JOL
CoA Note No.92
1 1 1 SKji.;:;..
THE COLLEGE OF AERONAUTICS
CRANFIELD
EFFECT ÓF BÓDY INCIDENCE ON TWO AFTERBODIES
WITH A REARWARD FACING JET
by
A. H. CRAVEN
NOTE
m,
92.
December, 1958.
T H E O O L L E & E O F A E R O N A U T I C S
C R A N F I E L D
The effect of body incidence on t h e forces
and moments on two afterbodies v/ith a rearward
facing j e t in. a subsonic uniform flow.
by
-A. H. Craven, Ph.D., M.Sc., D.C.Ae.
Prepared under Ministry of Supply Contract T/CEN/I473/FR3
SUMt/^Y
This paper contains the r e s u l t s of an experimental i n v e s t i g a t i o n
i n t o t h e effect of a j e t issuing from two afterbodies (one a r i g h t
cylinder ani the second conical) a t incidence t o a uniform subsonic
flow. The t e s t s were performed a t a Reynolds Number of 0,3 x 10
based on body diameter and maximum t u m e l v e l o c i t y ,
The presence of t h e j e t issuing from an afterbody a t incidence
s i g n i f i c a n t l y increases the magnitude of t h e noimal f o r c e , a x i a l force
and p i t c h i n g moment a r i s i n g fran t h e e x t e r n a l forces but not including
t h e d i r e c t r e a c t i o n of t h e j e t . On t h e blulY c y l i n d i l o a l afterbody
t h e effect of the j e t i s comparable i n magnitude t o the effect of
incidence. Hovrever t h e effect of the j e t on t h e conical afterbody i s
secondary t o t h e effect of incidence,
2
-CONI'ENTS
Page
Sumnary i
L i s t of Symbols 3
1 , I n t r o d u c t i o n l^.
2 , A p p a r a t u s 5
2 . 1 . The w i n d txjnnel and i n s t r u m e n t a t i o n 5
2 . 2 , The models 5
3» Scope of t e s t s 5
if. T e s t p r o c e d u r e 6
5 . R e s u l t s 6
5 . 1 . P r e s e n t a t i o n of r e s u l t s 6
5 . 2 . The p r e s s u r e d i s t r i b u t i o n on t h e 8
b l u f f a f t e r b o d y
5 . 3 . The f o r c e s and moments on t h e
b l u f f a f t e r b o d y 10
5 . 4 . The p r e s s u r e d i s t r i b u t i o n on t h e
t a p e r e d sifterbody H
5.5» The f o r c e s and moment on t h e t a p e r e d
a f t e r b o d y 12
6 . D i s c u s s i o n 12
6 . 1 . Accuracy of t h e r e s l u t s 12
6 . 2 . The f low around t h e c y l i n d r i c a l
a f t e r b o d y 12
6.3. The flow a r o u n d t h e c o n i c a l a f t e r b o d y 14
6 . 4 . Dependence of t h e r e s u l t s on C^ -14
o
7. Conclusions i6
8. References 17
Tables
Figures
3
-LIST OP SYTEOLS
C. a x i a l f o r c e c o e f f i c i e n t i n t e r m s of t o t a l b a s e a r e a
A
mV^
CT j e t t h r u s t c o e f f i c i e n t '
"^ o
Gyj t c t a l p i t c h i n g moment c o e f f i c i e n t i n t e r m s of t o t a l b a s e a r e a
M_ p i t c h i n g moment c o e f f i c i e n t on b l u f f a f t e r b o d y due t o b a s e
C., p r e s s u r e s
% p i t c h i n g moment c o e f f i c i e n t on b l u f f a f t e r b o d y due t o s i d e p r e s s u r e s
C-j normal f o r c e c o e f f i c i e n t i n terms of t o t a l b a s e a r e a
/ P ~ P o
0 p r e s s u r e c o e f f i c i e n t ( =
V i,n^
d body d i a m e t e r
m j e t mass flow
p static pressure (suffix o denotes free stream value)
r radial distance from jet centre
R radius of body
5 base area (= 11 R^)
U f r e e s t r e a m s p e e d
V, e q u i v a l e n t j e t v e l o c i t y i . e . t h e v e l o c i t y a t t a i n e d i n an
