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OCR for page 301
Unsteady Flow Quantities on Two-Dimensional Foils:
Experimental and Numerical Results
P. Creismeas, L. Merle, 0. Perehman, L. Brianson-Marjollet
(Bassin d- Essais des Carel~e i, France)
ABSTRACT
This paper presents the validation of ~ new m m xical
tool, based on LES method Ed applied by Bassm
d'essais des carenes This tool is applied to calcokte
flows on two-dimensiom~l foils at several Ogles of
attack it provi d s be k ow le dge of non- stat iorury
q mtities for non cavitatmg flow The validation is
conducted by comparison with experimental results
obtained at high Rey olds m mber m She G T. H. for
noncavitating mdcavitati g flows
NOMENCLATURE
p: press se coefficient; Cp = f
p Vref J
Pr ef Pa
a :cavitationparameter; (J= I
oVref
Pref: reference value for pres we
Pv : vapor p~essme
~ ret: reference value for flow velocity
p : vol mic mass of water
x : flow Ogle of attack
INTRODUCTION
The prediction of noise Radiated by ~ prop Her is still
ve y complicated at She desig tage it requites
advanced m merical tools which need to be validated
Bassin d'essais des cxenes has teen active m She
development Ed validation of new tools which c m
provide She k wledge of flow fluctuatmg quantities
Ed mme pnrticchrlv of tructmes which generate
p~essme fluctuations on She bodes The next step will
be the calculation of She noise Radiated by the bodes
when turbulent excitations at on it
This paper presents the m merical method which
relies on Large Eddy Simoktion LES) For
validation pmpose, we 3150 demise briefly the
exp ximental set-up which allows us to mea we non-
statiorury q mtities The comparison betw en
experimental And m m xical results takes ~ large pace
m this papa As ~ concision illu trations of
Rey olds m mber effects on cavitation pattern will be
prese ted m order to mphasise thei imports e Ed
She necessity to have ~ very precise description of the
flow Ed of its t lobule t shuctmes
NUMERICAL SIMULATION
To o x k owl age, very little work had been
published with comparisons between e periments ad
m merical results m hyd odynamic field (showing
p e. we fluctuations specha calculated by LES
method) Jordan (Jordm 1996) did calculation for
kminar flow with Rey olds m mber equal to 25000
Moreo x, empirical models for parietal pres we
fluctuations m m acelemted or decelerated flow do
not give aco crate results So, up to now, we do not
have mmerical tool capable to optimise She bade
sections wish respect to hyd odynamic excitation
LES is ~ method which calculates flow scales selected
by me m of ~ filter, G This one is convoluted to She
flow variables which scales arc inter d or are
moc?oscopic Let f(x,t) be She gerexic rume of flow
variables (velocity, press Be, etc ) we can w ite:
f(x,t)= f(x,t) + f'(x,t)
comp~tmn modelm~mn
Or
f(x,t) ~f(y,t)G(x y)dy
f(x,t) is the f 11 ad correct solution few) co tams
She i fommation which is lost 6 ough flltxi g ad is
called reside I or hi grid Cole By using eq 2 ), it is
possible to pe form ~ global filth g of She
Compressible Navier-Stokes equations,
aut =o
ax
(1)
(2)
(3)
Ou' al/ I ap aJu
a +U aJ paXJ+vaxtaxt (4)
OCR for page 302
where p is She density of the fluid, ass med to be
con tan, md V She viscosity After She filtermg
op mu on, She set of equation 3 md 4 c m be cast into
She following form,
aut =o
ax
ad d.'/ Y I aP+V a ,, a rS (6
at d., p ax, OxtOxt axJ
(5)
She subg id shess tensor [,/ contaming She
i formation from She subg id I.
