number Hat c m be achieved
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Representative terms from entire chapter:
boundary layer
in a controlled envi onment Naw~l resea.ch
estat lishments have invested in lage waler i nnel
fa ilities for such high Rey olds number te is The
U. S. Na y's Lage Ca itaiion Chmnel (LCC) cm
test tw -dimension i hyd of oils wifh a sp m of 3 05
met~ss, md cm a hieve cho d baed Reynolds
numbers approa hmg 108
The pmpose of fLis paper is to pres:~t fLe
results from fLe fu st pha e of a program to examme
the trailmg edge flow of a hyd of oil al high Reynolds
number A tw -dimensiona hyd foil wa
consiru led for testing in the LCC Presented here
a e La er Doppler Velocimeter (LDV) mea mements
nea fLe hyd of oil leading md hailing edges md m
the fa w ke These results a e compa ed to
numenca simulaiions of the flow
EXPERIMENTAL SET-UP AND
UNCERTAINTY
The expenments were conducted al fLe US
Na y's Lage Cwitaiion Chmnel (LCC) m
Memphis, TN This low i rbulence waler tmmnel ha
a 6 :I contra lion raiio md a 3 05 x 3 05 x 13 m test
section (Fig 1) Dnven by a 10,440 kW motor, a 5 5
m diamet~s a ia flow impeller delivers ieady test
section flow fiom 0 5 to 16 3 m/s al test-section
pressuresfiom 3 5 to 414 kPa(0 5 to 60 psia)
TT .~ J , R ntacto
—~ ;~ o \~/ 1
5 7e F ~ '-- ~ ~ (~°i,~
fI.p
,,, (.,,,,)
Figmce 1: Test Fa ility
The te i object wa a hyd foil of 2 134-m
chord (C) md 0 171-m ma fLickness (t) which
sp mned fLe full width of fLe LCC test section (3 05
m) The foil wa centered ve iicaly md
longii dinaly withm fLe test se lion with the hailmg
md leading edges falmg withm side-wal window
The foil wa mommted to the test section w ils by end
ta gs centered al 42% chord which tra smiited fLe
foil's li i-d ag-weight loads through mountmg plaies
to the siruci re of the LCC Ga ketmg between fLe
foil md fLe cha nel wa is prevented bypa s flow
The foil, though f lly iwo-dim:~siona, ha
the cross section of a generic propeller of moderaie
thickness md camber (f The shape (Fig 2a) is thai
of a NACA-16 (t/C=0 08 fC=0 032) wifh iwo
modiEcaiions Fir i fLe bottom (pressure side) of fLe
foil is flai al of 26% chord which simpliBed
fa ncaiion md fa ilitaies f ture addition of onboad
instmmentaiion Second, fLe foil temminaies m a
mti-smging tmiling-edge design typica of propelle~
This laier modiEcaiion is chaa teri ed by m
in~rea mg tsper staling nea 97/o cho d (Fig 2b)
thai leads to a compa t region of flow sepamLion m
the immediaie vicmity of fLe tmiling edge H
For all tests, the ch mnel flow velocity was
set through computer conhol of file rotational peed
of the LCC impeller d ive motor md monitored wifh
a tationaffy smgle-component Laser-Doppler
Velocimet y (LDV) probe positioned wifEm the test
section two chord lengths up tre m of the hyd foil's
leadmg edge This LDV probe provided file
measmed reference velocity, Up used in file data
reduction Local fluid velocities in file regions of
intere t were measured wifh a tl averse mounted tw -
component LDV This LDV system uses D mtec FO
probes with 111 mm beam spacing md 1600 mm
focal length for m m-water probe volume 0 17 mm m
diameter md 6 5 mm in length Laser wwelengths of
514 5 md 4SS 0 nm wise used for file tw LDV
Chalmers Both velocity ch mnels were Bang cell
shi ted to allow measurement of flow velocities wifh
rifler sign The flow components measured wise
sheamwise mem (U) md fluctuating (u) velocities
(positive dow sheam), End ve tical mem V) md
Duct atmg (v) velocities positive upward)
Reynolds shed stress, , was also measured The
LDV data processor were burst signal razzed
from D mtec, so flow tatistics were dete mined fi om
tabulations of mdi id al particle passages through
the LDV focal volume Continuous time histories of
flow velocity were not malyzed Thus, turbulence
spech a are not presented here
The LDV system was cahbhwed wifh a
reference velocity from a spmnmg disk attached to a
Compmmotor SM32 motor d iven by a Compumotor
TQIOX Sffxo Controllffs Bias enor in this
calibration is inhoduced through uncfftamty m (1)
di k rotational speed, (2) disk radms, md (3) file
Imear regression ht of the calibration curve Disk
speed unce tainty based on file mamfactur~s's pec is
+0 040 rew lutions per second The di k radius is 100
mm with m unce tainty of +0 35 mm arising fiom
the need to locate file disk center The unce tainty
introduced by file linear regression hit is no greatens
then +30 mm/s Based on these values, the maximum
calibration bias in the LDV velocity measurement
r mges fi om +1 4% at a flow peed of 3 m/s to +0 4%
at IS 3 m/s This h mslates into a maximum
fractional bias enor in the no malized mem
velocities (dimensionless) of +0 02 at 3 m/s to +0 006
at IS 3 m/s Through file no malization velocity, bias
also enters the no malized mem squares of file
velocity Duct ations, but is limited to a Faction of
+0 002 or less Precision :Tor is also present m file
calibration, but 1000 LDV samples are t ken to
produce each calibration cm e point, rendering this
emu negligible
In order to make proper use of facility time,
a nommal sampling period of 0 6 mm pa coo dinate
location was chosen for collection of all data sets
Since the LDV data rate ch mged with survey
location md flow speed, the collection period was
conholled (whet necessary) by varying the mumbo
of samples per coordinate location between 500 md
12,000 At some coordinates, fewer samples wise
acquned film sought rifler due to low data rate
(timeout) or failed data acceptmce criteria for file