i s e n t r o p i c expansion from j e t s t a g n a t i o n pressiJire t o
f r e e s t r e a m s t a t i c p r e s s u r e
X d i s t a n c e from j e t e x i t a l o n g a f t e r b o d y a x i s p o s i t i v e i n
u p s t r e a m s e n s e
a a f t e r b o d y i n c i d e n c e i n d e g r e e s
6 m e r i d i a n a n g l e
p f r e e s t r e a m d e n s i t y
_ 4
-1, I n t r o d u c t i o n
A previous paper ( l ) has given t h e r e s u l t s of experiments t o
determine the effect of an undeflected axi-symmetric j e t iipon the pressiMre
d i s t r i b u t i o n s around r e p r e s e n t a t i v e afterbodies i n a uniform subsonic
stream and the effect of afterbody shape on t h e drag of the body a t
zero incidence. The effect of j e t d e f l e c t i o n on t h e flow round a blunt
afterbody at zero incidence v/as t h e subject of a second paper (2) by
the same author.
I t i s of i n t e r e s t to examine the effect of body incidence upon
t h e forces on and the flow round an afterbody from Yiriiich a j e t i s i s s u i n g
and i n particiiLar t o i n v e s t i g a t e t h e conditions v/hich e x i s t i n t h e
v i c i n i t y of the base. The afterbody at incidence without j e t w i l l
experience a normal and an ajcial force by v i r t u e of i t s incidence.
The presence of a j e t s e r i o u s l y complicates an a n a l y t i c approach t o
t h e problem. Theoretical papers by Spence ( 3 ) , S t r a t f o r d (4) and
Craven ( 5 ) , and experimental i n v e s t i g a t i o n s by Dimmock ( 6 ) , Davidson (7)
and others have explored t h e analogous two-dimensional problem. Reference
(5) includes some consideration of the axi-symmetric problem but a
s o l u t i o n has not yet been achieved. However aji approximate apj;lication
of slender body theory leads t o the concliision t h a t , i n i n v i s c i d flow,
t h e i n t e r f e r e n c e between t h e j e t and t h e flow around t h e afterbody
i s zero.
I t i s the purpose of the present paper t o a s c e r t a i n how t h e viscous
e f f e c t s , including the a r e a s of separation, modify the r e s u l t of slender
body theory. Experiments were conducted t o i n v e s t i g a t e the effects
induced by t h e presorce of t h e j e t and in p a r t i c u l a r t o determine the
pressure d i s t r i b u t i o n s on t h e surface of a conical afterbody and on
the base and side surfaces of a bluff c y l i n d r i c a l afterbody a t incidence
from \7hich a j e t i s s u e s . From the p r e s s u r e s , the side f o r c e , base drag
and p i t c h i n g moment induced on t h e afterbody by t h e i n t e r f e r e n c e of t h e
j e t with t h e subsonic free stream are c a l c u l a t e d .
The experiments described h e r e i n are the t h i r d phase of a fiiLler
i n v e s t i g a t i o n i n t o t h e effect of j e t flow sponsored by the Minist.-»y cf
Supply under Contract No. 7/GEN1473/PR3. The author would l i k e t o
thank Mr. P.M.Burrows for t h e p r e p a r a t i o n of F i g , 16, ïlr, S. H. L i l l e y
for t h e design and erection of the equipment, Mr. H. Stanton f o r t h e care
and enthusiasm with v^ich he made the models and the aerodjmamic
laboratory a s s i s t a n t s Vi/ho were responsible for t a k i n g t h e experimental
measurement s.