decomp ed as ~Leorcrd 1974)
a,/ = / i// u~uJ + u,uJ +u uJ
+ ., -,, C)
L,/ is th Leonond tensor md describes be
mrerarions betw en the lihered scales, Csis the
crossing st ens tensor md describes She mtxations
between She filtered scales md the subg id ones md
R./ is called the R ynolds t nson md describes She
mrerarion betw en She subg id scales The
introduction of [/ involves the problem of mod llmg
She Senior itself or its effects Hence we need to build
ass mpti ms on th interaction betw en She resohed
md She subg id scales which preconcene the
behsvio x of th ones L t es focus o x attention on
She mod Hopi m Equation 6 represents the evolution
of the lihered q mtity u, m which She remit of She
mrerariom with th subg id field u Be t mskted
6 ough She t am
'' = grad (a)
ax/
Two ways exist to take into taco mt 6 is temm (Sagaet
1995) Enher -. tensor [,/ is calculated explicitly
Love 1980, L md 1992, Pope 1975) or s new temm is
introduced which has She similar effect on the
resohed field u as [,/ itself in this paper, only She
second spproah is considered The mbg id scales me
ass med to have s Brow i m motion sepxposed on
She motion of the lihered scales By serology with She
dissipation by molecular iscosity V, s subg id
viscosity is inhoduced, denoted VSM Bet thee is m
impo t mt difference between V md VSM. VSM is
not m mtrinsic property of She fluid md hence
d pends heavily upon the flow itself Th mbg id
viscosity has She sdv mtage of bemg robust, that is to
(8)
say s dissipative effect inhoduced 6 o gh VSM
which tends to tstilise the schemes How ver, such s
model is fix fr m capable of describing eve y
mechmism of She mrerarions betw en She subg id
scales md the lihered ones Th o gh She notion of
mbg id viscosity, we assume implicitly that She root
of the action of She subg id scales on the filtered
scales is energetic in other w ads, w only need the
energetic h msfer balance betw en th two kinds of
scales to describe She subg id tensor effect However,
She energy dsins fiom th lihered scales to the
mbg id ones is not She mly mechrni m which
d scribes the interaction herseen the two rages of
scales (Krsich m 1976) Two ocher mechrni ms m
be distinguished that are first s reverse t msfer of She
energy from She scales to the lihered scales, such s
mechmism is called bocbcottering (Ch~snov 1991,
Domarsd ki 1997) md secondly s t msfx Of
i fomm ti m Heated to the misoh opy from the g estest
scales to the smalle t ones These lest two
mechmisms me ipso focto ig ored by the subgid
iscosity spproah, md it c m be show Hot moon
1991) that the bakscstixi g md the misotropy
Hotel 1994, Piomelli 1996) me She root of the
whole dynamics of She turbulent bo mdary layer md
h rice carmot be neglected ~ mch area, s r mge of
scales, as wide as possible, must be dinectly
simulated The subg id is restricted to the smallest
scales to the gestest extent possible with minimal
effect on the lihered scales Boris 1992) The n mber
of discretisstion meshes ma! be close to She one
given by DNS criterion The ohssi al model used to
calculate She subg id viscosity is She Smagorinsky
model (Smagormsky 1963) An altermNtive is
suggested by Boris et at Boris 1992) md
(Kawamera 1984) The Mauri. -' iscosity, remlting
both from She finite vol me discretization md from
She m m xical scheme is used as subg id mod Ring
No subg id viscosity is explicitly computed md hence
His spproah is called implicit mod Huron The
rel tion betw en the m merical viscosity, md the
mbg id viscosity is not supported by s clear
mathematical Theory A d swbak of this spproah is
that the m merical viscosity is Ott ply xtfficial, that is
to say, not based m s comprebenimn of She simel ted
phenomena A second d swbak is the effect of She
mbg id scales on the filtered ones is s shictly
dissipative effect (Kawamus 1984, Sagaet 1995)
How ver, She implicit simulation is quite marngeat le
ff w keep in mmd that impo tan mesh refinement is
~equi cd m She mess where the viscosity appears
explicitly (m bo mdaries Dyers, for example) Such
mess present strong local misotropy charatxi tics
L She mess sphere viscosity effects are not
preponder mt, larger meshes c m be used md
OCR for page 303
numerical viscosity operates. In this paper, we intend
to resolve the following set of Navier-Stokes
equations,
Jui
=0
Taxi
aUi Suit _ l ap +~ 92ui
at ax j r Dxi ark ark
(9)
(10)
The numerical viscosity is introduced by a classical
second-order accurate scheme with a finite volume
discretization. The temporal resolution is performed
by a first-order implicit Euler algorithm. These
algorithms are carried through the commercial code
FLUENT. Table 1 gives the main characteristics of
the grid used for calculation.
