cylinder at different reynolds number
DESCRIPTION
cylinder at different reynolds numberTRANSCRIPT
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NASA TN
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TECHNICALD-455
NOTE
EFFECT OF I_EYNOLDS NUMBER ON THE FORCE AND PRESSURE
DISTRIBUTION CHARACTERISTICS OF A TWO-DIMENSIONAL
LIFTING CIRCULAR CYLINDER
By Vernard E. Lockwood and Linwood W. McKinney
Langley Research Center
Langley Field, Va.
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON Septembe r 1960
D-455
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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
TECHNICAL NOTE D-455
_FECT OF RETNOLDS NUMBER ON THE FORCE AND PRESSURE
DISTRIBUTION CHARACTERISTICS OF A TWO-DIMENSIONAL
LIFTING CIRCULAR CYLINDER
By Vernard E. Lockwood and Linwood W. McKinney
SUMMARY
A two-dimensional lifting circular cylinder has been tested over a
Mach number range from 0.011 to 0.32 and a Reynolds number range from
135,000 to 1,580,000 to determine the force and pressure distributioncharacteristics. Two flaps having chords of 0.37 and 6 percent of the
cylinder diameter_ respectively, and attached normal to the surface were
used to generate lift. A third configuration which had 6-percent flaps
180 ° apart was also investigated. All flaps were tested through a range
of angular positions. The investigation also included tests of a plain
cylinder without flaps.
The lift coefficient showed a wide variation with Reynolds number
for the 6-percent flap mounted on the bottom surface at the 50-percent-
diameter station, varying from a low of about 0.2 at a Reynolds number
of lo5,000 to a high of 1.54 at a Reynolds number of 350,000 and then
decreasing almost linearly to a value of 1.0 at a Reynolds number of
1,580_000. The pressure distribution showed that the loss of lift with
Reynolds number above the critical was the result of the separation point
moving forward on the upper surface. Pressure distributions on a plain
cylinder also showed similar trends with respect to the separation point.
The variation of drag coefficient with Reynolds number was in direct
contrast to the lift coefficient with the minimum drag coefficient of
0.0 occurring at a Reynolds number of 360,000. At this point the lift-
drag ratios were a maximum at a value of 2.54.
Tests of a flap with a chord of 0.0037 diameter gave a lift coeffi-
cient of 0.85 at a Reynolds number of 520_000 with the same lift-drag
ratio as the larger flap but the position of the flap for maximum lift
was considerably farther forward than on the larger flap. Tests of two
0-percent flaps spaced 180 ° apart showed a change in the sign of the lift
developed for angular positions of the flap greater than 132 ° at subcriti-
cal Reynolds nt_bers. These results may find use in application to air-
craft using forebody strakes. The drag coefficient developed by the flaps
when normal to the relative airstream was approximately equal to that
developed by a flat plate in a similar attitude.
INTRODUCTION
At the present time investigations are being madeby various agenciesto provide information on possible methods oI recovering rocket boosters.One such investigation by the National Aeron_utics and Space Administrationis concerned with the generation of lift on E_body of revolution movingwith its axis normal to the flight direction. In this method the lift isgenerated over the length of a body by the deflection of a small flap onthe bottom surface. A recent investigation (ref. i) on a circular cylinderof fineness ratio i0 has shownthat relatively high lift coefficients canbe obtained in this manner. The data of reference i showvery largelosses of lift coefficient for Machnumbersabove 0.3. It is possiblethat the loss of lift at the higher Machnumbersmay in part be a Reynoldsnumbereffect since Machnumberand Reynolds numberwere not independentlyvaried during the test. It was shownin reference i that the drag of aplain cylinder increased with Reynolds numberabove the critical for lowsubsonic Machnumbers; therefore, it is reasonable to assumethat thelift coefficient mayalso be affected by Reynolds number. The purposeof this investigation was therefore to determine the effect of Reynoldsnumberon the lifting characteristics of a circular cylinder in the Machnumberrange where compressibility effects are small.
