Wichita State University Libraries
SOAR: Shocker Open Access Repository
Wind Energy Reports, no.13
Center for Energy Studies
Characteristics of Wakes Downstream of Circular Cylinders and 12Sided Cylinders, as Determined by Wind Tunnel Tests
Melvin H. Snyder and W.H. Wentz Jr.
Wichita State University
Recommended citation
Melvin H. Snyder, W.H. Wentz. Characteristics of Wakes Downstream of Circular Cylinders and 12-Sided
Cylinders, as Determined by Wind Tunnel Tests. Wichita, Kan: Wichita State University, 1981. -- 101 p.
Digitized by University Libraries and posted in Shocker Open Access Repository
Citable Link: http://soar.wichita.edu/dspace/handle/10057/6043
Terms of use: in the Public Domain
~Av~oS'c:)..;J
7)(.
..
-
'0 L.St"U"T"
WER-13
WIND ENERGY REPORT NO.13
Characteristics of Wakes
Downstream of Circular Cylinders
and 12-sided Cylinders,
As Determined by Wind Tunnel Tests
by
Melvin H . Snyder
and
W . H . Wentz , Jr.
WIN 0 ENERGY LABORA TORY
WICHITA STATE UNIVERSHY
Prepared for
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
Lewis Research Center
under NSG - 3277
JanuarY , 1981
liER-13
Wind Energy Report No. 13
CHARACTERISTICS OF WAKES OOWNSTREAM OF CIRCULAR
CYLINOERS ANO 12-SIOED CYLINDERS AS OETERMINEO BY
WINO TUNNEL TESTS
by
Melvin H. Snyder
and
W.H. Wentz, Jr .
Wind Energy laboratory
Wichita State University
Wi chita. Kansas
This work has been funded by lewi s Research Center of the National
Aeronautics and Space Administration by Research Grant No. NSG 3277,
supplements 3 and 4 .
January 1981
ABSTRACT
To obtain models of the near-field wakes behind cylinders of the types used
as support structures for wind turbines, wind tunnel tests were conducted in the
Walter Beech Memorial Wind Tunnel of Wichita State University.
The tests were
surveys of wakes downstream of circular cylinders and of 12-sided cylinders.
Surveys were conducted at stations ranging from 20 to 90 downstream of the
cylinder centerlines.
Among the results of the survey are the following:
The wake downstream of a cylinder has three characteristics which may affect a
wind turbine blade passing through the wake :
a.
A velocity deficit compared to the freestream wind.
b.
Random turbulence of wide frequency range and moderate strength,
c.
low frequency (less than 100 Hz) periodic vibrations.
The velocity deficit profile for the near-field is significantly different than
published far-field profiles.
Turbulence associated with the mixing has highest
values on both sides of the wake centerline, where ~ values are highest.
The
magnitude of turbulence is about the same for 12-sided cylinders as for circular
cylinders.
The separation point and geometry of the wake of a l2-sided cylinder
is independent of Reynolds number (unlike a circular cylinder).
Rounding the
corners of a l2-sided cylinder causes some dependence on the Reynolds number and
reduces the strength of the periodic motion.
Spiral strakes on a circular
cylinder can eliminate the periodic motion of the wake--at the expense of increased velocity deficit and turbulence of the wake.
i;
SYMBOLS
o
Cy1 inder diameter
f
Frequency of periodic motion of wake
k
Number of bi ns
m
N
Number of statistical parameters calculated in wake analysis
Number of samples taken for turbulence analysis
Dynamic pressure, 1/2 pV'
o
Cylinder radius = "2"
q
R
r
Radius of corners
Re
S
Reynolds number
Strouha1 number
Ul Dca 1
laca 1 vel aci ty
Ux
Uy
Uz
uxz
x-component of
y-component of
z-component of
local velocity
u,
~Iake velocity deficit. 1 -
-U
Umean
=~
local velocity
local velocity
local velocity
component in xz plane
v:
u'rms
V~
x
y
z
o
a
X'
Free stream velocity
Wind-direction axis
Cylinder-axis direction
Dimension normal to x-y plane
1/2-width of wake
Orientation of 12-sided cylinder
Standard deviation = u'rms
Chi-square
;;i
INTRODUCTION
Wind turbine towers are often composed of cylinders, either as components
of truss-type towers or as single element towers.
Two types of towers and tower
elements in use are circular cylinders and 12-sided cylinders.
In the cases of
turbines operating with the rotor downwind of towers there have been some undesirable results of the blades passing through the tower wake.
These results include
fluctuating loads on the blades resulting in transient torque and thrust loads.
and also unwanted noise.
Published literature on wakes of cylinders and of cylinders is not adequate.
Standard fluid mechanics textbooks treat the nature of separation of the boundary
layer from circular cylinders at subcritical and supercritical Reynolds numbers
and relate the separation patterns to the pressure distribution on the cylinder
and the resulting drag coefficient (e.g., see references 1 and 2).
The wake pro-
duced by separation of the flow from the cylinder is marked by velocity deficiency,
i.e., decreased kinetic energy. and by unsteady behavior.
In reference 3, McCroskey points out that the
II • • •
characteristic unsteady
feature of nominally uniform flow past a bluff body is the strong tendency for
the free shear layers to develop into alternate vortices in the wake •... the
alternate vortex shedding with dominant periodicity is most pronounced for
100~Re~200,OOO.
This encompasses the vortex-street and subcritical regimes,
where the flow near the surface of the cylinder is laminar up to and past the
point of separation; transition to turbulence occurs in the wake •...
McCroskey states that at hi gher Reynolds numbers (0.2 x 10 6
<
II.
RN
<
3.5 x 10 6 )
a turbulent boundary layer separates farther around the perimeter of the cylinder
1
2
producing a narrow irregular wake.
"The dominant periodicity ceases and the
Strouhal number is usually ill-defined, although significant fluctuations continue.
These fluctuations are wide- band, but not completely random ... flow ... is
highly
sensitive to freestream turbulence. surface roughness, and three-dimensional
disturbances."
(reference 3)
Roshko has described the situation as "organized motion," such as vortex
shedding from a circul ar cylinder, superimposed on a background of general
turbulence (reference 4).
There ;s uncertainty regarding just what it ;s about the nature of the wake
which causes the noise and other effects mentioned above, i.e., ;s it the (1)
periodic structure of the wake, (2) veloc ity deficit, or (3) turbulence of the
wake?
To obtain a model of the wake, "/ind tunnel tests were conducted in the
Walter Beech Memorial Wind Tunnel of Wichita State University.
The tests were
surveys of wakes downstream of circular cylinders and of l2-sided cyl inders.
MODELS
Four models were tested.
Two models were circular cylinders, 0.17 m (6.7 in)
diameter and 0.508 m (20 in.) diameter.
There were also two l2-sided cylinders;
the smaller had a diameter of circumscribed circle of 0.182 m (7.17 in.), and the
larger had a 0.508 m (20 in.) diameter circumscribed circle.
The smaller models
were mounted horizontally across the 2.13 m x 3.05 m (7 x 10 ft.) test section
and the larger models were mounted vertically (Figs. 1 and 2).
The wake of the cylinders was surveyed at various stations downstream.
t,lost of the published details regarding cylinder wakes is for long distances
downstream (e.g., Schlichting, velocity deficit greater than 50 diameters
downstream- - reference 5; see also reference 6).
f'10st downwind wind turbine blades
will be operating in the range of 3 to 6 diameters downstream of the centerline
3
of the cylinder producing the wake.
Surveys were conducted at stations 2 0,
3 0, 4.5 0, 6 0, 7. 5 0 and 9 0 downstream of the cylinder eenterlines (referred
to in the data as x
= 200%, 300%, 450%, 600%, 750%, and 900%- -see Figure 3).
:
INSTRUMENTATION AND DATA PROCESSING
Pressure Probe Survey
Two types of instrumentation were used.
Pressure measurements were made
using a 5-tube probe (Figure 4) to determine local vel ocity .
Pressure data were
processed on-l i ne by the wind tunnel minicomputer and the data output includes,
at each station, local velocity and the components of the local velocity.
Tabulated data are presented in the appendix to this report (WER-13A
publ ished separately).
Reyno l ds number and Mach number are also l isted.
Re~
and
M~
It should be noted that
are calculated for the last point in the run.
In almost every run
using the 5- tube probe, the tunnel dynamic pressure was held constant so that
the Reynolds number and Mach number were practically constant throughout each
run.
Hot Film Anemometer
The second phase of testing of each model was a survey of the wake using
a hot-film anemometer.
Figure 5 diagrams this data system.
Linearized voltage
signals from the hot- film anemometer were fed directly into the minicomputer at
a pre- set sampling rate.
In the present tests 6000 measurements were made at
each station at a rate of 400 Hz, for a total sampling time of 15 seconds.
These
data were processed as outlined below in about 40 to 45 seconds per station.
Voltage measurements were digitized, stored, and converted to velocity values.
The velocity values were processed to determine the sample mean and standard
deviation (a).
The standard deviation of a velocity sample ;s the turbulence
4
intensity, when non-dimens;onalized by a reference velocity.
In the present
case, local turbulence intensity lias calculated, based upon the loca l mean veloc-
ity. and global turbulence intensity was calculated based upon the remote free-
stream velocity.
Umean
where N ;s total number of samples.
N
L:(u,-u)
Standard deviation = cr = u1rms
=
"Global Turbulence Intensity" = TI =
2
,. ,
N
u' rms
V
~
u'
"Local Turbulence Intensity" = TIL =
rms
u
Velocity distribution was determined using a method bins.
Based on the
mean and standard deviation results, a series of seven bins are used for determination of the sample histogram.
The central bins are of cr width, centered about
the mean, and the 1st and 7th bins are the "tails" for data respectively below
and above the central bins.
The entire sample is then sorted into these bins to
determine the distribution of the sample.
The number of measurements in each
bin. divided by the total number of samples is printed (Figure 6).
A Chi-square analysis was performed for each data set to determine how
closely the particular observed distribution compared to a Gaussian distribution.
The Chi - square parameter is a measure of the deviation of the observed distribution
from a Gaussian distribution using the same bins arrangement.
5
X'
=
E
N
(Bj - BG;)'
i =1
BG;
where B; : number of observation samples in the ith bin/total samples
BG; = number of samples for a Gaussian di stribution in the ith bini
tota 1 samples
large values of x2 indicate large differences between observed and Gaussian.
while small values for x2 indi cate that the observed distribution tends to be
Gaussian.
For the present case, the number ofdegrees of freedom of the di stribution
is given by:
~
where
k
and m
= k - 1 - m (see reference 9, page 202)
,. number of hi ns
=7
= the
number of population parameters determined from the sample = 2
(the two parameters are the sampl e mean and standard deviation)
Thus 1
~
=7 - 1 - 2
~
=4
Accordi ng to reference 9, x 2 values for a 4-degree of freedom population
are:
X' . 95
=
9.49
X' .05
=
. 711
These values signify that if the observed x2
>
X2 .95 there is 95% confidence
level that the sample is not from the assumed (Gaussian) distribution.
On the
6
other hand. if the observed X2
<
x2 .0S' reference 9 states the data may be suspect,
since the implication is that there is only a 5% confidence level that the distri-
bution is not Gaussian.
Spectral Analysis
Another technique for analysis of measurements of an apparent random nature
is spectral analysis.
In the present experiments, an analog spectrum analyzer
(Hewlett-Packard model 3580A) was utilized.
Spectrum analysis provides inform-
ation as to whether periodicity is present in the signal being measured. and if
so, the dominant frequency or frequencies of the periodic signal.
Spectrum
analysis measurements were made at selected stations in the flow field.
The results
were recorded in the form of photos of an oscilloscope trace of the power spectral
density (psd).
Figure 7 shows a typical photo obtained during these tests.
For
signals for which significant periodicity is present. the frequency or frequencies
at which peaks in the psd appear are tabulated.
These frequencies are then non-
dimensionali zed and presented in the form of Strouhal numbers (S = fd/Vw =
frequency * diameter/free-stream velocity).
CIRCULAR CYLINDER TESTS
Testing
The smaller (6.7 in. dia . ) cylinde r was mounted horizontally as shown in
Figures 1 and 3.
The wake was surveyed at stations x
and 900% using the 5-tube pressure probe.
inch from z
=
300%, 450%, 600%, 750%,
Measurements were taken every half-
= - 10 inches to z = +10 inches. Tunnel speeds were chosen to get as
wide range of Reynolds numbers as possible.