Cells
number
Total span
calculated
Size of
the axial
mesh
Size of
the span
mesh
Boundary
layer
mesh
Reynolds
number
NACA66
4 degrees
629069
0.06 m
6.6 lo6
BA
2 degrees
82Sl7
0.06 m
0.0025 m
0.0013 m
0.002 m
6 lo6
BA
4 degrees
1322885
0.06 m
0.002 m
0.0011 m
0.001 m
3.6 106
Table 1: Main characteristics of the
For all cases, the mesh was tetrahedral hybrid non
structured. Some difference appear in the way the
boundary layer was meshed. For BA foil, it was
hexahedral cells in the boundary layer and for NACA
66, it was tetrahedral cells. Figure 1 gives an idea of
the calculation volume.
/
1.14 m
0.06~
1 < ,\~=) < ~
\ 1 m 0.6m lm .
Figure 1: Main dimensions of the calculation
volume.
EXPERIMENTAL SET-UP
Two different tests were conducted in the small test
section (1.14 m X 1.14 m X 6m) of the G.T.H. During
the first one, we have studied a two-dimensional foil
with a NACA66 modified section. It was equiped
with 18 static pressure holes and was flush mounted
on the wall using the 6 components balance. During
the second test, a new two-dimensional foil (called
BA foil) with a section specially defined was tested.
This foil was also flush mounted with the balance and
a fluctuating pressure transducer was installed in it.
In order to reduce the lift of the two-dimensional
foils, at high velocity, we have limited the span of the
foil by using a big vertical plate (3.4
mXl.14mXO.048m) in the test section as describe in
figure 2.
BA
7 degrees
828371
0.06 m
0.0025 m
0.0013 m
0.002 m
3.6 106
Flow velocity
mesh. Figure 2: Top view of the test section.
0.45 m
The main characteristics of the foils are given in table
2.
Section
Plan form
Chord
Span
Maximum
Thickness
Maximum
camber
NACA 66
rectangular
0.6 m
0.45 m
6%
BA foil
Rectangular
0.6 m
0.45 m
7 %
2 % 3.5 %
Table 2: Main characteristics of the foils.
The tests were carried out with velocity range from 2
m/s to 13 m/s. So, the Reynolds number, based on the
chord, ranged from 1.2 106 to 7.8 106 which is close to
the full scale value for a section of a propeller. The
OCR for page 304
foil angle of attack was varied from-10 degrees to
14 degrees for the NACA 66 and from 0 degree to 8 n
degrees for BA foil.
Table 3 presents physical parameters which were
recorded on each foil. We note that forces and
cavitation measurements are available for both foils
but NACA66 will be used to validate stationary
information and BA foil for non-stationary values.
Static pressure
Fluctuating
pressure
Boundary layer
velocity
Forces
Cavitation
NACA 66
Yes
No
No
Yes
Yes
BA
No
Yes
Yes
Yes
Yes
Table 3: Description of the physical quantities
recorded.
COMPARISON BETWEEN EXPERIMENTAL
AND NUMERICAL RESULTS
The first step of the validation consists of a
comparison between measured and calculated mean
stationary information like pressure on the foil. For
that purpose, several control points were imposed in
the numerical grid on the foil surface. For each
control point and each time step, pressure was written
in a file. The mean value for a chord position is then
obtained by an average of all results. Figure 3 shows
the comparison for Cp value versus chord position on
the NACA66 at 4 degrees and 11 m/s. On this graph,
3 experimental flow velocities are given. For
numerical results, we plot both LES results and
Navier-Stokes stationary calculation with K-£ model
and the same mesh as the one used for LES
calculation.
The agreement seems to be quite good, especially for
the area close to the leading edge and flow velocity of
1 1 m/s.
To continue with the validation of the numerical
process, we decided to compare cavitation inception
parameter Hi measured during experiments (with
nuclei injection) at cavitation inception with
calculated-Cpmin or the value of -Cp at boundary
layer detachment when calculation shows a
detachment. Figure 4 presents the results for BA foil
at several angles of attack. Once again, the agreement
is very good at low angles of attack. At 4 degrees, the
error between -Cpmin and hi is 10 %.
0 0,05 0, 1 0, 1 5 0,2 X/C0,25 0,3 0,35 0,4 0,45 0,5
-1,5
-
-2,5 .
, X
-3,5
[1 . . + Keeps
. . ~ LES
· experiments 9 m/s
X experiments 11 m/s
: : :
Figure 3: Pressure coefficients on NACA 66 foil:
Comparison between calculation and experiments.
2~7
if.
1.7
1,5
1.3
1,1
O,9
~ r - - - - - - - - - - - - - _ _ _ _ _ ....