The investigation wasmadeon a two-dimEnsional circular cylinderover a range of Reynolds numbersfrom 135,00( to 1,580,000 based oncylinder diameter. The lift and drag forces on the cylinder were meas-ured and, in addition, pressure distribution_ were obtained as an aidin understanding Reynolds numbereffects. D_ta were obtained on twodifferent sizes of flaps located on the lowe_ surface at the 50-percentstreamwise position; other flap locations were also studied. For com-parative purposes data were also obtained on a plain cylinder (withoutflaps). In addition to these tests, tests w_re also madeof a configu-ration which had flaps 180° apart. These da_a mayhave application toairplane configurations using forebody strakcs.
L936
SYMBOLS
The data are presented with respect to the wind axes as indicated
in figure i.
c flap chord
cd section dra(] coefficient,Drag par unit length
dL_v22
3
L
9
3
c I
cm
Cp
d
M
P
Pl
R
V
Subscript:
section lift coefficient,Lift per unit length
d_Pv22
section pitching-moment coefficient about cylinder axes,
Pitching moment per unit length
d22_V2
pressure coefficient,
cylinder diameter
Mach number
Pl -P
P_V22
free-stream static pressure
local static pressure on cylinder
Reynolds number
free-stream air velocity
free-stream air density
flap angular position relative to wind, positive from trailing
edge down, deg
radial angle relative to wind, measured from leading edge
(either upper or lower surface), deg
max maximum
MODELS AND EQUIPMENT
The cylinder used in the investigation had a diameter of 8.34 inches
and completely spanned the test section of the Langley 300-MPH 7- by
lO-foot tunnel as shown in the diagram of figure i. The cylinder was
constructed of mahogany and lacquered to produce a smooth finish. In
order to minimize any effects which might be caused by air leakage through
the small clearance gaps where the cylinder passed through the floor and
4
ceiling_ the cylinder was equipped with end plates to prevent spanwise
flow. The standard mechanical balance system of the tunnel was used to
measure the lift and drag.
Tile flaps used in the investigation are illustrated in figure i.
The smallest flap was made of a strip of met_l 1/32 inch by i/8 inch
and when attached to the bottom surface had a chord of 0.0037 cylinder
diameter. The larger flap which was made of i/2-inch by I/2-inch angle
had a chord of 0.06 diameter. (These flaps lereafter will be referred
to as the 0.37-percent and O-percent fl_p, respectively.) The side of
the angle used for attaching the larger flap was placed in the downstream
direction. A third flap confign_ration was made up of two i/2-inch by
L/2-inch angles attached i_0 ° apart. All flaps were attached by counter-sunk wood screws.
One set of pressure orifices was instalZed near the midspan with
tubes spaced approximately 15° apart around the surface. The pressureswere recorded on film from an alcohol manome_ er board.
L
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36
TEST CONDITIONS
For most of" the tests in the investigation the dynamic pressure
was held constant and the flap position 5 _as varied by rotating the
cylinder through an angular range. For the lemainder of the test the
flap was held fixed at 5 = 90o (see fig. i) while the dynamic pressure
was varied. This variation of dynamic presstre corresponded to a range
of Re,molds numbers from 135,000 to 1,580,00( , based on the cylinderdiameter of 0.695 foot. The flow turbulence factor was i. All tests
were made at Mach numbers well below the crit ical Mach number for the
cylinder. The approximate variation of Reynolds number with Mach number
for these tests is shown in figure 2.
RESULTS AND DISCUSSICN
The lift and drag characteristics of the various flap configurations
studied in this investigation are presented in figures 5 to 7. Pressure
distributions which correspond to some of the data points of figures _ to
t are presented in figmres 8 to 13. Pitching-moment data are not pre-
sented. An approximation to the pitching-moment coefficient can be
obtained from the equation
Cm = i Acp c7
where _Cp is the pressure-coefficient difference between the upstream
and downstream side of the flap.