7
TABLE 1. CIRCULAR CYLINDER TESTS
Oynami c pressure, q
(p.s.f . )]
[N/m'
81.4
215.5
359.1
574.6
957.6
766.1
1436.4
3112.2
(1. 7)
(4.5)
(7.5)
(12.0)
(20.0)'
(16.0)'
(30.0)
(65.0)
Reynolds number
:
(Average)
0.17
0.28
0.34
0.42
0.52
0.47
0. 60
0.76
x 10'
x 10'
x 10 6
x
x
x
x
x
10'
10 6
10'
10'
10 6
*limited number of runs
Survey of the wake using the hot film anemometer was performed completely
at x
= 300% and
to a more limited extent at the other stations.
Frequency of the
periodic component of the wake \'las determined at all stations and for a complete
range of Reynolds numbers.
Two sets of spiral strakes were attached to the 17 em. circular cylinder
and the wake was surveyed using the five-tube probe at stations x
=
300% and 600%.
The strakes were fabricated from sheet aluminum. were 1.6 centimeters high (app rox.
10% of diameter), and made an angle of 30° with the cylinder centerline (Figure 8).
Initial testing was done with the strakes in the gOo position in the plane of the
survey (x-z plane), as in Figure B.
The cylinder was rotated 90° on it axis
putting the strakes at the 0° and 180° pOSition, in the plane of survey.
The large (.50B m dia.) circular cylinder was tested onl y briefly after all
of the l2-sided cyl inder tests had been completed .
It was mou nted vertically
in the wi nd tunnel to provi de as much clearance between the cyl i nder and side wa 11
as possible.
Only the hot-wire anemometer was used at x
= 300%.
8
Test Results
Reversed f low. which results from separation of the boundary layer from a
circular cylinder, was not found to be present in the range of 3 to 9 diameters
downstream at any of the test Reynolds numbers (.17 x 10 6
<
RN
<
.76 x 10 6 ).
:
Apparently the reversed flow region is confined to the region between the
cylinder and the x
= 300% station
(Figure 9).
Figure 10 more clearly shows the nature of the velocity defect in the wake.
U
u1 is plotted at five stations in the wake, where u1 = 1 - V~x
As expected, the
velocity deficit profile is affected by the nature of the separation from the
cylinder.
Critical Reynolds number is approximately 400,000.
At less than
critica l Reynolds number, the laminar boundary layer separates near the 90 0
pos ition on the cylinder.
At greater Reynolds numbers the boundary layer which
separates is turbulen4and it separates downstream of the 90 Q point resulting in
a narrower wake which should be characterized by more turbulence but with a smaller
velocity deficit at a given station because of the more effective mixing in the
wake.
These expected results are shown in Figure 10 .
Figure 11 summarizes the
effects of Reynolds number on the velocity deficit profiles at x
= 300% and 750%.
Note that at Reynolds number of 420,000, the wake is not symmetri cal on the center·
line.
This lack of symmetry is apparently due to turbulent separation on one side
and laminar separation on the other side of the cylinder, probably due to a small
difference in cylinder smoothness so that critical Reynolds number was slightly
different for the two sides.
Oil dot technique was used in runs 45 - 49 to visualize the separation point.
These tests seemed to confirm unsymmetrical separation at about R.N.
= 0.42
x 10 6 •
The shape of the wake velocity defect was nondimens;onalized by plotting
ul/ulmax vs. z/ zR' where zR is the semi -wi dth of the wake .
The resulting profiles
are compared in Figure 12 with the profile which Schlichting defines at a long
distance downstream (greater than 50 diameters--see reference 5).
Figure 12a
9
is for the subcritical wake (R.N.
(R.N. :: .76
X
10 6 ).
~
.17 x 10 6 ), and Figure 12b is the profile at
The non-dimensional profiles are quite sensitive to the wake
wi dth whi ch ; 5 chosen.
In both cases. the profil e approaches the "s tanda rd shape"
as the wake progresses downstream.
Growth of the wake is indicated in Figure 13.
The locus of 50% u1max
position spreads at an included angle of about 3° (1.5° to centerline) for the
subcritical wake.
The supercritical wake (Figure 13d) starts narrower and the
50% Ul max lines diverge at only about 2 degrees.
Turbulence intensity is plotted at the x
=
300% station for various cylinder
Reynolds numbers in Figure 14.
Highest levels of turbulence corresponds to high
subcritical Reynolds numbers.
It is also apparent that turbulence intensity ·has
a double peak--corresponding to the mixing regions.
corresponds to highest
Highest turbulence intensity
%r and lower values of turbulence are at ~+ 0 (at
the
center of the velocity deficit profile and at the edges of the wake).
Turbulence intensities are mapped in Figures 15a and 15b.
As described above, a periodic structure ;s superimposed on the general turbulence of the wake (or vice-versa).
represented in Figure 16.
The frequency of this periodic structure is
The variation of Strouhal number with Reynolds number
agrees very well with that reported by McCroskey (reference 3), i.e., below
critical Reynolds number, S
= 0.2;
above RN
= 400,000, S increases to greater
than 0.4.
In reference 4, Roshko illustrates the tendency for vorti ces in a wake to
combine,stretching the length of the periodic structure as it moves downstream.
This action should change the frequency of the wake in a way which may be significant to the perceived noise of the wake.
Figure 17 indicates some shift in the
wake frequency as the instrumentation is moved downstream.
Figures 18 and 19 show the velocity pattern in the wake after spiral strakes
were added to the cylinder.
measurements were made.
Unfortunately. due t o press of time, no turbulence
10
When strakes were added, two important results were noticed.
The reversed
flow (dead·water) region was increased in size extending beyond the 300% station
when the strakes were at ~90 ° (in plane of measurements).
Also, the periodic
structure of the wake was weaker, or else the general turbulence was stronger, so
that any periodic motion was completely immersed in the random turbulence so that
no dominant frequency could be measured.
The fact that the reversed flow region extended beyond the 300% station downstream of the +
_90 0 strakes. but did not reach 300% downstream of strakes at 00
and 180 0 , indicates that the spiral strakes produce a fairly strong 3-dimensional
motion to the wake.
12-SIDED CYLINDER TESTS
Testing
The mounting and testing of the 12 - sided cylinders was the same as that of
the circular cylinders.
The large [.508 m (20 in . ) dia. circumscribed circle,
.491 m (19 .32 in.) dia. inscribed circle] cylinder was tested first.
It was
immediately obvious that the periodic component of the wake was quite strong.
The buffeting wake forced the tunnel dynamic pressure to be limited to less than
1 k N/m2 to prevent structural damage to the wind tunnel control room windows.
Similarly. the strength of the periodic component of the wake of the smaller
[18 .2 cm . (7.17 in.)
dia. circumscribed circle. 17.7 cm . (6 . 95 in.) dia.
inscribed circle] 12-sided cylinder was greater than for the similar sized circular
cylinder.
The dynamic pressure of those tests was limited to 2.15 k N/m2
because of model and test section wall vibration.
Table 2 lists test ranges.
12
Also. the nature of the wake and the rate of wake spreading is more affected
by orientation of the cylinder than by Reynolds number.
This should be so.
On a circular cylinder (or other smooth shapes, such as an elliptical cylinder),
the nature of the boundary layer (laminar or turbulent, energy level, etc.) is
a function of the Reynolds number.
Because of this dependency. the point of
boundary layer separation ;s a function of the Reynolds number; the point of
separation is the primary factor affecting the wake geometry.
In the case of the 12- sided cylinder (probably any cylinder having a polygon
cross-section). the point of separation is fixed by the corner, not primarily
Reynolds number.
by
The corner, which produces an adverse pressure gradient. will
be the point of separation.
Thus the geometry of the wake is fixed by geometry
and is relatively insensitive to Reynolds number.
This hypothesis is reinforced
by the turbulence intensity plots of Figures 27 and 28 and the Strouhal numbers
presented in Figures 29 and 30 . The Strouhal number is not a function of Reynolds
number; it is approximately constant for a given orientation.
Turbulence
intensity of the l2-sided cylinder wake is of the same order of magnitude as that
of the wake of a circular cylinder.
However. the strength of the periodic
component of the wake motion is much greater for the 12- sided cylinder than for
the circular cylinder.
Rounding the corners of the l2-sided cylinder produces two effects:
(1) the strength of the periodic component of wake motion appears to be reduced
(observed qualitatively. not measured), (2) some dependency on Reynolds number
is produced (see Figures 27 and 28).
SUr~MARY
OF RESULTS
The run log and detailed listing of data and computed answers are contained
in the appendix (WER - 13A) to the present report.
The following results may be stated:
13
1. The wake downstream of a cylinder has three characteristics which may
affect a wind turbine blade passing through the wake:
a. A velocity deficit compared to the freestream wind,
b.
Random turbulence of wide frequency range and moderate strength,
c.
Low frequency (less than 100 Hz) periodic vibratio ns.
2. The velocity deficit profile for the near- field is different than the
published far-field profiles (e.g .• reference 5).
3. The turbulence associated with the mixing has highest values on both sides
of the wake centerline, where dU I values are highest.
dz
4. The magnitude of turbulence ;s about the same for 12 -sided cylinders as
for circular cylinders.
5. The strength of the periodic component of the wake structure is greater
for a l2-sided cylinder tha n for a circular cylinder.
6. The separation point and geometry of the wake of a 12-sided cylinder
is independent of Reynolds number (unlike a circular cylinder).
7.
Rounding the corners of the l2-sided cylinder causes some dependence on
the Reynolds number and reduces the strength of the periodic motion.
8.
Spiral strakes on a circular cylinder can eliminate the periodic motion
of the wake--at the expense of increased velocity deficit and turbulence
of the wake.
14
REFERENCES
1. Hoerner, S.F., Fluid Dynamic Drag, published by S.F. Hoerner, Midland Park,
N.J . , 1958.
2. Binder, R.C . , Fluid Mechanics, Prentice -Hall, Englewood Cliffs, N.J., Fourth
Edition, 1962.
3.
McCroskey. W.J., "Introduction to Unsteady Aspects of Separation in Subsonic
and Transonic Flow," AGARD,
4.
Roshko, Anatol, tlStructure of Turbulent Shear Flows: A New Look,lI Dryden
Research lecture, AlAA Journal. vol. 14. no. 10. October 1976 .
5. Schlichting. Hermann, Boundary Layer Theory, McGraw-Hill, New York.
6.
Schetz, Joseph A., Injection and Mixi"¥ in Turbulent Flow, Volume 68, Progress
in Astronautics and Aeronautics, A AA, 1980.
7.
Wentz. W.H., Jr., Howe. D.C .• Fiscko. K. A., and Habluetzel. T.. "Application
of Split-Film Anemometer and Mini-Computer for Measurement in Turbulent
Separated Flow," Business Aircraft Meeting and Exposition, Wichita. Kansas.
April 1979, SAE Paper 790601.
9.
Speigel, M.R., Theory and Problems of Statistics.
Shaum Publishing Company,
1961.
10.
Kuchemann. 0 .• and
York, 1953.
\~eber,
J . , Aerodynamics of Propulsion. McGra\>I-Hill, New
z
Wind Tunnel
Velocity
V~
Figure 1.
i,
---..,.'
_-=-:: ___
~
u.
,uz
-I-A--+X
Model Mounted Horizontall y in Wind Tunnel.
",,1.J.,
Figure 2.
Cylinder Mounted Vertically in Wind Tunnel.
~
"0
"-
0
..,
~
0
0
M.o()
X "l1;li' ; 0"1:
· -.T2.rr~
' ~
"~
' ~~~'~!"~!"~!(1~
, " I~
"~'''~
'' ~
'''~,~
,,,
-0.99",--1
Wind
+
t
1\
. \
1-1- -- ---- T.,.
Fi gure 3a.
_
1
" - - - '_ _ _<'
C.~.~II.I
Section - - --
5
IIhtl lll.
- - -- --1
Wind Tunnel Test Section Showi ng Wake Survey Stati ons.
45.8cm D. endplat.s
C.
1, 83m
Figure 3b.
- - - - ---1
Circular Cylinder Model Dimensions.
Pitch Ports (P, & P,)
Total Pressure
Port (P. )
3 . 175 mm
Yaw Ports (P, & P, )
P,
I
p-®:.-P
,
•
P,
~
3
1+-- 6.35 mm
Fi gure 4.
Fi ve - t ube Pressure Probe.