5
-2, Apparatus
2 . 1 , The wind tunnel and instrumentation
The t e s t s were performed i n a s t r a i g h t - t h r o u g h wind tunnel heaving
a closed working section measuring 3 f t . square. The compressed a i r
supply for t h e j e t v/as l e d t o the v/arking section in a 3'g" in. diameter
pipe along the c e n t r e l i n e of the tionnol. The supply pipe was threaded
a t i t s downstream end t o take the angled elbows necessary t o give the
afterbodies the required angle of incidence. The supply pipe was
encased i n a duralumin sleeve 4 i n . i n diameter, t h e space between t h e
sleeve and the supply pipe being occupied by the pressure tubes.
The surface pressiires on the models were read from a raultitube
water manometer.
2.2, The models
Tv/o models vrcre used i n t h e s e t e s t s :
-(±) a r i g h t cj'-linder 4" diamet er and 1 2" long
( i i ) a conical cylinder t a p e r i n g from 4" t o :f" diameter i n a
leng-th of 9" giving a b o a t - t a i l angle of 105 .
The models virere turned from l i g h t a l l o y . The i n t e r n a l c a v i t y of
each model was machined t o give a smooth i n t e r n a l flov/ i n t o a p a r a l l e l
sided j e t -f" i n diameter issuing from the model along i t s centre l i n e .
An i n t e r n a l gauze screen was f i t t e d between t h e model and t h e angled
elboTiT t o eliminate non-uniformities i n t h e compressed a i r flow from t h e
supply pipe i n t o the model's pressure cavity.
Polythene tubing for pressi:ire measurements was l e t i n t o s l o t s along
t h e model's generators a t angular i n t e r v a l s of 22-|- and secured Td.th
a r a l d i t o ,
3. Scope of the t e s t s
The t e s t s on each of the models covered a range of free stream
speeds from 50 t o 100 f . p . s . and a range of "equivalent" j e t speeds
from 0 t o 1500 f . p . s . The equivalent j e t speed i s t h a t c a l c u l a t e d from
t h e j e t blowing pressure assuming i s e n t r o p i c expansion t o free stream
p r e s s u r e . Defining the thrtist c o e f f i c i e n t C^ by
C
m V,
b
J 1
^ T T 2
^PU^ S
Tdiere m = j e t mass flovr (sliogs/sec)
V^ = equivalent j e t speed ( f t / s e c )
U^ = tunnel speed ( f t / s e c )
base area of model ( s q . f t )
o
the range of j e t t h r u s t c o e f f i c i e n t covered by these t e s t s was 0 < C <• 40,
6
-The miOdels were set at a series of incidences in the range
0 < a < 15 , Within this range of incidence, it is felt that interference
betv/een the jet and the tunnel v/alls does not affect the results
significantly,
4, Test procedure
The ordinary pressure plotting techniques were used in these tests,
The details are given in ref.1,
5, Resu].t3
5,1, Presentation of results
As in the previous work the pressure coefficients and forces and
moments were found to be presentable in terms of the non-dimensional
thrust coefficient C^. The j e t and free stream velocities are, thereby,
not used explicitly. This use of C_ is justified for two reasons^
f i r s t l y i t can be shown that the forces on the bodies are proportional
to C^ (e.g. Pig. 17) and for given C^. the resiilts are independent of
«J J
tunnel speed; i . e, the effect of Reynolds Number based on free stream
velocity is small,
The pressure distributions on the bluff cylindrical afterbody are
given m the form of isobar patterns as follows t
-Fig, 2 (a) Base pressure distribution at zero incidence (a = 0 )
for Cj = 0, 1, 2, 4, 10, 20, 40.