~ Experiments 6 m/s / l
as Experiments 12 m/s - ~ tin
~ LES 10 m/s ~
. .. . . .
. . .
1
. ' ~ l
. . . ! .-
. alpha (degrees)
0 2 4 6 8
Figure 4: Cavitation parameter on foil BA:
Comparison between calculation and experiments.
Now, as we consider that model gives good results for
knowledge of stationary flow, we will look into the
non-stationary informations obtained by LES model.
Numerical flow description:
Several representations are issued from the numerical
process. We can take a 'photograph" of the flow at
one time or we can "record" the temporal signal of
pressure for a given control point.
First we will consider some photographs of the flow.
Figure 5 gives a view of the velocity field for BA foil
at 7 degrees and 6 m/s. The field corresponds to a
OCR for page 305
vertical plane located at mid-span of the horizontal
foil. We can see a separation bubble near the leading
edge with a closure area situated, for this time step,
near x/c = 0.07.
:~
Figure 5: Foil BA, 7 degrees; V = 6 m/s. Vector
field.
Another type of photograph is obtained by projecting
on a surface the iso-value of some quantity. We used
to draw on a surface, located at 0.1 mm from the foil
surface, the iso-value of the axial or the transverse
flow vorticity. Hence, from figure 6 to figure 13, we
present these results for BA foil and NACA66 at
several angles of attack. They illustrate three types of
flow conditions.
For low angles of attack (i.e. 2 degrees: figure 6 and
7) the flow is attached all along the chord up to the
trailing edge where a separation occurs. The
calculated flow seems to be laminar along the foil.
We just observe some lines of higher intensity of the
axial vorticity regularly spaced in span. For the
transverse vorticity, the evolution is very regular all
along the chord up to the detachment.
Figure 6: BA foil, 2 degrees and 10 m/s: axial
vorticity.
Figure 7: BA foil, 2 degrees and 10 m/s: transverse
vorticity
For intermediate angles of attack (i.e. 4
degrees: figure 8) the photograph is quite different.
Near the leading edge, we first notice a laminar
attached flow with some lines of axial vorticity. Then,
several spots of higher vorticity appear along chord
and span. The transition between laminar and
OCR for page 306
turbulent flow takes place. The spots seem to be
periodically spaced. Near the trailing edge, we
observe a separation longer than the one observed for
2 degrees. On figure 9 we present an experimental
view of the trailing edge flow at 4 degrees and 6 m/s.
Bubbles injected in the flow upstream enable to
visualise the trailing edge separation. The accuracy
between numerical photograph and experimental
view is quite good.
Figure 8: BA foil, 4 degrees and 6 m/s: axial
vorticity.
Figure 9: BA foil, 4 degrees and 6 m/s: photograph
of trailing edge separation.
For higher angles of attack (i.e. 7 degrees: figures 10
and 11), we can see the presence of the previously
described (figure 5) separation bubble near the
leading edge. Then the flow re-attaches and after the
closure of the bubble we observe spots of high
intensity of transverse vorticity which indicate the
location of vortex. On the photograph corresponding
to axial vorticity, we also notice, in front of the
leading edge detachment, the presence of several lines
of higher intensity regularly spaced in span.
Figure 10: BA foil, 7 degrees and 6 m/s: axial
vorticity.
Figure 11: BA foil, 7 degrees and 6 m/s: transverse
vorticity
OCR for page 307
from figure 14 to figure 15, the calculated pressure
versus time for BA foil at 2, 4 and 7 degrees. The
local fluctuating pressure is non-dimensionalised by
flow dynamic pressure (i.e. 0.5 pVref24.
For BA foil at 2 degrees near the leading edge (figure
14), we notice that the three chosen locations give the
same time dependent signal. The maximum
fluctuation is + 1 % of the dynamic pressure. Near the
trailing edge, (figure 15), the fluctuation increase
quickly between 93% and 97% of the chord. This
correspond to the boundary layer separation near the
trailing edge. In such a detachment, we had to notice
that the pressure fluctuation can reach 30% of the
reference dynamic pressure.
Foil BA; 2 degrees; Vref = 10 m/s
O3 .
, .
: ' : : ' : ' : :
2,O ...
a'
Figure 12: NACA 66, 4 degrees and 11 m/s: axial ~ lO
vorticity.
o
0^ O,O
-
w
~ -1,0
c,
Figure 13: NACA 66, 4 degrees and 11 m/s:
transverse vorticity.