,
~ (12 3 "5)
OVH for calibration of
laeall ve loc ity
SIGNAl
CONDITION I NG
(llnear l zer)
''''''''0, /
MechanI S"~
r--
<
EJ
ISlg.Gen.
,
~""'-:::
-
~ F~IA AlleDlOllleter
--
~
I"
n
WI ND TUNNEl
1 1 ')',0"
,,
Figure 5.
I
PACER to control SaMpl ing rate
-,
OOTPUT:
, ,
_J __
~l--
r-
,,
I) 11111 "
CORE MEMORY
,,
I
I
,,1( 6000 SllIIPl es ) ,II
,- ,
L...
.
CPU
CRT (or qualitative observ alion
p~~
•
.'
~.
TI ,Tll
His t ogra.
2
X
SPECTRtJ4 ANA LYlEA
I ,"u ....
Hot Film Anemometer Data Acqu i sition and Processing System.
Velocity
Samp l es
+
SAt-IPLE
//
//
/
I
/
/
/
--0_
/I
--0
B2
B1
/
B3
SO RTIN G
I \
I \
I
I
0
-
\
B4
B5
L.....-_
0.-----...1
Mean tVe 10city
( BN
B7
B6
=
Number of samp le s in nth bin I Total samp l es)
Figure 6.
Sorting of Data Samples into Bins.
_ _... _
._----
Figure 7.
-- - - - -
Sample Spectrum Analyzer Trace .
Plane of Wake Survey
Wind.
Sirakes In 90° Position
Figure 8.
Spiral Strakes on Circul ar Cylinder.
, i
CIRCULAR CYLINDER
Se pt~. r
DIIIIII! l e,- · 1i .7 il\( "('~
PSf
!
, Ii I' ' I I ' I' '
J " f~ ' -, I
I
,
!
I
l,I - ~!' - i
i'
I
I'
Roo oo , ..
••
::'
I'
II .!
i
:
I
I
I
4
"
1
I
.. ; ' ::,
, '"
I ii ' 1 '
I I ' I,
i
,
.!
I
I
I
!
i
FI GURE
g A,
I
I
I
I
I
I,
~
;I
j
I'
~S"O
1
1
,
:,
I:
j
"~,"
'
I
I I Li
I
! I,
L
I
WAKE Of CIRCULAR CYL INDER .
I'
!:
t.
,
I
I"
no ...IL.i.:EL
;
RII/'I
,
,
,,
I; ,
'
t"
l
I
,
I,
, ,.. , ,
m':h~~n"'l
,"
hI-
,
I
I
J
I
I ,
'
'
,
..
;
."
I'
'
I
I
,
'I
I
I--!',H,r-I
,
,
,
,
,Ii
,
".
~
"
.1 " t
,I.'
' .
::
Run no . ~_
••
, ,I
I
I
,
j'"
,
i t:':',';' :, ,'6
I
1: "
,
I
I
7fO
-;,
,
~ lII3.~+:,I !' " h-H." +,'I++:
I
,
I
•
no .--L5L_
••
,
ii',;.:;:"
.:~· : "W1 'I ':;: ,'
..
I
"
,
:
II I
••
"
"
1'_
.
I
Run
1
t
1: I
I',
-
'I'
I Jd
'l'
I
I" '1 I'" i i
I
Ii '' !
I i i i l l : ' II ' I 'I II i
I I ,f I.;
'1 : i i i II !
!
I
'
'
I
'
. 1 ,- j i I I I I , , I t,1 i I ' , ~ It 1
1)1
I
r-
,
,I I
I' i ! I l
i :' 11 :I' Ii, I1, Ii I' :I I!I II' :1,II
I!
ii .
I ' II' II " : 1I
,",
,I;1- 1-1';+
I' l-r-I'l N
'
i ,
,
,
,
" '
t
1
,I
•
' :' ,!aW'~~t:, I,LI,
,
'
II I I
;:
i! !' ! !" I
:
'I' '
:'
,
It>1j- i
jl
'
Ro...
S
,
! ·i
il
l- -
1
I
~l:-
.I
I
!
I
I
l
300
L
1!
1
,I
- ';"1-'1':I,J: I'I ;1
" I I -I I. I
It,Ii I~ +I,~I
'
I
i III ( II !II
~ 0.173 . 106
I '
~
~ i ,l
1960
" . _ U
R. N.
I'
"
1'1" ,
: I .
"
" ;.''
, I. '
,
'",
,
' ..
,
,
"
I'
I
i
,i
, !
I!
I, ;
,
I, :,' !I f"~I
,
l.;
t
L
I
I,
1 CIRCULAR CYLINDER
q ~ ~ps'
Ola~ t e r ~ r..1 inche s
I I I !I I i'
1
,
I,
:
:
,
I
I
"
"+++' H
'I"':,
I'
i'
,
"
1,1
,,
I I111
i
I
!i
mi'
!
I
j
I I" I
I
t
"
1+,
"f
"I
I
I ,"
i
i
'
I i i i_:
I
I ',I!'
'
'I
i,
"
:'
,
,"
',
,
I
I
I,
!,
I
I i
,I
,
'I,
'I
,
: .,
j,
", '
oj
Iii
"
'
'II
I
FIGURE 9a. WAKE Of CIRCULAR CYLIHDEH.
I I' I
' 1';,;l
il1: I ,'
.'
,I
I,
;Ill! Ii:
r
i,1
I tl "
"+'I-"f
'P:! "
I
I
II'
I
'I: d'
\ "
1
i
~,r
'" '-I I;:'" '" '-1+,"+'-' I
-I-+-H-~'
.~
I
'
,
"
; 1'1 1-: I ! I i
I I I ! i! i I ii' I I 'I: I ['
I : I II I II I
I!
'I
i! 0
• <"J")
I
!
".,
,
I'
,
,j
i IIIi: !! i
•,
. ",
, -"";T
l '-"' ~
I
I"
I
• •
"
I
"
_~,
"I
I ii '
,
~~~'~- _I i i'
,
I 1
, III ' Ii'
I
I,
,- 11
,
"I
·1 Run no.
I
I ,I
"
.' I - I
j-
!'
I
I
I : i II
III ,I, i ! iii
i
'~-' "1,1+,"1--1
,j
II
I
R. H. ..!: O, ;;:72.10 6
,
I,
It"
Septftltler 1980
,•
,
1:1
i
'
I
-I ! I
I
I,
,,
I
i, ' II
I ,
'I
I
I
'I
'I I
Run no. 27
.I
~
gO"
I
I
'I
I, ' ,"
CIR CULAR CYLINDER
Stp tewl!r 1980
q • ~$ f
Dla_ ler · 6.1 Inthc~
It . N. ~ O .3 -'1 2. 1 06
_I
i i: I' +"!
II ,
,
Run
I :. .
i
,i
;
i- Ii
, Ii I;I
1
I,I "
fiGURE
9(,
, I !: I
I,
Ii i' ,'I , i , ',-
s
• Run no . 9£38
, x·
4$ - 0
S
I
I! I .
.;!
I :I : 'i , I ; I'
;~ , :'I'IiI Ir I I I' I iI"Ii;iI 1II !iI
I
I
tIl
I .'
! -, .
I
I
!
I
I'
j
I
I'
,i
I-
Run no . 1.s-143
,
! ••
600
i
1t ... 11 rio . 2 /
x·
S
TIt)
S
,-
"
_I
_
I
I
I
~
I, i i , I
I
I,
W
AKE OF CIRCULAR CYLINDER,
;. I
'i..
:~ I \'
i'
I
I
"
'.
.
I.:
.'.",
I'
'II
i - H ~I.,"
H--;~ni -"
i; i' · ,',-
'
I
,:,
1· 1.
l] I 'i-
:-, I
I
i :
I' : ,-' '
ii It' :IH
I I !1 1 ,
: I
I'
I :
Run no . ;1.8
x ·
I
1
,
'I
,-I
I 'I:!
f
, '
I
j
I
+:bl:",h,f"I,+ ,
-'
,
-
I
':u..LI_,---, c",'.i, - i.'L C"-'I..I_-' ,.1_.' ,:,
I
i
,
"
I
,
,,'.
I I';
,
I','I~','H+
' Ic', if.
,
I
, I ,f:fl:t§
Xl:,
I
S
900
,
,
,
I
1 1 11
I
",,
-
-~' i IJ;,ej,- 1
I
!
1
"
-I j llI, I,-iI ,,
I :1 ,...
I
,I ",
, I'
I , ,I
no .
3no
! I
,
II WI!I [.II.
- II ~ ','
j!
,
I
t
-I' 1 -'
,,
I ll' I I·
...J...i...:J..:t...
tl1-I-lJl--tlMr"ll"
.
.
~I·
j
I
i j i : I i Ij i
!
II
I.- ' I
, I
,
,I
,
I
-I
i
I
,I,
,
I
,
CIRCULAR CY LINDER
5<!pt~r
l !H1O
q • ~sf
DI • • ner· ~ 6.1 Indoe\
R . N.:::O . ~ / B J 106
:
,.
II,
I'
Ii,
'I
I:I
",!
.
! I,
r
"I'
r
~
..
1III it~-I-I _h.
..
Run 00'.
-.
'"55"
I
I
till· i III :
r
!I t I , i I
Run 110.
".
"'il
"r
ii'
.,
.
.'•..
I ! -,H,t.1.l -,i
/P 1 :19
.,£~c
!:-
• .1
t
I
..
++-ld·I···· !·~ 1+
I.
,.
1"
l
~z
Run 110.
" •
,
illl' ; i i
, : 111 ,i
7.r0
.
I
,
,
I
'I ! I I I, I' ,
,i, I' I'
I! -1 !
,II
I
II
i
,
I
'I
!"",
'.
:,1, .:"
',,' '.:
,I
":'1,
'.
,
.,,
. a ..
,
,
I
i ::,
,,.."
"
"
,
I
'1
.'•
I ~IIJ
'.
I
,
'I
I
I
'
I
"
II,.
I'
',;'.
FI GURE 90 . WAKE OF CIRCULAR CYL INDER .
i.
.,
H': I";H:~!+ I'
I .". ,",. "..".J
I, I
I
I
I
I
I
i!. I!
,I. ..
I'
'1' I ; I
. 1! i .
l'
I II'
I',
'
;.
:
I
i ; ,:
I :
'I
j
I.!
i
I! I~ ' Ij Ii:
I I ": i ' "[ i
i , I ~ I i , 'I: I II I, I Ii ,i i II ' ; , , i ~
. ! t ;1-,
i : !. '. I tI I : I j
I I !I .
I j !I ' I' "
R.N.~ o.r!l..r.J.106
iii/'ll,
'I j'I' Il '~:' ) ' j f ~ 'I-t' to!"! 1 /1: ' /1 1 il
:" I,~,I'I
1:,11, I'; ,r ': ,,'1"- 11I " ',[' l lj- -I'
l li- '- I jl 1- -11/';
, I _I:., ~,-,'I.ll l ' r" I !'.!
' I'l!" I! "'i-I, ',:,:~,~,'
,', I ",' I"
' I" I 'II , ,' " ,
CIRCULA R C YLIN DER
.;
i
S'p""" "eo
I
.
I
:
j
'I
q • ......i.Q..Jsf
PI_ter · 6.1 fIlChes
I
,:,'
I
:
I"
. ,-1 -i
-- ~J
-
I
-,
-~- -I - -:'1
';
. -1-
', '-I -,
1--
-
- .
-'I- : [ 'jI 1H
, ,-, I /"IJ
,
I
_' _I
-
Runno .
5"
r:-r- r::
-{':.°l-/ -f.l"i;;' ,, ' 'I' 7'0 1~~'i :--'j ,6 0_~r ~'t'
~-j' , ~:.2·:11'~·II·;!~I::i":;!: . il<if.t~,:~;:;~ :~'F.:,j; . :~
'
- --
L
.
-",
,
.'
I ,,
r-
' f I~I
.
.-
_._.-
. __ .. _-
••..• '
·-c
". I ·
I"
,. ,->
. ",",
I'~"
''I'
.~·-~;"" ..
,- " ,
i'·1
'!;' ,":,,';':
, 1, 7 ': ::,"":1
-,- 1--- --- -T
~:'Ti RIMlIIO.17
U
L,i','·i! Runno.
''''~I -
u -:-
'I'-;"~~
r:~.'.I;;·""-
-
_.
,"" "~"~
1'l,"·· I;!,I;i ; "
" I. III jl I. -,
-'.