LDV busts b such cases, measurements fiom
coordinate locations wifh fewer thm 100 samples
were discarded in po t-processing The main impact
of this te t-timmg cunstramt was felt m the separated
md reverse-flow near file foil's tl ailing edge at the 3
m/s te t speed Of he ise the 0 6-mimmte data-point
interval WE well matched to file expert ent The
vo tex-sheddmg oscillation time scale for file foil's
wake WE calculated (Blake 1565) to be 60 ms at 3
m/s md 10 ms at IS 3 m/s Hence, file data point
collection inrervl represents 600 to 3600
fmmdamental wake oscillations, so statistical
uncfftamty in the measured mem velocities md
tmbul:me qu mtities should be merely a few percent
This contention is backed up by file relatively smoodh
measured profiles show on Figs S - 24 in all cases,
the LDV's rmdom tract ation level (approx 1% of
the fieesheam speed) were incoherently subtracted
from the repo ted u md v Duct ation levels Sc titer
in file plotted datapoints is probably file best measme
of file extent of statistical convergence
The tw -component LDV measurements
were made at ti -e stations for a total of over 3,100
coordinate locations within the flow The hive
stations se how on Fig 3 md are refened to as
follow: (1) the inflow plane, with its nommal along
the flow duection; (2) the leading edge line, a
ve tical ire of data just upsh cam of file hyd of oil; (3)
the trailing edge region, a plme with Us normal
pe pendiculr to the flow md centered new file point
of separation, (4) file near wake plane, a pi me slicing
th ough file h ailing edge region with its nomm i along
the flow dihction; md (5) file far w he line, a
vedical line of d da h iLer dow sheam of the hailing
edge
4
EV~ORT
Figmce 3. Loc Don of LDV So e! s
3
At stations 2, 3, and 4, a reference position
for the LDV coordinate system was identified from a
distinguished point on the foil (i.e. leading or trailing
edge). The alignment of the LDV traverse with
respect to this reference point was checked every
time the tunnel speed was changed to correct for
deflection of the foil caused by hydrodynamic
loading. Nearly complete data sets at all five stations
were taken at four channel velocities: 3.0, 6.0, 12.0,
and 18.3 m/s with the bulk of the data (2,500
coordinate locations) being taken within the trailing
edge region (station 3~. The small amount of missing
data is from the lower tunnel speeds at which data
rates were too low to justify the requisite tunnel time.
This limitation set 3 m/s as a minimum speed at
which extensive measurements were practical, while
18.3 m/s represents the top flow speed for the LCC.
Thus, these experiments spanned the largest possible
Reynolds number range available under the
experimental constraints.
Throughout all data collection, tunnel
pressure was held constant and sufficiently high to
suppress cavitation that would alter the test. As
mentioned above, the tests were all speed controlled
and water temperature was monitored throughout the
experiment. Unfortunately, the available heat
exchanger capacity was not sufficient for full thermal
control and tunnel water temperature increased as
much as 1.3 °C/hr during tests a 18.3 m/s. Thus it
was necessary to intersperse 18.3 m/s tests with tests
at lower velocities throughout the course of the
experiment to stay below the tunnel's maximum
allowed water temperature of 40 °C. As a result, data
at a single speed and a station can vary in
temperature by as much as 9 °C, although water
temperatures ranged from 24 °C to 40 °C for the
entire experiment. The main impact of elevated
water temperatures was to decrease water viscosity
and thereby produce a higher Reynolds number for
the same flow speed. Thus, the chord-based Reynolds
numbers (Re) of the experiments reported here are as
follows: 3 m/s implies Re= 7 to 10 million; 6 m/s
implies Re= 16 to 20 million; 12 m/s implies Re=
29 to 39 million; and 18.3 m/s implies Re = 46 to 61
million.
EXPERIMENTAL RESULTS
The model and its mounting scheme were
designed to produce two-dimensional flow. However,
determining the actual extent of spanwise flow
uniformity was an important and necessary step for
the subsequent measurements made at a single
spanwise location. Thus, planes of LDV data-points
perpendicular to the flow direction were collected to
document spanwise flow uniformity far upstream of
the foil (station 1) and in the near wake of the foil
(station 4~. Sample results at 18.3 m/s for the
streamwise and vertical velocity components at
stations 1 and 4 are shown in contour plots as Figures
4, 5, 6, and 7. The left edge of each of these figures
lies in the center plane of the LCC (50% foil span).
The right edge of each figure lies close to the test
section windows (near 0% foil span). The top and
bottom edges of these figures lie approximately 500
mm above and below the foil, respectively. The
locations of data points from which the contours are
drawn are shown as dots on the figures. For the
streamwise flow results (Figs. 4 and 6), the velocity
componentis normal to the page. For the vertical
it. :~:=5~ ~
- it\ War/ 1 Woo,\ i~
0.05
O
-nns
-A 1
-0.15
-no
-0.25
0.3 i
0.25 _
0.2 _
n ~~
0.5 ~4 0.3 0.2 ~ 1
ZIS
Figure 4: Inflow Plane (Station 1), U/L
O.]
g0.05
-0.05 _
~ 1-
-O.] _
-0.15 _
-0.2 _
4
1.UD—11
~ 1.025— I// /
. . . . . . ~ _ _ . . . .
. ~7 - 0.5
. .
,.. (
At . . . . , . . . . , . . . . , . . . . , . . . .
0.5 0.4 0.3 0.2 Cl,]
ZIS
Figure 6: Wake Plane (Station 4), U/U ref
0.3
0.25
.
02 _
,_ :
0.15
0.1
90.05
O
-0.05
-n ~
n In
-0.2
/-'~.08~
. it.