Concerning NACA66 foil, at 4 degrees, we observe,
on the numerical photographs (figure 13), a little
separation bubble near the leading edge then a re-
attachment of the boundary layer and spots of
vorticity along the chord.
Numerical pressure signal comparison:
Let us go through the time dependent description of
the flow for different given control points. We present
x/c=O,1
, . ' x/c=O,075 ..
.. . x/c-O,025 ..
~ ~ _ ~
. . . . . . . . . . .
-3,0 . .
O,80 O,82 O,84 O,86 O,88 O,9O
T (s)
O,92 O,94 O,96 O,98 1,00
Figure 14: calculated pressure signal for three control
points.
For BA foil at 4 degrees, we have chosen to illustrate
the capability of the model to describe the evolution
of the boundary layer. In figure 16, three control
points are shown (i.e. 15%, 25% and 35 % of the
chord). At x/c=0.15, the time dependent signal is
similar to the one calculated for 2 degrees: low
amplitude of fluctuation. At x/c=0.25 we can observe
the existence of a well identified and regular
frequency (near 100 Hz) in the time dependent
pressure signal. It is a characteristic of Tollmien-
Schlichting waves which will lead to turbulence. The
pressure fluctuations are less than 5 % of the
reference value. Then at x/c=0.35, the flow is
turbulent and the fluctuating pressure at that location
is less than 1 %.
OCR for page 308
Foil BA; 7 degrees; Vref = 6 m/s
5O,O
4O,O
3O,O
2O,O
1O,O
1O,O
2O,O
-30 0
O,80 O,82 O,84 O,86 O,88 O,9O
T (s)
O,92 O,94 O,96 O,98 1,00
Figure 15: calculated pressure signal for three control
points.
Foil BA; 4 degrees; Vref=6 m/s
iL
.^
—x/c = O,35
. . . ~ x/c = O,25 . .,
—x/c = O,15 ..~
3,00 3,05 3, 10
3, 15 3,20
T (s)
3,25 3,30 3,35 3,40
Figure 16: calculated pressure signal for three
control points.
For BA foil at 7 degrees, the velocity map and flow
vorticity both indicate the presence of a separation
bubble near the leading edge. So, figure 17 shows the
fluctuating pressure at three control points (x/c=0.03;
x/c=0.07 and x/c=0.14. It appears that the fluctuation
amplitude is less than 5 % for x/c=0.03 and x/c=0.1.
On the other hand, at the control point located near
x/c=0.07, the recorded pressure fluctuation can
achieve the reference pressure. This information
corroborates the fact that this control point is situated
in the closure area of the detachment bubble. Once
again, for this angle of attack, the pressure
fluctuations near the trailing edge (figure 18) are high
and for a larger fraction of the chord than for 2
degrees. The detachment point is located further for 7
degrees than for 2 degrees.
2,10 2,15 2,20 2,25 2,30 2,35 2,40
T (s)
Figure 17: calculated pressure signal for three control
points.
Foil BA; 7 degrees; Vref = 6 m/s
3O,O t~--~
2O,O
.. -
~ 1O,O
*
,,, O,O
-
~ -100
c -2O,0 1
30 0 L....
. ~
. . .—~ x/c-O,97
--- x/c=O,93
....... x/c-O,9
2,10 2,15 2,20 2,25 2,30 2,35 2,40
T (s)
Figure 18: calculated pressure signal for three control
points.
Numerical and experimental Spectrum
The final step of our validation is the comparison
between numerical and experimental frequency
spectra of fluctuating pressure. For that purpose we
use the data measured on BA foil at 4 degrees and 6
m/s. On Y-axis we use dB referenced to 1 ~Pa. The
pressure transducer was a RESON transducer located
at x/c=0.61. On figure 19, we present four numerical
pressure spectra (i.e. x/c=0; x/c = 0.21; x/c=0.61 and
x/c=0.986) and one experimental spectrum
(x/c=0.614. The following remarks must be written:
one numerical spectrum corresponds to an
average of 12 spectra. Each spectrum
corresponds to a time step of 5.10-4 s and a
number of sample of 512.
the numerical spectrum is very accurate,
compared to the experimental one, up to 150 Hz.
For higher frequency, numerical model filters
earlier than pressure transducer.