,",,-' ,---' "
·,1 II',:"
,I, ,
-I' ' I'~II"I'" I'
"·!j ~li~~:~·~
. .
.
-~
, 1(: ~U ,,"i"':,,: -, -
- i",'i",~~"""'"
~I:-,t;,; -
riO
I, ."
,!:I~·~_t . ,-
'-·I~!. Run. lilr.;~
-· Runno.1if3
t,
~ , ~r_o_ j' '1- ~' /','
" ...:
,
/'
,.-,
,",,:
IJi":~:~('";' -,
""
•
:/'I---
,
- -
.
"
.~..
-, ,I ,
i ',
,'"
..., -
,
--
~~. '
r--
,
- -
-l'
I
'; I "l": ", "'.,
,.,,'"
9°1
-'
~, --I
~'
!
I,
'-t-·-
,
-j
I'.
•. ,
'";
' 1'- r -r - I T' . ;;~fl .. +:r··~1
'-1-1. ....... '-:;.
-. " ".'1 :"-"
"'I': . -:1' .
I I I f.l I !, i ! I -! "'I'
''':'~;''f"I
ni'1 -l "":",',
'-'I~', -1-" " 'I ---+,1:,-,,
" , :, " 'I I
I
I
Ilf'"
I '
\"",
1
'-II! ',: ; i II i ' i
I
I ' 'I , i : '
I: I" '/ : III j I, I I i l
,';t"
" I, "
"" I: , "",I: ",I, ', i j I I 'I'!!
I I, I' " I II,'
'- I
"", II I
" -,
"II'] t "'I I I'I'! ' iI
!1!1~;
'
I'1
'11:i:
i ll"l ··;'~"·'I' !' _:: t - -" -- 1-' -lll--'1
:I,' ;II' I ,I II "1',I ' I I !I -I - -, J- -,I- -" -,/"- ---, -I ~ I II ,I,-dI'I-I" , ~ Ii "I :I :' ,I I
"
, I I i i I I I , II
I I' : , "I 'I"- 1'" - ,- :- ,- , ', -';-' ,'-1
'I I' I I I i
,+
•
'·1
I
,'I.
,
,
,'J -'
.
.
:- -
1
I
'i
I I
I I 1: ~ i I
FI GURE 9E.
I I
I
:
II : t!
I :
I
--i
-1
,.
I
~ ~ : ! i , I! ~ ~~ ~I
':
'
. ,
",:
I , :
WAKE OF CI RCUI..AR CVlI NOER,
. ; .'::
t
~.,! i. .~ ~. i~ I'
I f-'-)
I "
.;
-
j
I .i
! I • ! I I !~. I J t
,- "
", ,'" -,
I
!
~ I II
l
I
i
~~
.---,
.::_,=--=L~
----=-~ -- .--_., ---,.-, -- ...........- "'"""-----:~-,,-...:=~
'.-
--
~ __.
~
~
,.--,- :z k.• .;i ;;~
~~~. ==:..:~:::::=+==-::::= ' 10; :: ;;
-_..
-_. _-
~.
-- . ~
.
___ ._
?> .D '" t"'I
.::====::.~
,._.:-"r-
- ' : II
~-
~: : __--'-'-':':':==.c .=-_~_._ c.: ===~'=·~==_i ~- ~ : s
?
~ ~__~:~=='_-,-------=.:==~'~~~~==~=~~i=
__-.: _.__' :." ,
--.
- --
"
g
-.c~ ~ ~
~
z
~ "-'~-'--=-,-'.~t'~--_ ,_~-~"~~'~·,"',~··-;~.~f2.·~~~E·~-~~'~~- ~
,; I
: ..
,__
._,_
~.,~_;,,
_ _.
' "'
I
'
'
I'
g
'
'
._
, -;
•
l_,~'"
--
L.
-_.'--
.. " ..
~
'
-
.,
-"
-------
-,-
;
--_.
~
',.
., -" -
~:---
.,. ... -ri-:-:--!-L(j7:'V-_!_ f.:t_t_~I·Ti.·'\-1:'''-·r!~'- J ~~::r~~·~·:··'i~st
0
.
__
•
-,
,-<1.-=:-., I
,--
r'
--.,
-'.-
~-,
J,r~"l·';·'I
"
.-....::.L·,~N
"
,_:_.~.-L
• yj"q"':
' " I "1'"
" " '
__
,,-'-'-"
,',
,
,- '
:""-
I
f.;.-r.-i...- "
"
." •
,_
. 1r-T-"
_ _ ' - --'-r'
r- -
"
:-J"--;:-:l-'
""--J,;,,.~';"
", " ~ '
, ' . , ,,'.:',
.. "
.-i'
""~-L
"
~ .. l "" '
,
,
',
.,'-
-- ;
, .,
i
0-
•
,
- - -
,-..
" ",' _ _
C ','-"
~
.
, -
•
-.--
', : ";'1 . ~""':"".1.
.
;-:
"i=,'
J ,[-'-r
'-'
.
:
--.
r::--'c:-------
' t ·'"f'"T
I,;
"
,. ':",,' r': - "' ,""-:,€}t,-l
'f I "
..
ri ~ r ~--' ~:",--
J=L·'I~ "l .,r" - ..
•
- -
I·!
, . ':~..:.,"
>-.... .;:- .'0:1 -::
:C-:=-' 0 _ , , _ , _
,-, ~- ..--.;.....---.
-
CIRCULAR C YLINDER
Sep l efllber 1980
....L!IpS f
q •
Dla.,ter · 6.7 inches
lio N. ...:.> 0,173
J
f
I
'i
I'
10 6
I ! , !
~
t
,
,
1
1
•
I
,
I
:
t:
I
t
,,
,
',I
!
I
I i
,
,
I
, I
II i '~I:
I
,
I,
! :I
I I ! II
I! I !-j
I .
'
~I
I
:" ' I ,
Ii ! 11 I I I • 111 'i II i . :': ~~~z , ": no.ZJt.j.to I
II'i,II'II.I, '
I " ,~s-o ,'1,
II: !! II II :1 -I i ' , ,
Rul'!
if6
••
'1
If
r r :++I
,I -H-l
,
1_ T -
nI-II - 1--,
:1
IIIiii'I I , 'II "
Ii", JI
! I I , I " I : , , !I !,I I"I
II
' I "I,' 1 I
I
'II
t
i! I
I,
I , ! '"
,
"
!;A'I\, ,'
,
I
b , ~u.ofu.'3
DEF ICIT, CIRCULAR CYLINDER .
t
" i
I,
,
I,
''I,'
,:
<-I
,
,
',1 :
,,
"
,
. I~ "
! '
iT:1
,,
,
"
:'i :._
"
'1
V(lOC I T~
!.
"
TI'
I",
I
.i,"
ii ! !I I1'1'1'
' i !i III I I il 1 :", I I : II I ! I I I 1-: j,,! I
FIGURE lOA.
!
I';
I,
,
'I
II'
,
1
! ~~-~-I~,I~ ::(t, I,~I
'FH'i , i
1-- I ,' 1,11_ HI' 1-+, 1
rI
900
i
,
I I'
r
,
I I
"t
II i,
I
•
I
",
I
i"" I
,I I
I
,I.!
I
'I,
,
,I
-I
I
,,
i
I
I
Ii
j,
I
I ' 1 I r I: i I!
j I' I j I i '
ttl
t, l
l-r:~I --'-~--~
,
,
~ ! -\
I- -:
,"
,,
,
,
r '--, ,:, 1--1
1-
,
,
i
,
ii , -lI
---1-- ,-1
1
,
-,
"
j
~
--
j i11'll
I II! III
I II' II t
I 11 1
,
'II I!
Ii
,
j
I
-
I,!
I
!
, II i II ! i
II
I
- i:!
I '' f:
I
I
I
I
,I
:
FIGURE 10c. VELOC ITY DEF ICIT, CIRCULAR CYL INDER.
~:::;:,A~,~YllND"
' i ' : . : : II' iii :I ! ' I i I : , I i ! i 1: : Ii: ' I i I, iii
"-L.iLP"
or'~I"·'."''''''''
6
R.N. ~ 0, 4 Z 0 )[ 10
it::;I'I'
1 1"II, l i" I'II~I I-I'
I .
' 1-" i'lii
l~ d
Ii; 1'1 i
i ! I ' i :I !
11"IIII'ilcl'II:I·!IIII!1
:
1
, I . I,
I
I
I
I I
"
l .I
.'
, .L, .
I
,j
I
" I ~ 1 i ; f ~ 'I iii I :' : I
1=
'" , Run 110. /0
I
1·1 Run 110 ../6
,'I
Ihm no. 2.2
I . x·Run no . S)(JO
it 9 .
t i i' II:
i!!)[ • ------1.Q~l d .' ". 450
T' 1
60
75"0
I j !
1 r r·· I t!
'1 1[I
,i, ,I
". y . ', I I '1 t i'; II
i j t' I
/1 i
'1 I I'" , 'I' ' ' ' iJ,f.'l;''''I''''''''''''
' ' "",,'.
,"I"""
".," .. ','_
,.. ," . "fo',
"'1 ' ..
,',,,,1'
_,
I'"
I"',
I ",, '"j
1.1. 1
I, T!
L j"
..
+
.~' -I:il- -~;:. " ~, -,"'"
".: " .. ',:.,:""..
I "1
I ,,\ ~ , ... /.. -H] .1,;' ;~'", ".': "'., "1\': ';, ",- 'K,··. -',' ;!., ". ,I".: ",I:... :·/'1:;' ' .. :' , . '... "
, ' : I
I,
':'
tI" I.. I'i '!,'
I
+~
Ii
1 .- l
'
I
I
'I
.
,
.r-··
, I , /'
f
Run 110 .
.
,
.,. .I. .I
'· rll 'j,. '"
../ '11"1
..... , -. "~'"
':
"f:
I
~
I'J.
.1
-1.··.:·,.
..' .
,
. ,I
:r;
Q
.l '
~"]": l;;:;1' 1,_:~':-'
.'(,t'·,,·,
c, , , , ",.,.',: ,. ! ,'"
,
I
.};; -:,
,j
'.
h':·"1]~;,·j
'1':';".""
' ~,;
,I!,~;
1
~t
•
I
- "'1"' •
T'"':~.
i ~F
1
·
",",
-I
• ,',
. "
-'I
I,
,",'~
j' • _ ,I .•1 (
..
I,. .
"'1' .jjl - ., ::; ,Ii: " 1: ~' ~-r fO.' it:, ~:~rl,: c\I~: ': ,,: .~~"': ,:, ';" ,";, ~~', ,1' "'1,: ;~~
., ,,' -" i ~7'~·"~"I-.':J';'l"\r';;I::· .J : >~I.' I,; I' ~.!. ',~ ~ ' "'.:".:
fl..
.
I
01
1
" ,','. '.",,"
!::.'~"
.+ 1:1
CD
.'
" . I
- --. :eI,'
l'
. , ' f H,
I I I
-,.
•
111iii"
•
eo
., I
1-
II
I
"-
,'I '
"
1 ·,,1,1,,1,._1.. . . - • T ',.
,", ~'·II..
'1-'1' '1'1' 11'1·
I,
I.
','
III
!D ' O" ., •.
I':'
III·
.'
. ' ", ,I.'
'-'·T·,..-_
.. ·~I
-
•
",
I ' r " I,.
.I .
'.-
:
~ I'
,
c
•
'10 I
II
""
I
" , '
1 .
I" ',
,~~·'-~'·'~··-·'--·I·"'·~·.,-·,···'~
'
.
'I,.
,,'
'
,1-',·"t', "7' ...: t, .•I
-!, _.
" ""[" II ,
.,j!J ~ . . "
- ..
.....
. ,
,.' . 'i
"':
''''
1
'r,
I
,.
L '1'1
, . ,"
. itt] ", ,~, .
- __ ,_ . .ll'J,I,I
Ill '
. . :, . •
",11-
" '~I'
"
':~II'
"':'
I+.
;'.
_""'l"nIi
"',.
.'
,
•
,
at
' ...~ k~
I
./
",.
1'01/ .
",'
",
I
~
+
I
', "1'1"" 'j' I
1"1' · ' '+'r~~;I' ' ("'IJ,r"'" ' · 'i:~lli!' '~, ',I ji I"'i' 'i " b
'.! 'Ii 1,·,·.i'·I:!i 1-"i " i !. 11 !I'
··\".~"Ufl ~:,"/I~; il;l ~r~}:'r: \· 'I;! '[~I:'i1I~~::I :J{I,:·~~:1111)1"'1 t:~I· '1:
1
i , il 1 :
~
1"'I
T1,1~,
:
,,"'!"