-0. 1 2__~
.~
- ~.1&
-0.16~^\
~ I ~ ~ ' .q8.~¢l2
- . . . . . . . . . . . . .~.
v -TWO r 'it:
2
_
0.5 0.4 0.3 0.2 0.1 0
Z~
Figure 7: Wake Plane (Station 4), VM ref
Am'
component results (Figs. 5 and 7), positive is upward
parallel to the vertical edges of each figure. At station
1, the measured velocity has been normalized by the
local free-stream, while at station 2 the measured
velocity is normalized by the flow speed far-upstream
of the foil.
Figures 4 through 7 illustrate several
features of the flow over the hydrofoil and show the
spanwise uniformity of the flow is good. Figures 4
and 5 show that the flow far upstream of the foil (1.8
chord lengths from the leading edge) is uniform to
within 1.3% and predominantly horizontal.
However, the contours on Fig. 4 also show that
within 0.10 to 0.15 m (3 to 5% span) the LCC's
sidewall boundary layer begins to degrade the flow's
spanwise uniformity. Fig. 6 tells a similar story
regarding the extent of spanwise uniformity, but the
flow results are altered by the presence of the foil. In
particular, the horizontal band of depressed
streamwise velocity is the wake of the foil resulting
from its drag while the increase in flow speed above
the foil is caused by the foil's lift. The nearly
uniform negative vertical velocity in Fig. 7 is the
downwash and is also a result of the foil's lift.
Measured results for stations 1 and 4 at the
other test speeds are essentially identical and have
been omitted for brevity. However, these omitted
results and those shown on Figs. 4 through 7 were
used to set the span location for the remainder of the
LDV measurements. Although measurements at the
center plane (50% foil span) of the LCC are clearly
preferred by symmetry, LDV measurements are
easier and more time-efficient - for optical and
mechanical reasons related to water opacity, valid
LDV burst data rate, and foil deflection - when the
LDV focal volume is closer to the test section
windows. To balance these two issues, the 25% span
location was chosen for the remainder of the
measurements at stations 2, 3, and 5.
Velocity measurements from 26 mm
upstream of the foil's leading edge (station 2) for flow
speeds of 3, 6, 12, and 18.3 m/s are shown in Figs. 8
and 9. As before, the results at each speed are
normalized by the free-stream speed measured far-
upstream of the foil. Here, the y-coordinate increases
in the vertical direction and y = 0 lies at the nose of
the foil. As expected, both streamwise (Fig. 8) and
vertical (Fig. 9) velocity profiles upstream of the
leading edge collapse well. The remaining small
differences could be due to imprecision in the LDV
calibration or are a mild manifestation of the effects
of increasing Reynolds number.
0.3
n75
O.7
0.15
n ~
~0.05
o L
-0.05
-0 1
-0. 1 5
__ ~ _ ~ v v.~.V.~.~.~ v ~ ~.~ v v.~ ~.~
_5 _ + 3.0~Js i ..~ l
_ ~ 12 Otis . ~ <
o 1 8.3 ~Js i j j ~ i
_ , . , .................................................. , . ~ j
. j j j j j j j ~ j i
. jj j j j j j i ~ i j
a. j i i i i ~ i j
_ , ... , . ................. .... ~ . ~ -
- , - , s O ~.~
. . j - - A -
. j i ij j ~ i i i
5 -- -.' i - - . ! ~ - ~ - - <
-o.2 - j tj . ~ ....
I,,,, i,,,, i, ~ ~ ~ i I,,, I,, ~ ~ I,,,, I,,,, I,,,, I,,,, I
0.7 0.75 0.e 0.05 0.9 0.95 1 1.05 1.1 1.1 5
UNrof
Figure 8. Leading-edge LDV measurements of
normalized streamwise mean velocity U/U ref.
° 3 ~ T- '
~ i
n7
0.15
0.1
120.05
-O. 1
-n 1n
................ ....................
n 25 _ j ~, j
. ~ use
.2 .. ......... ..~ ..... . .
5 . t 3.0 mJs ..'j ~.~ ........ ;
~ 6.0 mJs i ~ ii
_ ~ 1 2.0 rnJs . -j ~
. 18.3rnis i i ~ i
, ....................................................................... . ;~
O ~ $, am, ~ w lo ~ a- ° - - Q—- -it ~ _ _ j
-0.05 0 0.05 o. 1 o. 1 5 0.2 0.25
YA)rof
Figure 9. Leading-edge LDV measurements of
normalized vertical mean velocity V/U ref
The trailing edge measurements were the
main focus of this research effort and are shown on
Figs. 10 through 14 for flow speeds of 3 and 18.3
m/s, and on Figs. 15 through 19 for 6 and 12 m/s.
While some of these results may seem repetitive,
these figures have been included for completeness.
5
0.035
0.03
0.025
0.02
+ 3. 0 ~ Is
° 18.3~Is 1,,,, 1
SGALE
o
-0.005
0.035
0.03
0.025
0.02
0.015
0.01
0.005
o
-0.005
-0.01
-~.01'
0.035
0.03
0.~25
0.02
0.015
0.01
0.005
o
-0.005
-0.01
-0.015
~::::1:: :: ::: /::::::::1:::::':::::::::::1: I'::::' ~
0.015
0.01
0.005
0.93 0.94 O.95 O.gS 0.97 O.98 O.OO 1 1.01 1.02 1.03 1.04 1.05 1 06
Figure 10. Trailing-edge LDV measurements of normalized streamwise mean velocity
U/Uref, taken at 3.0 and 18.3 m/s
~ ~ It 't ~
-"' ' ' '''''' " ""' '' '' "''''''W:'''''', '
_ ~:
WUref...........................
_ ~
: O
_
_.....
_.....