(b) Base pressure distribution a = 2 , 5 , l O , l 5 C^ = 0
(c) Base pressure distribution ct = 2 , 5 , 1 0 , 15 ^j = ''
(d) Base pressijre distribution « i : 2 , 5 , 1 0 , l 5 C_ = 2
(^.) Base pressure distribution « = 2 , 5 , 1 0 , 15 Cj = 4
(f) Base pressure distribution a = 2 , 5 , l O , 1 5 0 = 1 0
(g) Base pressure distribution a - 2°, 5°, 10°, 15° C = 20
(h) Base pressure distribution a = 2 , 5 , 10 , 15 C = 40
7
-.Fig. 5 (a) Side p r e s s u r e d i s t r i b u t i o n (not i n isobar form) for zero
incidence p l o t t e d against -^ for C = 0, 1, 2, 4, 10, 20, 40,
(b) Side pressure d i s t r i b u t i o n « = 2 , 5 , 1 0 , 15 0^ = 0
(c) Side p r e s s u r e d i s t r i b u t i o n ct = 2 , 5 , 1 0 , 15 0.^ = 1
(d) Side p r e s s u r e d i s t r i b u t i o n a = 2 , 5 , l O , l 5 0 , = 2
(e) Side pressure d i s t r i b u t i o n a = 2 , 5 , 1 0 , 1 5 0^ = 4
J
(f) Side pressure distribution a = 2 , 5 , 1 0 , l 5 0^ = 10
(g) Side pressure distribution a = 2 , 5 , 10 , 15 C^ = 20
(h) Side pressure distribution « = 2 , 5 , 1 0 , 1 5 C^ = 40
The origin for the meridian angle 9 is shown in Fig. 1. The base
and side distributions are thus synmetrical about a vertical plane through
the body centre-line. Hence the isobar patterns for incidences of
2 and 5 and 10 and 15 are placed side by side for ready comparison,
In Pig. 5 the isobars are plotted on axes of the meridian angle Ö and
of the non-dimensional distance
(•-)
upstream of the base,
Typical radial pressxjre distributions on the base are given in
Pigs. 3 and 4. Pig. 3 shows the dependence of the pressure coefficient
upon body incidence
a
and Pig. 4 gives the variation with meridian
angle 0; both figures being plotted for fixed values of C .
By integrating the appropriate pressure distributions the coefficients
of axial force, nonnal force, pitching moment due to base pressure
variations, pitching moment due to side pressure variations and total
pitcliing moment about the centre of the base have been calculated and are
given in Pigs. 6 - 1 0 respectively plotted against C^ for given values of
incidence and against incidence for particular values of C^,
The pressiire distributions on the
tapered
afterbody are given as
isobar patterns as follows :
-Pig, 11 (a) Side pressure distribution (not in isobar form) for zero
incidence plotted against •^ for C^ = 0, 1, 2, 4, 10, 20, 40.
(b) Side pressure distribution a = 2 , 5 , l O , 1 5 C = 0
(c) Side pressixre distribution a = 2 , 5 , 1 0 , l 5 C_ = 1
(d) Side pressure distribution a = 2 , 5 , 1 0 , 1 5 0.^ = 2
(e) Side pressure distribution a = 2 , 5 , 10 , 15 C^ = 4
(f) Side pressure distribution
a
= 2°, 5°, 10°, 15° C_ = 10
(g) Side pressux'-e distribution a = 2 , 5 , 1 0 , 1 5 0^ = 20
(h) Side pressure distribution « = 2 , 5 , 1 0 , 1 5 C_ = 43
8
-Again the prossiire d i s t r i b u t i o n on t h e tapered body i s syirmetrical
about t h e v e r t i c a l p l m o tlirougli t h e body c e n t r e l i n e . By i n t e g r a t i o n
of t h e pressvire c o e f f i c i e n t s , the c o e f f i c i e n t s of ;:ixial f o r c e , normal
force and. p i t c h i n g moment about the c e n t r e oi' t h e j e t were c a l c u l a t e d
and are given in F i g s . 12 - 14 r e s p e c t i v e l y p l o t t e d as for the bluff
c y l i n d r i c a l afterbody.
I n a l l t h e curves drawn t h e j e t has not reached t h e overchoked condition.