FI'
I
'II!
,,·11,1_1I'.' 'III~
II'·
""'i"'I' . ,"" +1' "'1 11 +~"
. 1'1 I 'I'
r, II !' III'I ;,' 111I I I:I' i i i! I 1'1I,i'I'1 ~I , 1 ;1'~1':u}I/~I1'3,II 1'rl~'1'",q Ir' r~t'i~III "Tt::" :!tf:~ ~ ,I~{~~~"I~
"!I:;: '(;".1:,:1 I~~III - f i i
'
I' ,
, 'I I1'1'1' i I 1'. ['"
,I , 1 I 'I. ;'1
t "1 .
!
i.
1,
O
,
'. :
'
...
. ' 1 ' , ,'
"
'I
< ':
T
I !
j
!. !
I • I I
I
FIGURE 100. VELOCITY DEFICIT. CIRCULAR CYLINDER.
I :
I
,
I
I
I
I, l
/ ,.
I
r
I
I
.
,
,I:,
I;
;,
'
i I:I '
I:
I, I
C IR CU LAR CY LI ND ER
~pte.ber 1980
q ~ ....:J...Q...psr
R. N.
'I
il l
II 'I j i III! :I :. I ; , : I :'1' II : !
i I : l'I,I'
" Ii,:
"'I' I ' '
I' ,,:1 11 i,! I ,'i I ! I I, i :
ii,
I j I'
r
'
j:
11'
i
_
j
'
,
l
l
'
I' I!III
I-I ! - , ,I
'
'II' I '",10 1'1i~'''i i Ii; I f'tlll i
', I Ii I ! I rJ
tl tlJ I}' , '~Ll ;I ;',I,1 ! .L:~':~~ , I . ..L ~k I
Ola.tter " 6 .1 lllcbu
~ 0, Sg".. 106
I I
I
I
Ii:
! r
I'I
I
I'
I
,';
ItI I' I'
,'"
,
'I
'I
i
I,
, I
'I
/lUll
• ..
110 •
...>£ ,:-_
3 00
~
1
...
.rS"'O
1
• ..
600 1
• ..
I
7 SO
I"
1
• ..
I
9 Q 0
1
'
.'
, I·.
.,
,,,."
I,
"
I
'
"
.,'
i,
:i
,.,' ..,,.. ", '
r·
11,'11'
,
.
,.'.'
"
,li
,I!:
;. II
,.,r
.,'.
" ,
.,I.,
,;.
.,
!
:: ! I!
i !I
~,
,: ll:I I ! I'I ! I, I Ii
I I!!, r I
I
,
!! 1: i i i
l I il II II! I'
I
f'
I
1
, : II
I!
,,':,
I!! i I!
"
:,
, (~ u~';u ·3 i'
I:, I ' 11 iH-!- ll ll
FIGURE IDE, VELOC ITY DEF ICIT. CIRCULAR CYL INDER,
II-j--I--~"~.·I
I
I
, ,
,.
I
:
,
,,,
I,
,
I
,. I
!
I
f,
.1
1
i .;
.,.'
I
,
I
!
,I
•
FIGURE JOf . VELOC ITY DEF ICIT, CIRCULAR CYLINDER,
S'P'_' ''''
q a - L J Jsf
.It . H . ~ o,17~
I
tIl ;
I
, ' I I I'
t,~
,
'1'
I
!
I ; 1
i
,'
I'
I
[-
1-':"
.,'
! t I : '
1
1. j j
' I II
I j Run
-
1-
, f -'- ' : "
-
'I'
"~
"
,-
3o"
,
I
I !
ii,
l
I I(
I:
2,~Ii_
' I, ' ..
'I I · ·
ri '~ ".:{~: , ~:'~ifl :~'; Iid' ,I'; ~--f:f r: Ott ~~,
'I
-'!' "
T
~~'I'
i I Run no .] .
,;.. -, -. ~ ill" no . 13
, •• ~.r.,
r .. •."
......
',1
"
i
f
!lun 110 . .19 ,
Run no .
Z"-P"
9 !, "
..
-
t
~
---tJ .-
I
'::li!·i
I
R
-I"'; ~ ""-f:~
:,'-'i i·.';"' · :'ITi'I:·i~"I"h
"
;" m'
~",?T,
' i " "
· ... 'Ir
i
,',.,,'
",,-
-I'
"ti ''':!
.o:- i ll'''''' ',.
:w· ". ' ;: ('
I
t'
"I- " -:i " - : 11';;,-'-'
II:.
" I'
'('I~ '~·n~.
1'- ,'-.' III !
"',i'r l ; ~ -, ,~:Jt.~ -,''',
L'
p
" '"' '1''' fa·oJ"+
'i"'''',
;
" i ' ~ T,u
"il '""i.,:,:,;'
~":;:"I
~ a;~ ":~ '1'-:" ' ' !'rl• ,: .~ ~--",+,.- tj!'l'
",; :' : !,.. -,'"
'.. ::fi ,~,,; .':~·i~'~I:j'i~I::::'~~'~:'-'--' ~: "'~,JI~:':"~'::T:,t'lll,~,;
,t
...
1 1 . -', ~ ~,: !.
, ,. , , I, ,
' , ' J,
!.
l'
,
I"
I , I'
" ~.'
I."-,.t·
, ,~L - i
'''-~'''r''
","',,'
"~ "
" ,,', I :'
,
,~ " : ~ ""
~'-"" ' I ,MI ·;t
~.', -J..T~;,·
':i";; _., I ·.. ~!l' I' ~~";::f!IL"-' >~ -'~II':" t.;'li"_'':I-:'f. ··J:·'~'''''''t y:, - ~.! , ~" . ;I'I I~
'Ji
.r ,:' .\' ,
'"
r-T~'
• II
I ' ! I 1 '/"1 i i ll" l ' 'I ' i ':;1 ; I 1i i ! i
'I I1'I.II \:f,/11
I ;:1i 1· 1'" <I"'1..""1' i .' .,"',
I'"
I I" I I
,j , '1I""~I"l : 1 ' 1,_
~ 1"111,,,
I' ' 'I
I' , :
I,' ',i
I
no . I
I r I' "
!
'I
Ij
1' I , it,' I'I I !~! f : L
i'
!_.
.
'f,. ' l- -'I'I',"~.
· 6 .7 Inc~$
lI I06
l:
)
I
OI • .eter
I 'I" , I : 1 '
Ii' j ,
C'R CULAR CYLINDER
I"i:"~
,,i.. L ' I: '
': '
L~. i, i
;:' I ~ ,
!: 'I ,'I I J'I'" !I I:I IJ.1 II-l! '\~"" 'I ,,11, ",,
1 :' r ":.r !..
!-,' '" !I iT li I""J Ii 1't ,~I:• IL 1.'1 I11111I .,, °1,' I' /
, I
! ! I '~I '- 1 I 'I IT i i-I i: .:r 'l ,I' - -I ; :', ' . t Oil I I " I r' I i" t 'i! I: t 1 : , . I ' I i
,I Irl t, l 'f , - "1 'l~"'r:
1 'I !I I:, I f i i i Ii' I' ,
, "I: Ii! : i l l Ii i, I
1
I
I
I
"
'I!'
I
14
I
,
U'i
u
;-,.
1
J
[
-i
I"
-, II ,I Iii, h' I !
"
i,: I: I! '/111 1, I i,i, i! :,11,. ~ ,!t" il il :, I . I' , :1" I-I,-I'. ,I,.1!H(I I .•. ,j~-~,I~'":i I 'I'"- ~lIf If-III'
1'1·: I 'I:!
I I I . , '.I!fi' L
~.
0
0
.I
,2
'l'---
,3
i"
FIGURE JOG. VELOC ITY DEF ICIT , CIRCULAR CYLINDER.
1,i j t
I
"!
""1+
I
,I
,- I I • ! I
I'
:
x=300%
750%
20-
0-
- -0-
-20I
o
I
.1
lFigure 11 .
,
.2
/u
,
.3
.4
Ux
Effects of Reynolds Number on the Velocity Deficit in the
Wake of a Circular Cylinder.
'X
1max
ox =3001.
o 60,",
o 900X
r
o
.1
,
.s
o
Yz,
.s
OX:300~
o
o
•
"
Re= .76x10
"
600'
900"
o 4l
0
0
o
o
s
o
o
""
o
,,0
0 "
'
Figure 12 .
.5
o
M,
.s
o
Shapes of Wake as Affected by Reynolds Number and Distance
Downstream. Solid Curve ;s Schlicht i ng's, reference 5.
0
.____r---.::- - - -
_t- _-_~
--~~-TI '"'""
--- ---
.5u 1....
--=
-~t-l=4l -
--
J
I
___
--
Re=O. 171110·
Figure 13a.
Spreading of Wak.e of Circular Cylinder, Re=O.17x 10 6 ,
r"""?\
__
-l-~-
12'
_C-..l-
-
---'-.-
- - -!o=-"'- _ _ -1---"--- -
~ +-t----
--1t1.0. 27110·
Figure 13b.
Spreading of Wake of Circular Cylinder, Re= O.27x 10 6 •
-
-l.-.i--_
I......l>- -
U'max
I;"
I_
-
-I--~
-~-I-'-+- - --~--I
)
.5u ,max
------ -/--+~----j--,l
Figure 13c.
-
----
l--?
- -- - - ,..' -
Spreading of Wake of Circula r Cyli nder, Re=O.34x 10 6 .
,I-
---- ,
/
1
0
- - - - - - - - -- - -
4----~--~-
\-
.5 Ul
max
~I--+-~UT'-m-ax----~-i
----- ---= -1'0 -
Figure 13d.
-------
Spreading of Wake of Circular Cylinder, Re= O.59 x lO r.,
·30
. 25
-
>..20
,../,/
/
I
I
~
o
c
I
I
.10
I
I
~
:J
.0
•:J
1-,05
o
-10
Figure 14.
-5
z
o
( Inch .. )
5
10
Effects of Reynolds Number on Turbul ence Intensity in Wake of Circular Cyl inder
at x = 300%.
.1<1,4,15
Re= .175 x 10'
.15-.25
TI>.25
Re=OA2xl0'
Fi gure 15.
Maps of Turbulence in Circu l ar Cylinder Wakes.
0.'
0
,>
0.'
~
0
00
"•
0.'
z
0.3
•
",E
•
",
-'"•
0
0
0
0
o@
<8
0
0
0.2
0
8
00
0
I
Q
@
0
00
0.1
O ~~~~~~~~~~~~_ _~_ _~_ _- L_ _~_
o
0. 1
0 .2
0.3
0.4
O. S
0 .6
0.7
0.8
0 .9 x 10 6
Reynolds Number
Figure 16.
Reynolds Number Effect s on St rouhal Number in Wake of Ci rcular Cylinder .
0.6
0.5
-
o
>
0
~
•
0.'
o
~
.
...J
I
I
0.2
..{}--_--;tt:-~-.or-­
x=eoo"
cr
%
~
o
....
~
~
r
0.1
o ~0----~0~.1'---~0'.~2~--'0~.~3----~0~.''---~O~.~5----"O~.'6----io~.7'---'0~.•B~x'1~0~-REYNO LDS NUMB ER
Figure 17.
Apparent Shift in Strouhal Number with Distance Downstream in Wake of
Circular Cylinder.
.,
i
I
I
·1
I
,I
I ,.
~ I I '..!
i ,
,
1
,: i
,
T
1
!
T
,
!
1001
,,(
,I
""i,. ,~ " . , l;"I·'
.,
",
•
;j
"
...,
, ,..
"
I .• ,
..
i. "
-',
."
I,i',
...: "
'I'
'.
_,'
"
,II,
I.
"
,..
.
,
.,
'd- I'
:
;\1
"' 1
'"~
,
..' ."
~;
.'
..
" •
.r•
,
,
'
, .d'.
.,
I' .•
, I
EiE.I~"'.I;'
I
,
.
,
,','
,
'" :1
-'1;:
,
-;' ..
",h'
"
,
..
4-" ....1.,,11'·1'1
'..
'
1-
I ' !,,, ... '
."
:"R
1.1
"
II,.,
,
"
",.
. !'
',
t
. .,
.'