. _
..... ~
3. 0 r
1 S. 3 ~ Is ~ ~ A I ~ . . . . .
~ j - l T l l ~ ~ ~ j ~ ~ ~ ~ .
0.93 0.94 0.95 0.~S 0.97 0.98 0.99 1 1.0 1 1 .02 1.03 1.04 1.05 1.06
x~
Figure 11. Trailing-edge LDV measurements of normalized vertical mean velocity
V/Uref, taken at 3.0 and 18.3 m/s
_ f +
O
_......
1
1, . . .
· SGALE
, ~ , , , , I , , , , I , , , ; 1 , , , , I ,
O.93 O.94 O.95 O.gS O.97 O.gS O.99 1
, ;' ;; ; ; ; ;
1.0 1 1.02 1.03 1.04 1.05 1.06
Figure 12. Trailing-edge LDV measurements of normalized streamwise mean square velocity fluctuations
/lJref2, taken at 3.0 and 18.3 m/s
6
0.035
0.03
0.025
0.02
0.015
0.01
0.005
o
-0.005
-0.0
-0.0 '
0.035
0.03
0.025
0.02
0.015
0.01
0.005
o
-0.005
-0.01
-0.0 1 5
0.035
O.03
.` O.~25
o.~2
6.D rnis
o 17 n n,!
-~.~05
-1I'''''' 1\
_........
3.0 rRl~ .......... ~ U.UZ ~
183~Is 1,,,, 1
-0.93 0.94 0.95 0.96 0.97 O.g~ 0.99 1
X~
1.01 1.02 1.03 1.04 1.05 1.06
Figure 13. Trailing-edge LDV measurements of normalized vertical mean square velocity fluctuations
/Uref2, taken at 3.0 and 18.3 m/s
............................................ -
.................................... ~.4
, ~
t~
, ~. tj; .
°~' ~ t
............ °.~
.............................................
. ...................................
. ...................................
....... ...................................
r..................................
>...................................
...................................
...................................
t
°e \:~...................
, ...~;~.......................
,. E................................
, ;..................................
: ~
_.... ~ al .
. ~ ,
_ ~
0.93 0.94 O.95 O.g~ O.97 O.98 O.99 1 1.01 1.02 1.03 1.04 1.05 1 06
X~
Figure 14. Trailing-edge LDV measurements of normalized Reynolds Stress
/Uref2 ~ taken at 3.0 and 18.3 m/s
0.~15
~ O.01
0.~05
~:::::::1:::::::::::~:::::1
..................... - ~' ~'T''''''''']
- ~ tV
............................................................................... ~
: I JIl J~f
O.93 O.94 O.95 0.96 D.97 D.~8 0.~9 1 1 .D 1 1.~2 1.03 1.04 1.05 1.06
X~
Figure 15. Trailing-edge LDV measurements of normalized streamwise mean velocity
U/Uref, taken at 6.0 and 12.0 m/s
7
0.035
0.03
0.025
0.~2
0~015
O.01
0.005
-0.005
-0.01
-~.0 1 F
C.035
0.03
0.025
o.~
0.015
0.01
0.005
-0.005
-~.01
-~.01
0.035
0.03
O.~25
o.~
O.015
0.01
D.~05
-~.01
-0.015
V/Umf
_ .
- ~ 6.0 rnIs . . . ~ 0.2
o 1 2.o mis 1,,,, 1
\1
0.93 0.94 O.95 0.96 0.97 O.~8 0.~S
X
1 07
1.03
Figure 16. Trailing-edge LDV measurements of normalized vertical mean velocity
V/Uref, taken at 6.0 and 12.0 m/s
_
0.93 0.94 0.95 D.96 0.97 0.~8 0.~S
X
1.C4
L.................................
`=
.....~.........................
~ A,
~ it .. .
ant ~
b~ ~ 0
D ~ ~ ~
-_10+
1 no
..... ....
. V
~ ...
1.06
1 1 .0 1 1.02 1.03 1.04 1 .~ 1.(
Figure 17. Trailing-edge LDV measurements of normalized streamwise mean square velocity fluctuations
/Uref2, taken at 6.0 and 12.0 m/s
0.93 0.94 O.95 O.96 0.97 O.~E O.~9 1 1 .D 1 1 .~ 1 .03 1.04 1
xK:
Figure 18. Trailing-edge LDV measurements of normalized vertical mean square velocity fluctuations,
lUref2 ~ taken at 6.0 and 12.0 m/s
8
O.OB5
0.03
O.~5
o.~2
O.01 5
0.01
O.~5
o
-~.~5
-~.01
/Urof' 44'~ ~'
60m/s .................................. ~ v
12.~ 1,,,, 1
.......
.... ~
0.93 0.94 0.95 O.96 0.97 O.~8 0.~S 1 ED 1 1 .~2 1 .~ 1.04 1.05
Figure 19. Trailing-edge LDV measurements of normalized Reynolds Stress
/Uref2 ~ taken at 6.0 and 12.0 m/s
The unconventional grouping of the data
was chosen to ease the comparisons between the
lowest and highest Reynolds number measurements.
In both figures, the foil's trailing edge appears as an
outline within the left half of each frame. The
vertical and horizontal axes show the spatial
coordinates normalized by the foil chord. Here x/C =
1 lies at the tip of the foil's trailing edge, and y/C = 0
corresponds to the vertical location of the flat
pressure side of the foil. The vertical lines within
each frame correspond to the location where the
various flow quantities were measured. The
horizontal distance from these vertical lines to the
measured data points represents the measured field
values. A scale that allows numerical determination
of the field values is provided inside the foil outline
of each figure. Negative measured values appear to
the left of their vertical location lines while positive
values appear to the right. For example, consider the
measurements at x/C = 1 on Figs. 10 and 11 for the
normalized mean velocity components, U and V. On
both frames, U and V go to zero at the tip of the foil
and the measured data touch the vertical location line
that passes through the tip of the foil. Using this as a
reference point on Fig. 10, U above the foil tip is seen
to have a weak reverse flow region and then a
smoothly increasing value as y/C increases.