5. 2. The pressure d i s t r i b u t i o n on t h e bluff afterbody
5 . 2 , 1 . The base pressiures (Pig. 2a - h)
The general t r e n d of t h e pressvire d i s t r i b u t i o n on the base remains
u n a l t e r e d as body incidence i s increased. The base suction increases with
r a d i a l distance t o a peak at r _ , 7 approximately and then decreases
R
(Pigs. 3 and 4 ) . Por any pjurticuL-ir value of C_ and ^ (except very c l o s e
t o the j e t e x i t ) , the vo.riation of pressiire coefficient with meridian
angle shows a steady increase in suction from 8 = 0 t o 135 and t h e r e a f t e r
reiTiains sensibly constant (Pig. 4 ) . I n other v/ords t h e maximum sviction
occurs over a narrow band situatexi a t £ _ , 7 approximately and s t r e t c h i n g
R
for abouit 1^3 on e i t h e r side of the plane of symmetry. The r a d i a l p o s i t i o n
of the pealc suction moves outwards as t h e incidence i n c r e a s e s , e, g, peak
r o
suction occurs at -^ = .70 for a = 0
a t £ = .71 for ct= 5°
a t ^ = ,73 for a = 10°
and a t ~ = .78 f o r a = 15°
o
i n t h e case 6 = 18O , C = 43 (Pig. 3 ) .
J
Furthermore t h e r a d i a l p o s i t i o n of t h e poo-k section moves outvr^.rds as
meridinn angle 6 changes from 0 t o 9Ö and then s l i g h t l y inv/ards again
t o 6 = 180°, e.g. in t h e case v/hen a = 10°, C_ = 20 (Pig. if)
peak motion occurs o.t ^ = .64 f o r 6 = 0
at I = ,70 f o r 6 = 45°
at I = .75 f o r 6 = 90°
a t I = ,72 for 6 = 135°
and a t ^ = .73 f cr 6 = 180°
9
-At zero body incidence and at =; = 0,6 approximately for all values
of C_ there appeared a suction peclc followed at a slightly Larger radius
by a second and larger suction pealc, The same effect is noted v/ith the
afterbody at incid.ence but in a modified form. At 6 < 45 the effect is
absent. As 6 increases the effect becomes apparent but the foil and
subsequent rise covers a much larger region than for zero incidence,
The magnitude of the angle of incidence does not scan to affect this
phencmenon.
The jet choked at a particular value of C for a given freestream
«J
speed, A small increase of C^ above this value caused a rapid decrease in
suction over the base by abouT ten per cent of its value v/hen the jet
choked. The values of the pressijre coefficient remained constant if
C-was further increased. The effect C-was the same for all body incidences.
This feat\ire has been omitted from the isobar patterns to avoid confusion,
5,2. 2, The side pressure distributions (Pigs. 5a ~ h)
As on the base, the presence of the jet increases the slight suction
on the side of the body. As in the previous experiments it v/as found that
the jet had negligible effect at distances greater than two body diameters
vtpstream of the base. For any value of C^ and any value of
^
the suction
J d
rises with increase of meridian angle 6. At small incidences this trend
is maintained over the whole range of 6, At incidences greater than 5
however a suction peak occurs betvreen 6 = 67 and 90 and further increase
of 6 results in a reduction of suction until at 6 = 180 (the upper siirface)
the pressure is not appreciably different from that on the under surface
( 6 = 0 ) for the same values of C^. = —,
J d
Except at points close to the base (-^ < ,05) the side pressixre
distributions for choked and overchoked jet coincided for the same tunnel
speed and incidence,
10
-5 . 3 . The Forces and Moments on t h e bluff afterbocty
The force and moment c o e f f i c i e n t s \7ore obtained by dividing the
p a r t i c u l a r force by -g-pU^S, S being the maximum c r o s s - s e c t i o n a l area of
the afterbody, and the moment by -g-pU^Sd wtere d i s the maximum afterbody
diameter. The o r i g i n f o r moments i s t h e centre of the j e t o r i f i c e ,
5 , 3 . 1 , Base drag (Pig, 6)