L
9
36
Lifting Flaps
Effect of Reynolds number.- The effect of Reynolds number on the
aerodynamic characteristics of the cylinder with the 6-percent flap
(b = 90o ) is shown in figure 3. The lift coefficient shows a large
variation with Reynolds number over the complete range tested. At the
subcritical Reynolds number of 165,000, a cz of approximately 0.2
was obtained while just above the transition range (R = 350,000) a maxi-
mum c_ of 1.54 was obtained. As the Reynolds number was further
increased, the lift coefficient decreased almost linearly to a value of
c_ = 1.0 at R = 1,580,000, the limit of the tests.
The lift data of figure 3 are replotted in figure 4 along with some
selected pressure diagrams for both the plain cylinder (nonlifting) and
the lifting cylinder to indicate the type of pressure distributions asso-
ciated with the lift generation. The plain-cylinder pressure distribu-
tion for a Reynolds number of 190,000 was obtained from reference 2. It
is apparent from the pressure diagrams of figures 4 and 8 that the pres-
ence of the 6-percent flap (b = 90o ) causes an appreciable alteration of
the pressure distribution. On the lower surface the negative pressure
loop of the basic cylinder is almost completely destroyed. On the upper
surface the pressure coefficients show a material gain over that of the
basic cylinder as a result of the circulation established by the flap.
In addition to the effects noted on the upper and lower surface_ the
circulation also produced a considerable increase in the negative pres-
sure coefficients over the rear of the cylinder which results in a con-
siderable increase in drag coefficient. (See fig. 3.)
A further study of figures 4 and 8 shows the cause of the decrease
in lift coefficient with increase in Reynolds number mentioned previously.
These data show that, as the Reynolds number is increased above 426,000,
the separation point in general moves forward on the upper surface
(about 40 ° in the range of Reynolds numbers from 426,000 to 1,308,000).
This forward movement of the separation point reduces the area affected
by the high negative pressures. Also noted in this range of Reynolds
numbers is a decrease in the peak negative pressure coefficient ahead
of the separation point.
The forward movement of the separation point and the reduction of
the peak pressure coefficient with increased Reynolds number may also
be observed in the plain cylinder data of figures 4 and 9 for Reynolds
numbers greater than 950,000. The reduction of peak pressures on the
8
The negative lift shown in figure 7 for the subcritical Reynolds
number (190,000) for values of 8 > 130 ° apoears to be associated with
laminar separation on the top surface and a turbulent reattachment on
the bottom surface. On the top surface the typical subcritical Reynolds
number pressure distribution is indicated in figure 13(a) with separation
over more than half of the upper surface. On the lower surface the pres-
sure shows a pattern similar to that for the supercritical Reynolds num-
ber in that the negative pressure coefficient increases behind the flap.
Evidently, the turbulent flow from the flap reattaches to the cylinder
and the turbulent boundary layer allows the lower surface separation point
to occur farther back on the cylinder. The asymmetry of the resulting
flow produces the negative lift force.
The two flaps 180 ° apart (see fig. 7) _ay also be considered as a
drag-producing device in which case the cylinder fitted with flaps
(c/d = 0.00) has nearly as high a maximum drag coefficient at a Reynolds
number of 520,000 as a flat plate normal to the airstream. At 6 = 90o
the flaps with separated flow behind gave a drag coefficient of 1.8 which
is close to the value of 1.98 quoted in reference 5 for a two-dimensional
flat plate. The value of cd = 1.8 represents a sixfold increase in the
drag coefficient when compared with that of the plain cylinder at a
Reynolds number of 520,000. (See fig. 3.)
L
9
36
SUMMARY OF R_ULT[
A low-speed investigation has been mad_ on a two-dimensional lifting
circular cylinder over a Reynolds number range from 135,000 to 1,580,000
to determine the force and pressure distribution characteristics. The
results are summarized as follows:
i. The critical Reynolds number for th_ lifting cylinder with a
o-percent flap deflected 90o was approximately 350,000.