Below the foil, U appears to change
discontinuously to a positive value. The
discontinuity occurs because the f~nite-size LDV
focal volume can only be centered about one or two
focal volume diameters from the foil's surface on
closest approach because of optical constraints. In
addition, the measurements near the topside
(underside) of the foil must be made from above
(below) with the LDV optics tilted slightly downward
(upward). Thus, all the profiles for x/C < 1 (and
some for x/C > 1) are constructed from two or more
separate traverses of the LDV system.
Perhaps the most important feature of the
data shown on Figs. 10 through 19, is the Reynolds
number dependence. This is most clearly seen in the
profiles of the turbulence quantities for the newly
separated suction-side boundary layer (see Figs. 12,
13, and 14~. Here, the peak values in the turbulence
quantities are interpreted as lying at the center of the
developing shear layer and the height of this shear
layer above the foil surface is clearly different for the
3 m/s and 18.3 rn/s tests. Thus, the vertical extent of
the near-wake is slightly larger at the lower flow
speed, and this increased wake width extends out past
the right edge of each figure.
The mean velocity profiles are consistent
with this trend. On Fig. 10, the streamwise velocity
profile is clearly inflected at x/C = 0.986 (-30 mm)
for the 3 m/s data while the same profile is fuller and
not inflected for the 18.3 m/s measurements.
Similarly, the vertical velocity at the same location
(Fig. 11) is less negative close to the foil surface at 3
m/s than at 18.3 m/s. Taken together these mean-
flow findings and those for the turbulence quantities,
all suggest that the suction side boundary layer
separates closer to the foil's trailing edge at the higher
speed.
Thus, a simple interpretation of the suction
side flow emerges. For the fixed geometry of the
foil, increasing the Reynolds number through
increases in tunnel speed act to thin the suction side
boundary layer. A thinner boundary layer better is
able to resist separation in the adverse pressure
gradient that exists on the aft half of the suction
surface. Thus at higher Reynolds number, the
suction side boundary layer makes it further past the
knuckle and separates closer to the trailing edge and
9
thereby alters the size of the reverse flow region and
the characteristics of the near wake. This phenomena
is believed to be similar to the Reynolds number
dependence found for the maximum lift coefficient of
subsonic airfoils for chord-based Reynolds numbers
of 2 to 12 million (see McCormick 1979~.
Several compelling reasons exist why the
observed Reynolds number differences are genuine.
First of all, the data shown on Figs. 10-19 were
collected over a three week period and most if not all
of the plotted profiles were pieced together from
measurements made at different times on different
days at (unfortunately) slightly different water
temperatures. Yet, where the various profile pieces
overlapped the agreement between pieces was good
(typically better than +1%~. Second, the Reynolds
number trend is monotonic. Although this is difficult
to ascertain from the figures, the measured Reynolds
number variations march in a consistent manner with
increasing f ow speeds in the proper ordering to
match the conjectured simple interpretation described
in the previous paragraph. Thirdly, the measured
variations cannot be explained by alignment or
positioning problems. The downward shift in suction
side separated shear flow is approximately 1 cm as
the flow speed increases from 3 to 18.3 Is. This
shift is far larger than the positioning error of the
LDV system (10.1 mm) or the lift-induced deflection
of the foil at 25% span (2 to 3 mm). And finally, the
measured results are consistent with classical
measurements of turbulent shear flows. ~ 0 05
Although the flow near the trailing edge is
more complicated than any simple free-shear flow,
the turbulent fluctuation levels found in this study are
in reasonable agreement with classical shear layer
characteristics. For example, measurements in the
attached pressure-side boundary layer upstream of
the trailing edge nearly match classical results
(provided in {,)-braces below) rom the smooth-wall
zero-pressure-gradient flat-plate boundary layer (see
Hinze, 1975~. The measured normalized peak
is 0.006510.001 (0.0067), the measured normalized
peak is 0.0016~0.0002 {0.0016), and the
measured normalized peak Reynolds shear stress
= 0.001010.0001 {0.0014~.
Likewise, the measured turbulence
characteristics in the region downstream of both
suction- and pressure-side boundary-layer separation
are reasonably well matched to classical free shear
layer measurements. For comparison, the results of
Wygnanski and Fiedler (1970) are provided in {,)-
braces below. The measured nor alized peak
is 0.025~0.002 {0.031), the measured normalized
peak is 0.01710.002 {0.020), and the measured
normalized peak Reynolds shear stress =
10
+0.009~0.001 {0.009~. Although not conclusive in
themselves, these comparisons suggest that there are
no major problems with the current measurements,
and the observed Reynolds number dependence is
genuine.
The final measuring station (5) was one half
of a chord length downstream of the foil. Figures 20
through 24 present mean flow and turbulence results
from station 5 for flow speeds of 3, 6, 12, and 18.3
m s. Here, the data from the four speeds collapse
reasonably well although some results do display
weak trends with increasing Reynolds number.
However, whatever variations are apparent here (like
the decrease in vertical velocity fluctuations with
increasing flow velocity, see Fig. 23) are much less
pronounced than those found in the trailing edge data.
This is especially true for the normalized Reynolds
shear stress (Fig. 24) which collapses well in the
wake even though it did not collapse near the foil's
trailing edge (Fig. 14~.
0.3
0.15
0.25 _
0.2 _, ., .. ~ 3.0 mis
6.0 mis
~ . O
0.1
o
-0.05
0.1
-0.15
-' ~
· ,
0.05 0.9 0.95 1 1.05
U/Uref
Figure 20. Station 5 (Far Wake), U/U ref
1.1
0.3 i 3 v ~ ~. 3
o.z5 ~~ ~ .