,'r
•
.I'
,
"
'
,
,
"
,
,I'"
!.'
"~:
,
,
,
I
I
,
6
-i'
'.'
".
,
j
.I ;
:,.;
,
.
I'
.
Run
j.
I\O .~
1-1\: :!
,
.1'
R. N.a 4.18 • 10
"
-I
l-II,l
.·~"os
1
' .N" .
i
I.
.
Runno . ~
I·
.'f. . ,f·..1~". · . 1
"
.,,
1'i.\1.' --.
I . ·~I·i,
,- j-
CI RCUlAR CYlIIlO[ll
Sept . 1980
With Straku 4t t 9(P
q .
..,
- Ol.-ete r ·6 .1In .
I
,
•
It
Ii'II '
'r. ,.
iii II-i l-I iii1 ,-"! IIHl-t- I ..
,
~
,
1
j
i
~I
'
_
,
:
1
,
-r
,
]I h I- -f: H.""_'_'.,,
, ! ,
,;
t-
'," , ,:,
FIGURE 18A. WAKE OF CIRCULAR CYLI rIDER WITII TWO SPR IAL STRAKES, RE
.
I
I
I
I
0
I
, i
I
I
1
rI,
1
I
I
Ii
I I ;
f [-l '
I, I
, II
I I
,
I I I I I I IIi
I
I
I
I,
I
,'I'
.,j,'
I
Sept. \9"
CIRCUlAR CYlIND(R
O
Willi Str.ke~ It !..,.9IJ
'I . 7 . S psf
otalleter • 6.1tn.
!
I...
I' .
I,
1
,I
:!:.!
.,
,.
.i '·
I
I+j:
I
I
i'.
,
1
.I ,:
I
Run I'O.~
)( . .,,,0
I-
I_ L
I
I
:'1
I
,o.
"'/,~'I
I
Run no . .l..1li:.....
S
I
••
f! ~()
,
"
R . " .~O• .JS"1 10'
R. M;1>" O. ,si 10'
,.
...•. ;
I
t':
.! .
,
,,'
.10"
,
'~Jt
hi
; ~ I ;:
I'
:1'
'f
,
:1
,"1,1
"
. .1:,
I
,
1"
1
I
,I :.
L
I Ito I
I
I
I
,
,
' "
i i
I' .
., Ti l'
,
I
0
"
:;:
I
".
.,i',
I
:j,it'
1-'1:'
,,:,'
,,
"
,Ii:.;
I' '
'"II ~ :
,,(,i,
:., 'I
II ,:
;!."-,
,I
' , t-
,'. ,,
:1,."'
'I,,:
":
.I
o: !:
)1,
"'.:,
I!.
,,
ii'
,,
"
.1
I ., ii
I
I
r' '"
.,
t. ,
•
,I
:"
i'l
i'l
.I
Ii
'j
I
:,:.,
"';
I
'il·
I
!!.
I.
,o,
..
i_: ,I
I"
"Ii
·U
1",. ,
•
I
'i'
;.".
'.1
,! I
-:!:-'
!.,
' I
I' .
.,r ,
••• 1
FIGURE 18B. WAK£ OF CIRCULAR CYLINDER WITH TWO SP iRAl STRAKES. RE • 0,35
,
,_ ..
,,
, i?
"I I
':'1,
:. ,
I
:I, '
I :.
I
I
'I
"
"
I"
CIRCULAR CYl lllD[1t
,i
t
Sept . 1980
With Str~~es li t !...90°
q
--L£...Jls f
Olilleter· (j.l1n.
'-,
j' ,
It·
I
,
Run no. _~
,
300 1
R. II .-=
O. ~llt
6
10
1
·:11'1·:
'1·,10
Run no . ..l.ELIt.
(.00 1:
10'
,,,
"
'.
"
,I
.,'
"
"
,i
"
"
"
C'
.'
"
'"
·'1
I
I
",..
OJ ••
,i'' ,'"
"
,
,.
"
,;
"
"
·i,
FIGURE l8c,
,i,
W
AKE OF CIRCULAR CYLINDER WITII TWO SP IRAL STRAICES. RE
"
,
,,
i It I! ' -I, I~'ttf:t ~,
I
,-I ~IRCUlAa
CTlI lfOfR
Sept. 1980
With Str' l es 4t ~90°
q • ...J.Q.pS f
Il h . fIl er · 6. 7In .
:.,'
1 ",~1I ,
1
I
Ru nno.~
• •
1
'j;
1
-lJ",I1
"
"
j,
300 S
6
R. N."" o.iOJ. 10
II
I'
1
"
j
",
"i.}
·1·'
"
,'I
":;"
"
",
"
,i ,it
,- •. '10
',',,11I 1'"J._. ;'I,'.:.,'1'
,
"
,"
,
.... :
I
I, ,
",
"
"
,
..,:'
I.,'i,
': I
FI GURE 180. WAKE OF CIRCULAR CYLINDER Willi TWO SPIRAL STRAKfS. RE .. 0.60 x 106 ,
,. "",, ,.. ,-
I
'hl
i
,
I
",
i,.
I
. i.
':
"
I,
i
!'
I, ,"'I':;;1~' -r1.,,1:\,
. I~~I
'r,_
'":1
1
, ,- - I-
I
,
I
Dla.ne ter " 6.7 in .
,
I
I
I
. j'
-.1."
I· t.,
--,
,I
I
" I
,
,I",
1I !
f'
',! j: , .
.~','
.',"
~-
_
".
,
'"I
.::
_i lfL'
"
-I
.".
;"
,.0-
I-
-
-,
"
-I
,
',,'
I
I
I.
Run no . ..2.l...-
II "
1-14-f 'I"
',:i,',
•
I
I
FIGURE 19A. WI'IKE OF CI RCULAR CVlI !tDER WITtI TWO SP I RAL STRAKES, RE • 0.18 X 106 •
II
T I Jf I1 I1,1' I'"I,,:
111"1tt
.,
I,:
i
I
ClliCUtAR CYLINDER
SePt, 1900
With Str.kes .t 0° and 180
q ~ ...l:Lps(
DI'.:lter • 6. 7 In.
II,
",
,"
11,1.
"
;'
I
.j"
1
.,-"
.I
I
r
Om
:1
••
',',
I
lIunno.~
•
--S,,'
~()O
,,
"
i:"'r,',i , ..L,J,"J'
,', , J
1,'1 "'.,.,.
..
'I! ,
"., ,-,,
'II
I'
'
"
"
,
"
,I'
,
"
"
"
"
,.. ,
,:,'
'I: "'
'.iI •
,1,1 I"
FIGURE 19B,
"
WAKE OF CIRCULAR CYLINDER WITH TWO SPIRAL STRAKES. RE · Q.34xl06.
I
I,
,'
,
". I
il
T
I,
'j',
.I
", .
j
I.i'
,"I.~
': ·1,
" .
,,
'1,
.. '
'
, ,
' , I .• '
,"
.'
"1,;1
,','.
;.~il",.II _ I '+U ~; ,
"
i"-:.,"
I, ""'jI
• ,I
RlIn no .. _
I
"
.'.
.,
,
::
"".
,,
'"
"1
,!i.
"
>' 10
"
,.
I.t
!..
.1
", -I
, ~.
,.
,,!C!-,,2...._
6"0
l ·
ji'
'i
"
.!."
,
I. i
,,
.,
"
,
,,";
,
,.
"
..
FIGURE 19c.
,
WAKE OF CIRCULAR CVlINDER WITII TWO SPIRAL STRAKES, RE • O,q}X!IQ6,
U·: ~;:,~i.
..J
' ...
I__ i! l:I·J....l"J
'I
I,
,I J
1
, ,
.-,
I
I
I
J II
~ II
, ,, 1,1 I
I'
CIRCULAR CYLlIIDER
I 'I:"I,"I'l ~ I,J, LI'"
,
Ii'
!
",' , ,
..,
f
Septa 1980
q •
1c2.Psf
1
Dlueter • 6.1 In.
I
",I
1
,
Run 110 . 100
I
"
II
"'I'l r'~I;!'
"
With Strikes It 0° .nd 180
I,~ 11
'I "II
1 ""
•• _ k2i2-'
li:
" !.'
6
10
' / I.
"
~I '
",
l~
I"01
.
"
,"
i
'IJ
,
I
I'
"
"
,
,
r
i'
:!I'.i'
"" r '1
~
"I
,,,",
,,
,',,
,,
FIGURE 190.
WAKE OF CIRCULAR CYLINDER WITtI TWO SPIRAL STRAKES, RE. O.60xl06 " ,
i:
I
Run no. 110
~~~t x=
0%
R.N.=.f72x 10 6
I
I
,
,,
I
,,
.: I
,
CIRCULAR CYLINDER
September 1980
q = /. 7 pSf
Diameter
Figure 20a.
=
6.7 inches
Velocities Upstream of Circular Cylinder at Sub -Critical
Reynolds Number.
no. / 0 7
x = -2S0%
R. N'=.+/ 6 x 106 .
~~
CIRCULAR CYLINDER
September 1980
q
Figure 20b.
=
/~
pSf
Diameter
a
6.7 inches
Velocities Upstream of Circular Cylinder above Critical
Reynolds Number .
II -S ided CyllndnRUII Ito.~
Ito•. 1980
I -/-
q-I.S"p,f .
R. N. _
./9)C 141>
2
8
»
--
12·Sided Cyllndtr
!101'. 1990
Run
/.,
1Io.~
,.
q.~$f.
R.N._
.36XI(J"
»
I
•
~
....
Ol...eu r . 1.17 lllChu (pol nt_to_po i ntl
Figure 21.
Wake of 12-Sided Cyl inder, a = O.
IZ-SIdtd Cylfn4u
RoIn Ho.~
!Iov. 1960
q ·~s ' .
R. M. _
•
.,.9
/6
/0
x/pI-
1l-S1d'" Cyll,...
b . 1980
•
: ••
M~ ;
Itu~ Ho.~
/7
II
.P:J-9/ X /()1.
F
Ol_ter • 7. 17 hlClIfl (po'nt-to-polnt)
Figure 21, Continued.
§
~
lZ·Sldtci C, U nd ...
Ib,oll Mo . ____
~ . 1980
q ·....3..Q...psf .
R. N.':'
"
. 68 .II' / b"
/6
6
~
-.
I.
~
F=:
~
r==
~
F~
Ol_t... • 1 .17 111(.'"
~
E
( pol nt·to-poillt )
12-S\6_ C,IIIICI...
.... ltaO IIull Mo . ____
•
q
19
o..6..£..psf .
R. N. .:. . 77 ~ 14"
~
7
I
r----
,,-.
1:11
~
~
§
~
~
Ol_te,. • 7.11 Inc llH (poillt - to - poillt )
Fi gure 21 .
Co nti nued.
-
/7
n.S I4"
t),lll1C1
Qc.t. '980
er
IbIn MO.
~
".L-ust . • 0/.. z"•. . I1._. ~l -II'
(I
-
s;
••
n-Sld" t),ltrtder
Oct. 1980 11\1" MO. --""""""
(I • .-2.-Plf . • do 'II , , l.lI. p'. 7 2
)l
I~·
Figure Zl~ continued.
7
/8
-
••
,
;;
•
•
/.
8
n. stdeli ty\1tidA"
Ott.. ,')eO
!bill 110. -.....-
,, ~~f . .
t. II.
~
.9
.. .
e
~'
J( "
,
-
-
";:
!
»
»
s
»
»
-•
»
,,
,,
•»
.
.•.
•
••
•
;-
•,
••,
•
•
:
r--!
~
~
c:==±
§
20
\1.!o\cle4 C.1\ \~d'
Ott . \980 ltuft ItO· - - - "I •
~'f .
t . •. -
ttL -0 ·
111
1, "5/
'
"
9
-
,,
>
>
,
•
,,
"
1,
;
1
,
>
»
»
•>
•
"~, 'i"
~I
\2.~Sld~ C,\\flllltf'
~t..
q
\980
~".,. -""'­
~~'f.
l. M."" I., f)
f19
,. .".
~/'·
ure 21t continued .
12·S1cled CyHnder
Nov. 1980 Run Ito.-+q - /. S" ps1.
R. II. fI::I .19 ~ / tJ to
••
~
f-I---
Dt • .eter • 1. 17 I ndIes (pol nt · to· pol ntl
•
12·51." Cyllnc1.,Il0'l . 1980
Run 1Io.-+q • -./!i......jsf •
R. N. _
.3b .. /
27
(} f>
r
Dtlflltter · 1.11 InCMS (polnt - to -pol ntl
Figure 22.