2. 'i_nelift coefficient which showed a wide variation with Reynolds
nmllber varied from a low of about 0.2 at a Iieynolds number of 165_000 to
a high of 1.54 :_t a Reynolds number of 350_(_00 and then decreased almost
linearly to a w_lue of 1.0 at a Reynolds nu_iber of 1,580,000 for the 6-
percent flap deflected -20°.
3. The drag coefficient of the 6-percelt flap configuration varied
linearly from a minimum of 0.o at a Reynold_ number of 350,000 to a maxi-
mum of 0.9 at a Reynolds number of 1,580,000.
4. The lift-drag ratio for a 0-percent flap deflected 90 ° varied from
a low of 0.15 at subcritical Reynolds numbers to a maximum of 2.54 at the
2Z
beginning of the supercritical range. It then decreased with increasingReynolds number.
5. The pressure distributions for the 6-percent flap configuration
showed that the loss of lift with Reynolds number was the result of the
separation point moving forward on the upper surface. Pressure distribu-
tions over a plain cylinder also showed similar trends with respect to
the separation point.
6. Tests of a 0.37-percent flap gave a lift coefficient of 0.85 at
a Reynolds number of 520,000 with the same lift-drag ratio as the larger
flap but the position of the flap for maximum lift was considerably
farther forward than on the larger flap.
7. Tests of two 6-percent flaps spaced 180 ° apart showed a change
in the sign of the lift developed for positions of the flap greater than
132 ° at subcritical Reynolds number. The drag coefficient developed by
the flaps when normal to the relative airstream was approximately equal
to that developed by a flat plate in a similar attitude.
Langley Research Center,
National Aeronautics and Space Administration,
Langley Field, Va., June I, 19GO.
REFERENCES
i. Lockwood, Vernard E., and McKinney, Linwood W.: Lift and Drag Char-
acteristics at Subsonic Speeds and at a Mach Number of 1.9 of a
Lifting Circular Cylinder With a Fineness Ratio of i0. NASA
TN D-170, 1959.
2. Bursnall, William J., and Loftin, Laurence K., Jr.: Experimental
Investigation of the Pressure Distribution About a Yawed Circular
Cylinder in the Critical Reynolds Number Range. NACA TN 2463, 1951.
3. Schlichting, H.: Lecture Series "Boundary Layer Theory" - Part II -
Turbulent Flows. NACA TM 1218, 1949.
4. Polhamus, Edward C., and Spreemann, Kenneth P.: Effect of High Sub-
sonic Speeds of Fuselage Forebody Strakes on the Static Stability
and Vertical-Tail-Load Characteristics of a Complete Model Having
a Delta Wing. NACA RM L57KI5a, 1958.
5. Hoerner, Sighard F.: Aerodynamic Drag. Publ. by the author
(148 Busteed, Midland Park, N.J.), 1951.
10
\\\\\\_4\\4\\\\
Flop -- -_-
It
;\ \\\\\\\\\\\\_'_
I
i
Cylinder
End plate
Mode/ in 7 - by I0- foot tunnel
_-- Tunnel wall
I
o_
Lift
_- __ / _-Flop
Wind _ -_-- i --J
C/d=O.06_3
c=.500._ _L --i
-_.50
• 7-- -- []-=Jc=.500._L___
.37- percent flap
6 - perce n t flop
F_ps /80 ° apart
Flop configurations
Figure i.- Diagram of model and flaps used in the investigation. (All
dimensions are in inches.)
ii
2.0x
_o
I
lO
R
.8
.4
.2
00 .05 .lO .15 20 25 .30 35
M
Figure 2.- Variation of Reynolds number with Mach number for the
investigation.
12
Cz
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iii _iili !!i;?_!! ,,h_;i_a
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0 :_: _ _ i'!ti'!i :::i]?t]:l.._, ,4+,1 ,,*[tlFI+I
,.,+ ............ +,.,,_
.... ,.,,,
[ ,,,tt'-_::::ti :i .... ,
::::[:::i ::i_,_:', ', ',_,;:; ........ + .... ,,.