0.15 - ........ ............. j A ~ ~ 3 mi$ 1. '''''i'''''' '''''''"''''''''''''''''
a3r ---- --------~-+ O.° ; yO0541.-- - - -- - -.--.------------.- - -- -.- -
0.15 _ . . ... .... ..... . ^+-o ~OA O A ~ .q ~
OZi i '6o^4~d,~-' °~ ~
o.1st- ------;----~,;~,^------. - I ~ 3.0rnis 1. t - $
9, 0.05 ~ t ~; ' ~, (t ~ ~ ~ ~ ~
0~ ... ~ q~' - O 0 001 O ooz 0 003 0 004 0005
-o.as _ ,.—~ ., , ' ..... , < ~ ~2~~U~~~f~
O. 1 _ · ~ b ~ ~ A~ 4 _ -
_. . ++ ^~ °~° a. . . . Figure23. Station 5 (Far wake) ~v2>/U f2
-0 15 ~ , , aP°;~$. ' o~ . ~ re
o :z ........................................................................................
· I I ,, I,,,, I,,,, I,,,, I,,,, I,,,, I
-0.06 -0.05 ~.04 -0.03 ~.oz -o~o 1 0 0~0 1 0 04 _ . - ~
YlUref . ~
+ ,
Figure 21. Station 5 (Far Wake), V/U ref t. ~ ! r~ PG~
— .A o D 0~ A . . ~ 12.0 mIs
O —'- ~ ~' ~ - i - - ' ° 1 ~ . 3 mis . <
~ ·~ O 2 +O O · · .
0 3 ~ ..... ........... .... ........................ ......... ........ .... .................... ~ ~: , DA o, ~ O r ~ + o ' ;
O Z5~ t ~ j t
O Z ~ ~. ~ ~ I Z C) I ~ ~ ~ 04
S~ 005 s ...........................................................................................................
a~, - ~ . ~ .t)O 1 5 -0.00 1 -0.0005 0 0.0005 0.00 1 O.W 1 5
o ~ ~—~2~ v~~Uref
-°.°s ~ -~- ~. - - -.. - - - -- - ---- - . ~ Figure 24. Station 5 (Far Wake), /U ref2
.- 0, ~ ~, t . ............................................................
-0.15 _, ~ 0 ~ . As with the near-trailing edge
-o ~ s ~ . measurements, these wake measurements can be
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ compared to classical results. The measured peak
~ 0.00 1 0.002 0.003 0.004 0.005 0.006
cu2>Nref2 Reynolds shear stress normalized by the wake
def1cit velocity is 0.06~0.01, and this compares well
Figure 22. Station 5 (Far Wake), /Uref2 to the range of values (0.04 to 0.08) found by
Narasimha and Prabhu (1972) altho ugh 0.06 is
somewhat above their equilibrium peak value of
0.045. Likewise the measured peak streamwise and
vertical velocity fluctuations are approximately the
same and this matches the expectation for two-
dimensional wake flows (Townsend 1976). However
the measured fluctuations levels in the foil's wake are
a factor of two higher than those in a classical two-
11
dimensional wake flow. This difference may arise
because the hydrofoil's wake has both wake-deficit
and shear-flow characteristics that are produced by
the drag and lift loads on the foil, respectively.
PRELIMINARY COMPARISONS TO
CALCULATIONS
Computations of the flow over the foil were
made using Mississippi State's UNCLE flow solver
(UNsteady Computation of FieLd Equations) which
is based on the Reynolds-averaged Navier-Stokes
MANSE equations (Arabshahi et al. 1999~. Time and
resource limitations only allowed calculations at the 3
m s and 6 m s to be completed. The computations
were run as a two-dimensional model, and did not
include the tunnel walls in the simulation. A C-t pe
grid containing 170,000 points was used for the
computation. As shown in Fig. 25, the point
dis ribution was densely packed near the foil surface
and in the trailing edge region; y + values near the
surface are less than 0.5.
o.£ ~
O.1~
Figure 25. Computational Grid
In order to correct the computed data for the
effects of the test-section walls and the bounder
layers developing on them, a free-stream velocit
correction was computed in the following manner: at
the location where the computed surface pressure is
zero, measured velocities equidistantly located above
and below the foil are averaged. The computed
surface pressure was zero at x C = 0.98. This method
is based on experimental results by Jiang et al
(1990) who determined that the axial location where
the surface pressure is zero is least affected by tunnel
walls, and best represents what the unbounded
velocit should be. This value was computed to be
1.065 for the 3 m s case and 1.064 for the 6 m s case.
Comparisons be ween the computed results
and the experimental measurements were performed
at x C locations of 0.978, 0.992, 1.0, and 1.028 as
shown in Figures 26-33. Computations were
completed at Reynolds numbers of 9 and 16 million
and the results match favorably with the experimental
measurements of the mean flow. The q-m turbulence
model gave more favorable results than the k-£ model
in matching velocit profiles at the trailing edge
region.
................
: O
.
- RANS
Ex~nmont
-
_' ' ' ' ' · ' · . ~ 00 0 0 00 ~ P~ - ~ .
_ : . jet
_ .......................
_...............................................
.
.................................................................................................. .......................
. . ; ; ; ; ; ; , ; ; ; ~
.7
0.7 ~ 0.7 0.4 0.6 0.8 1 1.7
U Unit
Figure 26. Normalized mean streamwise velocit at
x/C=0.978, 3.0 m s
n7
0.1
0. 5
-lo. 5
-~.1
-~.15
. !
.7 _ .
-0.7 ~ 0.7
RANS . ~ ~
O Exam mont . ~ ~
_ ~ ' ' ~ ~ '
. . .!