OCR for page 309
up to x/c=0.61, the pressure level is roughly 130
dB for low frequency.
we observe for x/c = 0.21 the signature of the
Tollmien-Schlichting waves near 100 Hz.
between x/c= 0.21 and x/c = 0.61 we note that
energy switch from frequencies lower than 125
Hz to frequencies higher than 125 Hz.
near the trailing edge, the pressure fluctuation is
very high and the spectrum can reach 30 dB more
than at mid chord.
170
160
150
:4 140
° 120
1 1 ~
100
90
145
140
135
12()
110
105
100
95
| experiments
| ' empirical IMFM model
' empirical IMFM model with
_ Corcos spatial attenuation
f (Hz)
10 100 1 ()()(
Figure 20: pressure spectrum on foil BA.
Comparison between calculation, experiments and
empirical laws.
. ~ x/c = O,6 1; LES
· 0 .°:: :0=-0 - - - - - - - - ' ~ x/c = 0; LES ....
;0~004 ~ x/c = O,21; LES
.. ... ... ... - . ... . ° x/c = O,986; LES ... '
`. x/c = O,61; experiments
----''':'''';'' '''-''''''
F (HZ)
Figure 19: pressure spectrum on Foil BA; 4
degrees; V = 6 m/s. Comparison between
calculations and experiments.
dip (f) dB ref. 1
The main purpose of this development is to be able to
calculate the boundary layer excitation on a foil in
order to calculate the foil vibro-acoustic response. On
figure 20, we illustrate the usefulness of our model.
So, up to now, propeller designer had empirical
models based on boundary layer characteristics.
These models were developed from flat plate
experiments. In that way, the adverse pressure
coefficient distribution cant be well represented.
During tests in G.T.H, we measured velocity profiles
in the boundary layer at the pressure transducer
location. Hence, we had a measure of the boundary
layer characteristics corresponding to the pressure
measurements. Using empirical models and measured
boundary layer characteristics, we obtain two of the
curves presented on figure 20. It is clear that it is far
from (more than 10 dB) both the reality (experimental
curve) and LES spectrum. With LES calculation, we
are able to know the exact low frequency level. Then,
since the model, at the moment, filters to early, we
can use this low frequency model to calibrate
empirical models.
EFFECT OF REYNOLDS NUMBER ON
CAVITATION
Another purpose of this project is to have a better
understanding of the flow on a foil in order to predict
more accurately the type and the development of
cavitation patterns. Hence, with the photographs
shown here after, it is clear that the boundary layer
state and its characteristics are very important for the
evelonment of cavitation
a) Foil BA: ~ = 0.85 ;ot= 2 decrees; V = 8 m/
b) Foil BA: ~ = 0.85 ;ot= 2 degrees; V = 10 m/s
OCR for page 310
\ ¢~ · 1 ~ ~ _ rat rid r _ ~ 1 ~ r 1 ~ I
b) Foil BA: ~ = 2.4 ;ot= 7 degrees; V = 5 m/s
d) Foil BA: ~ = 0.85 ;ot= 2 degrees; V = 13 m/s
Figure 21: effect of Reynolds number on cavitation.
Flow with nuclei injection.
For small angles of attack (i.e. BA foil at 2 degrees;
figure 21) we note a strong effect of Reynolds
number on the cavitation pattern. For velocity lower
than 8 m/s and o= 0.85, we did not observe any
cavitation. Then from 8 m/s to 13 m/s, cavitation
appears like little fingers attached to the foil surface.
As the velocity increases, their number and length
increase too and their attachment location moves near
the leading edge.
At this angle of attack, the LES calculation at 6 m/s
indicates that the boundary layer is attached to the
foil. Some lines of axial vorticity are also visible
along the span.
The evolution of cavitation with Reynolds number
must be linked to the ratio between boundary layer
and roughness height.
For high angles of attack (i.e. BA foil at 7 degrees;
figure 22) photographs show sheet cavitation related
to separation bubble which was observed on
numerical photographs and with numerical pressure
fluctuation versus time. When the velocity increases
at a fixed ~ value, the length of the sheet seems to be
constant. But we observe some little cavitating fingers
attached to the leading edge upstream the cavity
detachment line. Their number increases with
Reynolds number.
a) Foil BA: ~ = 2.4 ;ot = 7 degrees; V = 4 m/s
c) Foil BA: ~ = 2.4 ;ot = 7 degrees; V = 6 m/s
d) Foil BA: ~ = 2.4 ;ot = 7 degrees; V = 7.2 m/s
Figure 22: effect of Reynolds number on cavitation.