The base drag i s presented as t h e a x i a l force i n t h e d i r e c t i o n of the
afterbody's centre l i n e . The base drag c o e f f i c i e n t increases with increase
of C^. for a l l values of body incidence. The increase i s l a r g e i n i t i a l l y
but moderates as C^. i n c r e a s e s ,
A second important feature i s t h a t for any value of C_ other than
zero within the range of these experiments, the drag decreased as t h e incidence
increased up to 2 - 5 , depending upon the C^ involved, t h e r e a f t e r increasing
v/ith incidence,
The effect of overchoking t h e j e t i s the same as reported previously
(ref, 1 ) ,
5 . 3 . 2 . Normal force (Pig. 7)
The normal force, j e t off, measured p o s i t i v e l y i n the d i r e c t i o n
6 = 180 and perpendicular t o t h e body centre l i n e shows a considerable
r i s e as the incidence i s increased. Furthermore the effect of t h e j e t i s
t o produce a normal force augmenting t h a t due t o incidence alone. I t
i s evident t h a t , except for t h e Large incidences, t h e normal force depends
only s l i g h t l y upon the effect of the j e t . Indeed i t i s only a t a = 15
t h a t an appreciable i n c r e a s e in C-^ occurs a t values of C_ g r e a t e r than 1 0,
5 . 3 . 3 . The p i t c h i n g moment
A l l p i t c h i n g moments are measured about t h e centre of t h e base and
talcen p o s i t i v e i n t h e nose-up sense,
5 , 3 , 3 . 1 . Moment duo t o base pressures (Pig. 8)
The p i t c h i n g moment due t o the v a r i a t i o n of the base pressure
d i s t r i b u t i o n v/'ith incidence and C_ i s found t o be p o s i t i v e f o r a l l values
of C^ and c' within t h e range of tno experiments. Increase of C^ and a
cause a r i s e i n p i t c h i n g raomont except a t high incidence and low C^ where
t h e r e i s a tendency for the value of G.. t o f a l l for f u r t h e r increase of C .
11
-5 . 3 . 3 . 2 , Moment due t o the s i d e pressures (Pig. 9)
The moment due t o the side pressures i s nose-up for a l l values of
incidence and C,.. The magnitude of C|^ increases sharply with increase of
o ^
incidence up to 2 for a l l values of 0^.. For C- < 20 t h e r e i s a f u r t h e r
J
tl
s l i g h t increase up t o a = 10 and then a small decrease as a approaches
15 . For C^ > 20 t h e value of Cy, decreases with increase of incidence
u n t i l a t a = 15 i t d i f f e r s only s l i g h t l y from t h e values for C.^ = 2C.
These r e s u l t s are t o be expected from the side pressure d i s t r i b u t i o n s
(Pig. 5a - g ) . For a = 5 f o r the h i j g e r values of C , and a = 10 and 15
for a l l C the pressure d i s t r i b u t i o n s shew t h e peak suctions occxirring
in the region 6 = 90 where t h e y have l i t t l e effect on moment. The pressures
on t h e upper and lower surfaces are n e a r l y the same and hence an almost
canst.-ait value of 0,, i s t o be expected a t the h i ^ incidences,
%
5 . 3 . 3 . 3 . Total p i t c h i n g moment (Pig. 10)
The sum of the base and s i d e moments i s t h e t o t a l p i t c h i n g moment
acting on the afterbody. I t i n c r e a s e s , i n general, vd-th incidence and C^.
However, for small values of C , the increase of G^ Virith a i s very small
for values of incidence greater than 5 .
5 . 4 . The p r e s s u r e d i s t r i b u t i o n on the tapered afterbody (Pig. 11a - h)
The pressure d i s t r i b u t i o n s on t h e tapered afterbody v/iiich Vircre
symmetric about the body centre l i n e a t zero incidence ncav shovred marked
v a r i a t i o n s vri.th change.in meridian a n g l e , although t h e v a r i a t i o n along
generators shov/ed t h e same general t r e n d s as a t a = 0 . I t vra.s noted t h a t ,
a t the higher incidences, suction pealcs developed at 6 = 45 approximately.