Wake of 12 - Sided Cylinder. a = 15°.
1l-S1ded Cyllf1d~
~. 1980
Run
!tI.----....
q
t.
.8
-E.Jlf.
N......
-19, /,, ~
-
Dl_tt" - 1.17 lnctltl (polnt-to-901nt)
1l-S1111" 'yHIIder
Nino. 1980 Run 110. --....
q -.2.fJJlf.
t. II. - . 60 X ItJ'
23
3'<"
I
:
C=:
=
-
Figure 22,
Continued.
•
12·S1ded C,l1nd.,.
Mov. 1980 ItIIn Mo.-+--
:.~/: ~~9 .r/"~
d..
--
/$"
~
I
;:
lZ·Stded C,l1nd.,
Nov. 1980
•
ItIIn Mo.-+--
q~J:rpsf .
a.
M..... • 7T
37
~I
X /~'
~
f----.
Figure 22,
Continued .
•
1l.Sld" CyllllCler
Oct. 1980
tJ. _ IS·
Run 110. -'I>--
/
q./'S'pSf,
•. II ...... SZ It I ' ·
OJ_tar · W !nelles (polnt- to-po lntj
-
I
I
12-Stded Cylinder
Oct. 1980
llin Ko . ~
q • .-:!.......Pst • • d.. -/~·
~. II. .... . 71 X I""
Figure 22,
Continued.
I
2
13
•
II
II
lZ·Sld" Cyllnd.r
Run /10.
Oct. I9fJO
q
~
"1Jsf . • ..c.
It. N. -
.98'"
"r-
/,, 6
Ot_ter • 20 Indlel (polnt-tO-lIOlntl
•
it-Sided eyl tnde ..
Oct. 1960 au . . 110.
~
oBJIf .• «.-1$"
q
R. N. __ I . ."
,. "II 6
DlI~tt... to t n(hn (polnt_to_polnt)
Figure 22,
Continued .
I"
3
1+
-
i
-;:
;
I
I,
:
=
~
,
12._S1dtG t~lIndef'
Or;t. \ 980
ltull Ito . ----...q ~..l.U'f .•
l . II . /.
tJ. ., ~S'
~9
•
/I'~
Figure 22. continued.
lZ-Slded,
.JL.
Run NO •
x -210 %
q -..L£ysf. d ::()I
R.N •• ,/9 X / 0·
0
"
~,
I
Run No. 2-. x -304%
q - /.5" psf .
tI.
~O'
,.
r
...L..
Run No •
,.• q
-~sf .
R.N ••
R.N ••
, /1
x
-"'0'7.,
dl
=0'
X / 0·
••
•
~
~
•,
;;
I
••
!
I
~
u
•
..,
~
-:
"
"!
.j.
,•
I
I.
,•
,
I
;.,
i'
11'1
•
•
o
•
"
'"
.I'
I
I
,
!.
Figure 23.
Velocity Deficit in Wake of 12-Sided Cyl inder, cr.= 0° .
Run NO._3_. x -)tl7
q .~Sf.
R.N." ,~7
)( 10·
Run No . ~. x .~"7..
7. -;-
q .~sf .
0< ~ot1
R.N . "
- .. ,
.
0(·0·
3'60 )(
10·
1--I
,
'~ .•
,
1
.,
.y,
-;.:
~',
, "
•
-
1-;
·.c. 1
r' ,.
«
~
~
z
~
u
,.
1
,,.
~
~
~
,.
~
. . . .l : . · . ,
.. , '
,-,",
" ' :
~:
. 12 L,
-,
I
I
.§E .
:,'
-
.-
-
,
1
;
,
I
.•,,' --.: .. ,'.
1 -
.
,I,
.- - ,
~~~~. '
:
.~
,.
.,
I
',e'-, ,
"
.1
;
,
I~
.~~
i~.
I:'
I
,
.1
,,
:T,
<FE-t= 'T'!
,
L
"'j
'-!
,•
i
OL,__-'.:~,..-,~,,.-.0-,.- :-. ::::-J=
I,:::;':::j:ti.:::,j.
, '! ~!
Figure 23,
Diameter" 7.17 inches
Continued.
fp~i'
t)
12-S1ded.
Run
.LL....
Ho •
x
Run No . ~. x ·Idt) 7.-
-u() ?;
q .~sf.
q .2JLJSf. "d ~Oj)
R..f(.· ,59 )( 10"
o
d:-O·
I
R.N.· ,59 ' x 10"
,
••
•
~
•••
I
Q
,
••u
,
~
<
,
,
~
~
w
z
.'"
~
«
w
~
z
,
w
u
~o
,
,
i
0
«
,
'i
~
w
u
z
~
~
I
~
Q
.
~
!
,
I'
!:
,
~
"
i
-,
I
-',
i",
--":
;-.
,
Q
,
"
.1
!-
! ':
Diameter· 7.17 i nches (po1nt-to-point)
. ___,
Figure 23,
.2
1-,Of',
_ J ..• _
. j
I
,
.3
Continued.
,
,~~.~:t:;:.::"~=t:;=1
! '
_, ~, " _ ,_"
~_1
-I' "I.. .!
I
1':
I
. ~
;
1'- , :,
"
- j-
;
1',-
.j
I
'I. '
, l'
'J
!"
.
~~'f
!
-" I
j
I-
.,
. I
I
.' i
"
"
Icc !
I" "
I.:--r '
.i ;; ~
,
,
.1.
I
,
',.
f
i .
,
.1
1
I .
I.
,I
,
- .-; 0
' I--~
"
J.
,
'"
.2
,
,
":,
.3
U,,/u
' -, ' , . , T , 'T
Figure 23.
"
Continued.
"
,I
' ,I
12-Std!d •
Run
no.1E-.
..L.
x ·2()"7; - - Run NO •
x
cI..:O o .~ q -.-li.,psf..
q ·..2.LJlsf.
I
-;;a , '/~"
R.N . -
I
. C'!
.
.
.
,69
)(10"
.
.
-';" I ._ •
.
.•_R.N . "
_
! , -!
,
.::0
,
,-=:~ ~~ R.N .•
.3007; Run NO . ..J.L. x
'~
cl. ::,O··-='= q .~sf.,~ -0' .
)(/0"
"
. I·
,.
._c_
~~~~"".,
.'9
~-'
"
1
.~
-.:: - , .
I"
.
.
~.~-- ~
,~
,
.~
I
.,
.,
, ..'
... ~
, :,
I
t',_
.~ .
~r';.~.
I
t: -. ,I
i'
j
j'
.j
. ,
: 1
!.
~-'f
l-c
,.
-!
,.
'i_
I
I
' ~.
'
~
I.:---r '
-.-
:j
,
..
..,
,.
"I
1
_
.f-,
1 . i'
1:'
', .,, ~
'
.1 :;-:,
,
': .
,
,
I ,... - ..
.j
.; 1
,
'"
,.
I
.
I..
; I
'
--;0
.1.2
, .•
Continued.
,.
~1.
. 1
.,
I .
T
~
I-'"-l~;;:
,
-,,3
. .~, Ur" IT '
Figure 23.
~
i
J.
,
f
.. ~
'T
.. !
,I
eMU, ... "'.>0_. .' ,"Tlo t.
12-S1ded,
~ . I . '"
',un Mo·J..S_, x -ZO{) 7;--. Run No.~ . x -3M 7,;'"1 Run NO.-'3....-. x .. #d~ ~
I
o
.. 4 S- pSf. ,01- ~". _ _ q .. 4 5 psf. ,
R.N." .71",,::
:: 1-- .
I(
R.N." I 77
'-._ ;
.. ..
/0 "
~
. ~ - i-
,
j
__:"'_"1,
;;
!
I,
~I .:.
.:.
I(
c::(
;ao· -·;
/0 "
_
_
,
.7 7
R.N. "
, __ '
1
J(
/0 "
,-=-;
!.I'
, j--
.
I
' ::~
q • 4.s- psf., 0/.. '
r.'-,;"
: .1j
_.I ~
L':; .- '0. .. :-.-
i ' :
.! -:.
.-
,
-,-
,
'.
,
'-'
W
L:i
%
,
,
'3
,
.
!'
1
,
, .
I·
I
.. .
,
,
--:
, ..
I, i .
,
,
.
,
.I
o
,
,
,
i '
.j.
, '--'
-1 -
j
,
,
,o
.-: !. ,
Diameter· 7.17 i nches (poin t-to -polnt)
Figure 23.
, . ,.
.1
1
f----
u~
,
'
,
- I _.
l
! i
Continued.
-I-.
,I,'
I
rT
!
i
.3
,
,
i
-.
.2
,
,..
,
,i
.L.. .I
,
,
+,
...':c
I
:l,
i .l 1._
Ofameter • 20 1nches (pofnt-to - po1nt)
.'
12-S1ded,
Run No.~, x .Je1t1 7q .~st.
101...
~Oo
- ------..-
0---
Run No . ...LL. x -:79/ %
q •
-- :- ~
,.
/ . 5' pst.
I
~
..
o~
R.N. - .,-/ x/of,
"
Figure 23,
Continued .
. . <>- ---
Diameter .. 20 i nches (pol nt - t o-poi nt )
e-
Run No .L -. x . J 647,;
"''"'''+ -0--
Run No. ~. x
q .~ S f 'J .,(.=O·
"-
q .~ s f.~",. t:)­
R. N.· .7 Z
,,
)(
R.N ...
10 "
--, -
w
Z
~
~
w
~
Z
w
V
,
.
w
V
Z
r
<
i
·-1
~
~
Q
.,
I
I
i
"
j.
,
I
I
,,i
Figure 23,
Continued .
"391 7;
Diameter. 20 inches (poin t-to- point)
.
.~ . i _.
I
,I
I
u.
i_c .
.,.
i ...;,;. .
I
"
0
0
,
~
~
'"
,
T,·e
, ,.
i-
,.
-1: i
:
I
,
..•
o
0
•
, ,
,
;
0
0
r'
I
I
Io.
...:
.
,
t ..1...-
,I
Figure 23 .
' .J..
Continued.
..
i
!
· ~L ;
I"
~.
I '
I
;
-I.
Diameter · 20 inches
Run No . ....2..-. x -3t't'7,; __ _ _~ _
!.
q .~sf. , 0(;: D·
.
- -, ----j-e-
R.N . · /. 31 ' .11' 10"
••
•
!
•• •E
• c•
( po i nt-to~poi nt )
12-Sided .
Run NO . ~. x
-3917.
q • --L£Jsf.
0(
R. N.· /. 31 Jr 10 "
' .•
~
--- '--
~
0
c
-,
~
-,
,-
-,-
w
z
,
,-
~
~
w
~
Z
w
u
iii
~
~
w
U
Z
;,;
~
c
"; , ..
,
'!,
,
,
-- ,
,
; ..
I
I
I ,I
T
.c'-
i
Figure 23 ,
I
Conti nued.
-0
•
12-Sidtd.
Run No .
..t..L. x - JOO7;
,0/..
q -2..£..psf.
••"
••
R.N.· /. (, (/
~
•
"'
'J(
;cOt?
10 "
Run NO . ..zL. x
- - '-
q
-)9-17..
_2.£Jl Sf "ot.._0 4
R.N. · /. 5.9
'J(
10 "
'e
i,"
,
0
•
:~
~
•
'"'
I
,
L
~
•
.i
"
-
I
I
"
I
"
,
-
...J,
~
0
•
i'
~
1 - Ux/
Dfameter • 20 i nches (po l nt-to-pol nt )
U
Figure 23,
Continued.
12·Sided,
Run NO . ..JL. x -300 7. - -' Run No. ?". x-0/4() '7,
q -..-!.:..f.psf . , o(= /~.(I = q - ~ sf . • "/"' ./ ~'
,., R. N.- ./9 lel O"
_;.. R. N.- ./.9: x l e ·
Run No. 70 .
q -
/.S' psf .
o
••
.'l
0 ,
~
~
~
z
~
~
~
~
z
~
u
i!i0
~
~
.. ,
°
~
u
.I
z
"'
~
~
0
.
~
,
~
;
-,
rI
,"
-,
I
I
,
".
"
i
i
!
0
or·
r
;
--0
_ •• ..0
1
.r
- UviJ
T'
Fi gure 24 .