_ ~ ~ ~
...... .................... , ~ i
_.............
_ ~ ~ ~
_........................................
........................
................................................................. .......................
0.4 0.6 O.S 1 1.7
U!U~'
Figure 27. Normalized mean streamwise velocity at
x/C=0.992, 3.0 m/s
~ i
f.~:: :.
/ 0.5~
._ ~
o.~r
0.15
n 1
~..
-
~5
O
~~05
~ .
.
0. 1 5 r
i i i ~ i: 0.25
— 1 RANS 1 . 0.2
- | ° Exporir ont | ~ 0.15
- . . ~ 0.1
_ 2 ;' -
_ ~~~~ ~
i . l
g~ L....................................................................................
o.2 ~ o.2
0.4 O.6 0.S 1 1.2
UIU~!
Figure 28. No malized mean st eamwise velocit at
x/C=1.000, 3.0 m s
n7
D.1 ~ ...................
,
0.05
o
-0.05
-~.1
_ _ _1=:~x J '.
_ ' ' j ' l''
, ' - - ~
-~.15 _ .... i . i i i i - i
_ . , , . . . ~
o.2 O o?
1'''''''''''''''"
0.4 O.6 O.6 1 1.2
UIU~'
Figure29. Nor alized mean st eamwisevelocit at
x/C=1.028, 3.0 m s
-~. 5
-0.1
-0.15~- ; ; .; . ~ ........ ;
0.2 0.4 0.6
UIU~
, ......................................... .................................. ...................................
_ i i i i i
_ "' 'i '''''''"'''''i''''''''
_ ~ NO i i
~ 0 E porir ont ................. , ~ ;
_ . . . . · · 1
~ ~ ~ ~ )
_ ~ . . . . . ~
............. ' ' ' ' ~
· 00. 0 ~ ~ ;
- - - - O 0 00 . - - - -
_ i j j j ; .....................
......................................................................................... .....................................................
....................... ;
i
i
.....................
~ ii
i i
I 1 1 l l l l l
o.e 1 1.2
Figure 30. No malized mean s eamwise velocity at
x/C=0.978, 6.0 m/s
n75 _................................................................................................................................................................
· i
5
— RANS |
0 Expertrnent 1- -- .............
n7
O.15
O.1
~ .
.
_ _
0.05
-~.05
-~.1
-~.15
-~.2 _
-~.7
i' i . P
i i , - ~
_ ~_~ '
_ i
-', , ', . ''.
.. ... ... ... ... ..
- ; ; ; ; ; ; ~ ;
O O.2 0.4 0.6 O.8 1 1.2
U'Um'
Figure 31. Normalized mean streamwise velocity at
x/C=0.992, 6.0 m/s
O.15:
Oo~ _...............................................................................................................................................................................
., ~ , . . '' . . O s
i i i . . ,
o.2 _ . . . . ...........
RANS . .
0 Exponmont ....... i
.
D.1
-~.05
~ 1 _.................................
-D 1 ~
_ j j j j j j ~ -
.. _ . . 1
, , , , . ,
. . . . . .
. _ ~
. , . , j ~ i
l _ , , 0 0~
................................................................................................................. ,
.......................................................................................................... .......................
_.................................................................................................................................................
..
-~.2 O O.2 O.4 O.6
UlUm!
-I I 1 1 i i i i i 1'
...................
. O
_ I I 1 1 1
O.S 1 1.2
Figure 32. Normalized mean streamwise velocity at
x/C=1.000, 6.0 m s
L, al
o.~F
O.15
0.1:
O.05
o
-~.Os ~
-~.1 _......
-~.15
~ o.2
_ . ~
RANG
~ 0 Exporimont
............... . ~ ~ ' '. . j
.
_ . . . . .
- . - ~ ' '
_ ; ; ; ~
v
.............
l
........
O.4 0.6 0.S 1
Unjust
Figure 33. Normalized mean streamwise velocity at
x/C=1.028, 6.0 m s
SUMMARY AND CONCLUSIONS
1.2
Controlled tests of a two-dimensional
hydrofoil at chord-based Reynolds numbers from 6 to
60 million have been performed. Two-component
Laser-Doppler Velocimetry measurements have been
made upstream of the foil, near the foil's leading and
trailing edges, and in the wake of the foil. Spanwise
uniformity of the flow over the foil was verified.
Results for mean flow and turbulence quantities have
been presented.
Although this investigation will continue,
the present results lead to three conclusions. First,
the foil's near wake flow features appear to be
Rey olds number dependent. This is shown most
prominently in Figs. 12 - 14 where all of the profiles
of the normalized Reynolds stress components on the
suction side of the foil near its trailing edge show
clear differences between test results at 3.0 m s and
18.3 ms. Second, the observed Reynolds number
dependence is consistent with suction side boundary
layer separation occurring closer to the trailing edge
at higher Reynolds number. Support for this
conclusion can be found in measurements of the
mean flow and the turbulence quantities. And
finally, classical RANS-based turbulence models
appear to hold some promise for simulating the mean
flow over this hydrofoil. However, the results
presented here in Figs. 26 through 33 should be
considered preliminary.
ACKNOWLEDGEMENTS
The authors of this paper wish to the
acknowledge the contributions of Paul Tortora and
Ronnie Bladh of the University of Michigan; William
Blake, Ken Edens, Bob Etter, Ted Farabee, Jon
Gershfeld, Joe Gorski, Tom Mathews, David
Schwartzenberg, Jim Valentine, Phil Yarnall, and the
LCC crew from the Naval Surface Warfare Center -
Carderock Division; Lafe Taylor, Min-Yee Jaing, and
David Whitfield from Mississippi State University;
and Pat Purtell and Candace Wark from the Office of
Naval Research. In addition, the authors wish to
thank the Office of Naval Research for supporting
this research effort under contract nos. N00014-99-1-
0341, and N00014-99-1-0856.