Because of t h e p o s s i b l e e r r o r s d\Je t o t h e proximity t o t h e elbow,
the p r e s s u r e d i s t r i b u t i o n s on the p a r a l l e l p o r t i o n of the afterbody
( / d > 2.5) are not given.
12
-5.5, The forces and moments on t h e tapered afterbody
The farces and pitching moments are in t h e d i r e c t i o n s and senses
defined i n paragraph 5 , 3 . 3 .
5.5.'. The £ocial force (Pig. 12) / ' • . . '
Increase of incidence causes a l a r g e increase i n t h e a x i a l f o r c e
c o e f f i c i e n t and increase of G f u r t h e r increases C . The effect of t h e
j e t i s only very s l i g h t f o r C^. < 10 at a J l incidences and f o r a l l C^
at zero incidence. For G^ > 10 the j e t i n t e r f e r e n c e s i g i i f i c a n t l y augments
t h e drag due t o incidence.
5 . 5 . 2 . The normgg force (Pig. 13)
As vd-th t h e a x i a l f o r c e , incidence i s t h e major f a c t o r affecting
the normal force, t h e j e t i n t e r f e r e n c e having only a secondary effect.
Values of G_ l e s s than 10 seem t o have no effect a t a l l and fcjr C^ = 40
t h e increment in normal force coefficient due t o t h e j e t i n t e r f e r e n c e i s
only 30fo of t h a t due to incidence. I t should be noted t h a t a s v/ith ordinary
conical afterbodies the normal force i s negative.
5 . 5 . 3 . The p i t c h i n g moment (Pig. 14)
The p i t c h i n g moment i s negative for a l l values of C_ and incidence.
Up t o a = 5 increase of incidence causes an i n c r e a s e in t h e magnitude of
the p i t c h i n g moment c o e f f i c i e n t . Further increase of incidence i s accompanied
by a s l i g h t reduction i n the magnitude of G,^, The presence of the j e t has
a n e g l i g i b l e effect on t h e p i t c h i n g moment,
6, Discussion
6 . 1 , Accuracy of r e s u l t s
The j e t supply pressure duri.ng any one t e s t was maintained a t the
required value within l i m i t s of 2%. The tunnel speed could be kept
accurate t o v/ithin ^% and the surface pressures were measured t o 0.02 in.
of water. The o v e r a l l error i n t h e pressure coefficixjnts and t h e f c^'ce and
moment c o e f f i c i e n t s i s t h e r e f o r e expected t o be l e s s than 5%.
6. 2. The f lov/ around the c y l i n d r i c a l afterbody
I t i s found t h a t s e t t i n g t h e afterbody a t incidence causes major
modification of t h e t o r o i d a l vortex system which i s s e t up when t h e j e t
i s s u e s from the c e n t r e of the bluff base of the \jndeflected aftei-body ( r e f . l ) .
Except in t h e v e r t i c a l plane of synmetry the flow on t h e base i s no longer
r a d i a l but c\Jrves from an attachment l i n e at £ - , 3 approximately t o a
13
-s e p a r a t i o n l i n e a t ^ = . 8 approximately. Thi-s i -s -shown i n Fig, 15 which i -s
drawn from a s e r i e s of surface floi',"- p i c t u r e s . There i s a l s o a v/eak flow
i n t o t h e s e p a r a t i o n l i n e inwards f rem t h e edge of the base (£ = 1) and t h e
R
a i r e n t r a i n e d i n t o the j e t a t i t s exit c u r l s i n t o t h e j e t from the attachm.ent
l i n e . The s e p a r a t i o n and attaclment l i n e s shov/ l i t t l e evidence of e c c e n t r i c i t y
f o r small incidences b u t a t t h e higher incidences a degr"ee of e c c e n t r i c i t y
i n t h e s e p a r a t i o n l i n e i s a p p a r e n t l y equivalent t o £ _ , - ] , This i s c o n s i s t e n t
vd-th the form and extent of t h e r a d i a l pressiore d i s t r i b u t i o n . The presence
of t h e s e p a r a t i o n l i n e i s t o be expected i n view of the ad.verse p r e s s u r e
gradient outboard of t h e peak suction a.t £ = . 8 approximately and t h e
^ r
attachment line is confirmed by the minimum suction that occurs at ^ = ,3
approximately. This and the degree of eccentricity can be seen more
clearly if the pressure coefficients are plotted against radial distance
far a series of meridian angles at one incidence and a.t one meridian fingle
for a series of incidences (e.g. Pigs, 3 and 4 ) .