77-7t7:-_ ._'_,;T;: ,*:::_::H,
,[, _/61:[:_.[ii! .::_:_ ,_, ....-:}'_ri," ,,-,t ............
,.;, :+i, ',:;;I;:: ....
:!i:[[i:[ ...... )','" i :_
4 i:'it'+l: r' ;z.t :L_ :: ,
oiii!!!i_:ii iLii_i !i_!ii_ii'tt-tt,'t
_:;_ ::4:;;:: -!_!iiff_
[::i::'i:i !:!!ii!i ii:!!:!!i30
Z
! I
_t.
*t"
!i:40 50 60
Figure 5.- Effect of flap angular position cn the aerodynamic character-
istics of a lifting cylinder for two Reynolds numbers, c/d = 0.06.
I
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15
',.o
I
&Cd
Figure 6.- Effect of flap _ngular position on the aerodynamic character-
istics of a lifting cylinder for two Reynolds numbers, c/d = 0.0057.
16
c_
Cd
ct
R
o 190,000
n 520, 000<> 1,0,38,000A 1,216,000
I10 120 1,30 140 150 160 170 I_0
8,deg
,iiiif!ii:
Iiiii : i::J;;ll:ii: /2
,4''++,'_ •
+4+.+_.-
ot,!t,*r!.
Ti_;'i:;
!t::I_:ti
i,,!i,l_,l
ii!:t!_:i
I
',D
Figure 7-- Effect of flap angular position on the aerodynamic character-
istics of a cylinder having two flaps 180 ° apart, c/d = 0.06.
3Z17
_o
o_I
0 50 t00 150
Figure 8.- Effect of Reynolds number on the pressure distribution about
a lifting cylinder, c/d = 0.06; 8 = 90 ° .
i8
,:i _: liib - _ + I i _ Lower surfoce i i
o_- _ ..,, .... t: i! I ' '
I + . _ i R=601,O00
Cp
/
0
G
-I
I
t,Ok.>i
Figure 8.- Concluded.
!- T _ _ Lower surface _-o Upper surface
R=502000 R = 1,005,000
'q:)
I
0
Figure 9.- Effect of Reynolds number on the pressure distribution about
a plain cylinder.
2O
I
!
!xD
O_
(a) R = 520,000.
Figure i0.- Effect of flap angular position o_] the pressure distributionabout a lifting cylinder. Tick refers to flap position, c/d = 0.06.
21
Dc_
I
_/I"L
]i_
#=60 °
I:ii!
0 50 /0"0 GO
_,deg
= I00 o
(b)
i ' [ I
I T "
I
R = i_216,000.
G =/20 °
Figure i0.- Concluded.
22
!',D
G"
50 /_
8=90 °
cp
: J150 0 I50
(a) R : 520,000.
Figure ii.- Effect of flap angular position on the pressure distribution
about a lifting cylinder. Ticks indicate flap position, c/d : 0.0037.
23
_D
I
0 50 I00 /.50O, d_
'/0 ° I
5O t00 150
(b) R = 1,216,000.
Figure ii.- Concluded.
24
9o
3o
2O
@
i0
g
III
10
3O
6O 7o 80 9o ioo 11o 12o
17o
tI
_4
C
9o 60 70 8O 9O zoo no 12o
Figure 12.- Effect of flap height on the pressure distribution about a
circular cylinder. 5 = 90o; R = 520,000.
4Z
25
<O
O_I
I
0
/
-2
i8=140°
0
(a) R : 190,000.
Figure 13.- Effect of flap angular position on the pressure distributionabout a cylinder having two flaps 180 ° apart. Ticks indicate flap
position on respective surfaces, c/d = 0.06.
26
!koRNO'x
f
10
(b) R = 520,000.
Figure 13.- Contirued.
27
Lower surfoce
Upper surfoce
L
ii
0
Cp_/
Z =120 °
/50 0 50
d;,de g
(c) R : 1,038,000.
Figure 13.- Concluded.
NASA- Laagley Field, Va. L=936