REFERENCES
Arabshahi, A., Beddhu, M., Briley, W., Chen, J.,
Gaither, A., Janus, J., Jaing, M., Marcum, D.,
McGinley, J., Pankajakshan, R., Remotigue,
M., Sheng, C., Sreenivas, K., Taylor, L.,
Whitfield, D. (1999) "A perspective on naval
hydrodynamic flow simulation," 22 nd
Symposium on Naval Hydrodynamics (National
Academy Press, Washington DC), pp. 920-934.
Blake, W.K. (1986) Mechanics of Flow Induced
Sound and Vibration Vol. II. (Academic Press,
Orlando).
Crighton, D.G. (1985) "The Kutta condition in
unsteady flow," Annual Review of Fluid
Mechanics, Vol. 17, 411-445.
14
Hinze, IO (1975) Turbulence. 2 Ed MeG=lw
Hill, NewYork), pp 638-643
Jimg, C W. Liu, H L, md Humg, T. T. (1990)
"Dete mination of wind t nnel wall effects md
conections" in Proceedings of file 19th
Intennational Towmg Talk Co terence, held m
Madrid, Spain, Vol. 2, PS-2 4,310-317
McCo mick, B W. (1979) Aerodvnamics.
Aeron mtics. md Flight Mech mics (John Wiley
& Sons, New York), pp 76-82
NausimEa, R. md PrsbLu, A (1972) "Equilibrium
md relaxation in tmbulent wakes," J. Fluid
Mech, Vol. 54, Pt. 1, 1-17
Simpson, RL (1989) "Turbulent boundary layer
separation," A mmal Review of Fluid
Mech mics, Vol. 21, 205-234
Tow send, AA (1976) The Stru ture of Turbulent
Shear Flow (Cambridge University Press,
Cambridge), pp 202, 217
Wmg, M, Lele, SK, End Mom, P. (1996)
"Computation of Qu d mole Noise Using
Acoustic A Logy," A AA Jom al, Vol. 34
2247-2254
White, FM (1991) Viscous Fluid Flow, 2nd Ed
(McG awHill, inc. NewYork), pp 433 435
Wygmmski, I A d Fiedler, HE (1970) "The tw -
dimensional mixmg region," J. Fluid Mech,
Vol. 41, 327-361
15
DISCUSSION
S. Cordier
Bcssin d'Esscis des Carenes, France
Ship propeller fmish tends to be degraded es the
ships me m service Could you discuss the
i fluence of surface finish on the type of results
you are presenting?
AU? HOR'S REPLY
Surface roughness c m lead to prem.t ure
tr msition to t rbulence m the boundary Icyer Ed
dismpt the flow within the boundary Icyer She
surface of the H FOIL hr. been highly polished
to m RMS su face roughmess of 0 25
micrometers or less, Ed et He Rey olds
mmmbers of interest, the hyd of oil c m be
coned red h.d odynamicclly smooch k+ < 0 5)
Consequently, mat rcl boundary Icyer h msition
is expected to occur near the leading edge, Ed
th exact location of h msition may vary
somewhat with Rey olds mmmber How ver, the
boundary layer has completely undergone
t msition by She time it reaches She trailing edge,
Ed we do not e pect that smell variation in
upsheam h msition location to i tluence the
tnailmg edge flow For fully rough flows k+
>30), the surface roughmess c m signffi mtly
affect She developed boundary Icyer flow it is
possible that c propeller bade in service could
e habit such roughmess (> 25 micrometers RMS,
say) its effect on She flow would depend not
only on the RMS level, but the topology of the
roughmess elements Ed Heir location on the
blade surface Since the focus or our
experiments was scientific in mature we choose
to study the simplest case (i e smooth) first
However, we are intere ted m investigating the
effects of roughmess m the future
DISCUSSION
F. Di Felice
Instituto Ncziorul per St di ed E perienze di
A chitetturc Ncvale ( [NSEAN), Italy
LDV provides velocity measurement et c pomt
Ed results are shown on c relerence frame
refened to She model Did you take into account
the model defommations? If yes, how?
Mecsmements show find points near the surface
How do you solve the problem of the liquidation
of She optical access when mecsurmg the
velocity component normal to the profile su face
(vo ti 91 I'
AU? HOR'S REPLY
A experimental procedure was devised to
measure velocities close to She surface of the
hyd of oil With She probe volume located m the
area of mterest, She LDV heed was tilted to the
minimum Ogle from horizontal et which all four
LDV beams cleared the hyd of oil Since this
Ogle is k own, its effect on the measured
streamwise Ed t msverse velocities could be
taken into account How ver, in all cases the
Ogle effect was negligible in comparison with
other sources of en or Ed so was disregarded
She charmel flow was then set on condition so
that the hyd of oil assumed its lift-loaded shape
At this time the sharp tip of the hailing edge was
located Ed used es the spatial reference pomt for
the LDV mecsmements (7he point was located
by observing She appearance Ed disappearance
of the surface loser flare es the LDV probe
volume was scarmed vertically across the tip of
the trailing edge ) Using this relerence point with
the hyd of oil's k own Ogle of attack Ed
surface contour, my given paticl coordinate for
the LDV date may be related to my point on the
hyd of oil surface
She LDV spatial coordinates were arranged m
vertical columns rising from the hyd of oil
surface he order to ensme that data was acquired
es close to She surface es conditions allowed,
each column beg m with c coordinate just inside
the hyd of oil surface Ed marched outward fi om
the su face et incr merits of 0 2 mm Probe
volume diameter was 0 17 mm ) Cocrdirutes
below the surface Ed so near to the surface es to
be effected by surface flare timed-out before
producing data Such date d opouts w re
discarded m post-processmg