Flow with nuclei injection.
1
For NACA 66 foil, as illustrated on figure 23, the
sheet cavitation appears also near the leading edge in
correlation with calculated separation bubble (figure
124.
NACA 66; is= 1 ;ot = 4 degrees; V = 6 m/s
Figure 23: sheet cavitation developed on NACA 66
foil. Top view of the foil.
The cavitating unsteady flow is illustrated on figure
24 a) and b). These correspond to the same flow
condition at two different times. We can observe
cavitating structures carried along the chord by the
flow. This type of cavitating flow was already
observed on small foils by Kawanami (Kawanami
and al. 19984. Their spatial repartition seems to be
OCR for page 311
periodic. The time frequency between two
consecutive structures is 50 Hz.
a) NACA 66; is= 1.75 ;ot= 6 degrees; V = 6 m/s
b) NACA 66; is= 1.75 ;ot= 6 degrees; V = 6 m/s
Figure 24: sheet cavitation developed on NACA 66
foil. Top view of the foil.
CONCLUSION
This paper presents results of an evaluation of a new
numerical tool, based on LES method and developed
by Bassin d'essais des carenes. This evaluation was
conducted by comparison with experimental results
obtained at high Reynolds number in the G.T.H. for
non-cavitating and cavitating flows. The accuracy of
numerical calculation had been obtained after many
mesh tests.
The numerical tool provides the knowledge of non-
stationary quantities for non cavitating flow.
Moreover, the LES calculation gives pressure
coefficient repartition more accurately than standard
Navier-Stokes calculation. The boundary layer
development on the foil is well represented including
transition or Tollmien-Schlichting waves. Pressure
fluctuations acting everywhere on a foil can be
quantified which is important to minimise radiated
noise at the design stage of a propeller or appendages.
The accuracy of the numerical model applied to real
flows (with adverse pressure gradient) is better than
that of empirical models for the prediction of pressure
fluctuation spectrum. Moreover, the knowledge of the
boundary layer development help for cavitation
patterns.
This type of calculation is still time consuming,
however, we are looking to include it into a more
complete design process.
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DISCUSSION
I C lik
We t Vi ginic University, USA
It is surprising on one h Ed, Ed encouraging on
the other h Ed, to see that the mthors attempted
to perform LES using c commercial code,
FLUENT The time accuracy is first order The
use of unshuctured Ed non-unifomm grids will
reduce the spatial accuracy to cam ost fu st order
Hence, She mmmericcl viscosity will be let ge
acting es c filtering mech mi m The only way to
obtain reasonable results is to use ve y smell
time tep Ed ve y smell grid sites How m my
grid po mts w re located m the boundary Dyers?
Whet was the time step used? Is She time step
usedrektedto She resolution limit of 100 H in
the pow r spectna of pressure fluctuation ?
A of her issue is She dependence of She
cclcubtions on Rey olds mmmber without using c
sub-grid scale model Could the simulations
predict dependence of separation point on the
Reynolds mmmber? As for validation of unsteady
calculations the only results shown concern She
pow r spectra of pressme fluctuations But there
mything beyond 100 H seems to be numerical
noise it is necessary to compare the unsteady
pressme fluctuations duectly to measurement to
seeiftheamplit de mdthefrequencycmbe
predated
AUTHOR'S REPLY
The cell si e in She boundary layer is Opt ally
I I mm following the chord Ed I I mm
following She sp m The fu st grid point is located
et y+= I Ed w mesh in altitude up to y+=100-
200 using c geometri 91 ratio of 1 5 with
hexched ons 200000 grid pomts are located in
this zone (16% of the total amount of the cells
mmmber m She domain ) The time step used for
the simulation is 0 0005 seconds Ed it is not o
priori related to the resolution limits of 1 00h
No simulation ht. been performed to es Butte
the dependence of separation point on the
Rey olds mmmber Perhaps we could pay some
cttff~tion on this subject m She fut re
Concerning the mmmericcl noise, it is very
dangerous to perform comparison betw en
mmmericcl Ed experimental results The
mmmericcl noise is the result of c diffusion of the
rounding error Ed es c result it is not et all
representative of physical noise The objective is
to make it es low es possible so that it c m be
as mmed to be negligible
Representative terms from entire chapter:
leading edge