,3
.j
,,
I
,"
,
I
,
Oiameter · 7. 17 i nche s fpo i nt· to- point )
Velocity De f ici t i n W
ake of 12- Sided Cyli nde r, a = 15° ,
Run
Ko .£L.
)t
r/l= / S'
12-S 1ded ,
D<. " / S'
12-S1ded,
-Zdo 7;
~ Run No . ..1..L.. x a 3407.
,
Run NO• ...&.L. x
_
q·~ Sf .
!...:
R.N.- 0.36
1_
I(
ta"
"'fl'''''7.
q • -1i.......P sf .
R.N ••
'1'·-"""
1
"
i
.!
T
'I
I
I
w
Z
~
~
w
~
Z
w
u
"
o 0
0
~
~
w
u
z
<
~
~
o
,"
,
-,
i'
o
,
..
I
I
,
"j
I
,
I:
i'
o
l -U0j
~ lamet e r
Fi gu re 24,
• 7. 17 l n c he ~ (Qo lnt-to- polnt)
,
Continued.
12-S1ded,
Q(.-
No . ~,
Run
12-Slded,
/5".
x -ZdtJ %
Run
q • ...L£0sf.
,
R.N .· o . .fe)(
o
Q(. -
No.~,
/5'
x -3(1(17,. --:
12-Slded .
Run
Q(.::o/5'
Na . ~.
x --14'%
q·~sf.
q .~sf.
•. N. '.<l..=!..!!.c~=_,
10"
'
,"
,.
i .,
.• j '
.....;
..
,
,
,
,I.
i
!
1ft ~ , I
,..".
L·
"
•
-,
.!
"
-,
0
..
.' .,::,
~
,,
,1
,.,
,
I
........
. !:
!
,;
.1
I
"
,I
1
.,
,3
- Uvii
Diameter· 7.17 inches (paint-to-point )
:< ••
.,
Figure 24,
Continued .
,
.,
;:
,
,
I .
c ,'
xo
~
0
,
~~"
,.
, .l··
..
.,
. ~~
,,
,,
I
I
~ ....
;t:t ,
,.
,
~l
~ ;.
""
!.
'i'
I
-,
o
,-",=,
""
,1
.;
1 - 'U
"
!
!
!
-co
,'0
,2
=': r , >0i
. 'I
ET
"
"
'
'
'.'
.
, ' r ' r ' l iI
.
,
'.'
! .
.,!
,
i:.·r
I . 1 ,
1
.j
T
IT
,,
.,
r·
"
iT 1
Iii
..
" ,
" ,:
I
'·i',
I
.:
i
F+,
'I I_I.: . ~,
.
-'---'- ' ! '
.
.I
.. i
j
F.
.,
,
1. __ l
I
,j:
1
! I
:
..,
iL.i
'.'1 .
01 ametel'" • 7. 17 inches (point. to-po i nt )
. ,.L~" """
·T T ;·
Figure 24,
Continued .
,
_
~· LL
12- S1d@d, "" ... / 5 '
Run /io . ;i:~. I( - Z J'd?;
q
.l(
",- . / 5"'
Run No . ' 7 . x
q •
-1£;>' f.
R.N.·
12-S1ded .
12 - S1ded .
-3""%
.:::f:£Js f .
q • .!l.£Jsf.
- 0.
R.N.-
10 "
"" .
Run No . .,2L. x
o
I
I
~
~
~
~
z
~
U
%0
o
0
~
~
~
u
".-'
~
<
~
~
o
-j
-,
,
I
-,
'1 "
.!
,
j-.
o
_I.
o
.1.2
.3
1 - U"m
I
Diame t er · 7.11 inches (pof nt-to-polnt)
:.,
Figure 24,
,
Continued.
Otallleter • 20 inches (pol nt-to-po i nt)
~
12-Slded.
,_ _~
12-Sided.
-L. ,
R" ' •.
-3007. - . ..• .. Ron ••. ...fL.
q ·~sf .. at. z/s., .';--' -:: - I ~ q .~sf.
,
1£:: '·
! . :"
.
' -~
.
j
,
.
.
.. ·':. I~
.
-
'...: ~. :
,
:
i
,i'-"
: ...
. ! ~,
-'"
, .
.
.~.'
:'
: I ,
,. , i :e
-
·1
;
, .
'
"
j- .
"
,otr/S"
------- I ~ R./(.-.SI..9 )( 10"
R.N.-.S//,. >c/o,.
. ...
, -3917.
c.:.. l'. ..i;
'-Ie
~
'
:!r,
, i
I:
-, -!·_L
!
, ' ';''';;
' ,-0:.: _! "
,
.
, l'
1
-
.!
~
~
z
~
~oro
=
:
..i:.e
' . .~
. ,
. . ... ,., . , . r '
~
-,-
~
=
,.
..
_
-
-
•
.
-
,
i
_
.
~
~
, ,,
~
o
__ . i
,
I..
;::
.1 . '
...
,
I
:,
j.
i
1=-;
ii
:.. " ;
.
i ,
,,
:.:
1
"
·1
i :.
i
1
,
'---+1-"..-'..~-':
Ie
....
,.:::.'-T1'L:c.1
"
"
.I
i ,.
.,... .
- "
I
; i
."
., =
-'
.,
., I·· .
..,
'r- I~
~
I
..
',. i'"
I"
.,
.~ ;,.
~
-,
_: ;
1'-' .
_ _ I _l
. , . ,.
:
:
,
:.~
,
.L
-, ,.
Figure 24 , Continued .
"
• • ! ,.
I
Diameter· ZD inches (point-to-po1nt)
12-S1decl.
x
"' ~#07..
Run No . fl.... x -39/%
q .~sf . d..=IS~
R.N. -.7/2
'I(
q -:!.;.EJaf.
lOt.
t.
.,
R.N.·
do .. /.5'I(
10 "
.i
-_.,
,
;
-
w
z
~
~
w
~
z
w
u
.,
··1
w
u
z
.,
I
I
,I
"'
~
~
I-
0
I
...
,.!.
, ,.
1
.
I
Fi gure 24.
Continued.
I
;
..
D1acnetel" • 20 inches (poi nt-to-point)
12-S ided,
Ru n
"
~
•
x
-3d" ?; --"._ jo---
Run No.-.LL. x -3!J/
--2-P sf . ,aI.. ==
q
R.N.- .972.
R.N .· .98 6 )( 10"
l(
10 "
.-' f
••u •e
• •
~
~
Ho.-2-.
q ·....£......psf., 0< _IS-
0
0
~
~
'"
N
i
i':
.,I,
~
z
~
~
~
~
z
~
u
i!i
~
,;
~
[,
~
u
z
,
.:,
:1
'!-
<
~
-
,
~.
,
~
0
,,
, ..
i
,
.. ,
,
I
,
~
~
~
J
:!
"!.
J,
:L
-, ,
0
~
i
,,
,
-- .... --
,
Figure 24,
Continued.
Z
/S"
Oiameter • 20 i nches (po1nt- to-point)
lZ-Sided,
Run No.
I~
, x "3.9/%
q .~sf., o/.s/5'
R.N.· /. 3 /
•
• 1
,'"
c.c:
,-c'
,
l(
10 "
1 - ,.
,
: . "' .
',',
:H;',
-,
,
- ,.
' _C ~ '
:
:.,'
"~h"
;
I
,
,
!
:'
,I
, ,-
", !
';
f
I
I
.. ..
~
c ...
'
,
!,
~
~
:c '
.
~
.'.. ,:
•
, I~c
,,
:::::'
1
,
:'
;
,
-:.
:
-• .
,
.'
! '
,
, ,'
•
'f
·i-:"'i·
_~_L~~ _ _~~~,~
-
~
Figure 24 ,
;,
"
:
I
0
I
,
FT
,
-i--
i
:1,
.:.
-'
,
~
i
I
T,'
,..
!
Continued .
,
Diameter· 20 fnches (point-to-point)
Run HO . .£..... x -3't:'%
Run Ho.~. x - 39/
q·~sf .
q ·~sf. , ~
R.N.· /.58
-.
;:E -_
-
/. ~(/ lc 10 "
10·
e --
o
~
, .,c.=/S'J(
... :
N
,
--
,
0
,,
i:·
!
·i
-,
o
1 - Ux/
%
=/.:r"
U
Fi gure 24 .
Continued .
-
- - ---
-----,-
'-=""--- -
-1-
-
/,'
----t--f
-
--1-7--
Re = 0 .36 X 10'
Figure 25..
Appare nt Sprea d of Wak e of 12-Si ded Cy l inder at a
= 0,
Re = .36 x 10'.
--
---~---t-
---
1
------t- ~Ulma)( -J
~.;;;:;;,,(-
-.C~.- - - - r '----{.
Re = 0 . 59'10'
Figure 25b.
Spread of Wake of 12-Sided Cylinder at a= 0, Re= .59x 10'.
U'm
~--------------~r----~-4----- ~--~-------~--~
-----~
--
p' -
--~=~~--=--T
--L
Figure 26a.
- .,r-....,L
Spread of Wake of 12- Si ded Cylinde r at ,, = 15 ° , Re= .36x 10'.
~-..
:::-
- - - 1-
- -
-
-
-
-
L
-
-~=-=--==-=-=;ji'
r-"'7~
)------
-----------r
Re= .61·10
Figure 26b.
-----.--1-
•
Spread of Wake of 12-Sided Cylinder at a= 15 ° , Re= .61 x 10'.
j
L
--...~-
J1"
- - - - ----=------=
- -=---=-r~
Re
Figure 26c.
-
-
----!=-:d. -
-
=.78 -10•
Spread of Wake of 12- Sided Cyl inder at a
= 15° ,
Re
= .78 X 10'.
-
---+--1
·28
Reynol d s N o.:
.19-10·
.26
. 60
.0 •
.02
°
o
Figure 27 .
2
•
6
8
I
In c h es
Di a met ers
Turbu l ence In t ensity of Wak e of 12 - Sided Cylinders, a = 0°.
Radius of Rou nded Co me rs ;s Expressed as Percentage of
Radius of Circumscribed Ci rcle.
.28
--
.26
/.24 __
.22
.20
.18
-
.,./
--
/'
b
r-::~~t;~~:::
/
------ -
---
I
/
/
/'
/
1
/
'
/
_----_
(,..-
/
;'
./
/.-r-~-- ,
.--0", .
::::s..
/~
"i
,/ /
/
/ -/
........."
Reynolds No. :
~----~
"
\ ""
,
'~
~
'\"
"19 X 10'
\\
"- '\!
•
,
~
........ "
.59
\
\
.77~\
"
\
\
\ .\
\
\
\
\
\
\
\
.14
I-
'~"
.60
,
.16
>
\
\
\
,
\
\
\
\
.12
I-
\
\
\
,,
\
Z
'\
\
\
.10
\
\\
\
\
w 08
U·
Z
\
\
\ ,\
\
, \
Sharp Corners
w
""
'\
..J
::l.06
C!l
a:
::l
I-
.20 X 10·
/
-- --
4.6% Radius Corners
-- - - - -
9 . 2% AadlusCorners
""
"" ,
.04
~
.02
o
o
Figure 28.
2
4
8
6
z
1
I nches
D iam e ters
Turbulence Intensity of Wake of 12 - Si ded Cyl inders at a = 15 ° .
o e< = 0
12-Slded Cylinder
0 0(:15"
0.5
,>
-"
D.•
•
0.3
C
"•
°
°
D
,
-,•
.<
E
z
-"•
°
0
0. 2
°0
0
0
0
°
°0
0
0
0
0
0. 1
0
0
0.2
0.'
0.6
0.8
1. 2
1."
I..
1.6
1.8
2
It
11)6
Reynolds NUmber
Figure 29 .
Strou ha 1 Number of Wake of 12 - Sided Cylinders .
VR
CIt
0 ()
0.5
0
0
12-Slded Cylinder
.,-•
0
o.•
-,•
0.3
D
E
z
,•
.-•,
.<
6
0.2
~
~
'1
~
0
IS"
III
0
IS"
0
0
.046
.046
.092
'1
IS"
.092
0
>
,
()
t
~0
0.1
o oL--~---L--~--~~~~~~-7~~~~~
0.10.20 . 1
n.4
0.5
0.6
~.
7 .
0 8
0 .9
10 6
It
Reynolds Number
Figure 30.
Effect of Corner Rounding and Orientation on Strouhal Number of Wake of
12 - Sided Cyl inde.r s at x = 300%.