In the lower plane of symmetry ( 8 = 0 ) there is relatively little
variation in pressiire coefficient v/ith radius. The surface flow patterns
near 6 = 0 show little accretion of fluid and the attachment line is very
indefinite. As the meridian angle increases so the radial variation of the
base suction coefficient is increased until in the region 135 < Ö < i 80
the pressure variation is greatest. The separation is strongest in this same
region as indicated by the high suction lobes in that region on the isobar
patterns. The boundary layer v/hich separates from the base appears to roll
up and form a pair of spiral vortex sheets. These vortices originate near
the base in the lov/er plane of symmetry and increase in strength as they
move round the base until they separate in the region 135 < 6 < 1 80 .
They pass dov;nstream and eventually must marge into the jet (Pig. 1 6).
There are no features in the surface
flaw
patterns which correspond
to the first suction peak at £ _ o.6 (Pigs. 4 and 15). The form of the
pressxire distribution is, hovrover, consistent v/ith the development of a
laii.inar type boundary layer up to £
=
0,6 follov/ed by a laminar separation
and turbulent reattachment. Turbulent separation then occurs, as stated
above, at £ = o. 8.
The pressure distributions on the side of the bluff a^fterbody suggest
that the f lev/ over the afterbody with jet is not significantly different from
that at the some incidence vn.th no jet. At 2 incidence it v/ould appear
that the cross flow does not separate for any value of 0^., x\t 5 incidence
separation occurs at 6 = 135 except for C^. = 40 and in this case the
effect of entrainment into the jet is sufficient to prevent separation on
the side surfaces. At the higher incidences separation occurs as one would
expect at 6 = 70 approximately, the separated boundaly layers rolling up
to form the characteristic vortex pair,
14
-The mixing region beyond about two body diameters dovmstream of t h e
base contains throe i n t i a l l y d i s t i n c t flov/s; t h e j e t , the p a i r of vortex
sheets shed from the base and the p a i r shed from the sides of the afterbody
(Pig. 16). Yavmeter i n v e s t i g a t i o n s i n t h e wal<e did not give s u f f i c i e n t
d e t a i l t o determine t h e exact nature of the mixing processes betv/een t h e
vort-'jces and the j e t . Prom t u f t i n v e s t i g a t i o n s i t vra.s found t h a t t h e i n n e r
separated regions close to the base of t h e body extended t o about one body
diameter dov/nstream of t h e base,
6 . 3 . The flov/ p a t t e r n around, the conical afterbody
At loT/ values of C.^ (C_ < 2) the flow around the conical afterbody
i s l i t t l e affected by t h e j e t . The flow appears t o separate at about '^ne
body diameter upstream of the j e t exit and only for G.^ > 2 i s t h e entrainment
i n t o t h e j e t s u f f i c i e n t to cause reattachment. At the l a r g e r incidences
the pressure d i s t r i b i i t i o n s show evidence of boundary layer separa.tion a t
6 = 45 v/ith t h e separated boundary l a y e r s r o l l i n g up t o form t h e p a i r
of r o l l e d - u p vortex sheets c l i a r a c t e r i s t i c of a body of revolution a t incidence,
At the higher values of C^. t h e entrainment effect of t h e j e t i s t o reduce
t h e strength of t h e v o r t i c e s since l e s s flow i s fed into them. This has the
effect of reducing the suction peaks on t h e s i d e s of the body.
6 . 4 . Dependence of the r e s u l t s on C^
' — • • " ' Ü
I f t h e r e s u l t s f o r the norntal f o r c e acting on the bluff afterbody are
expressed i n the form log(C,.^ - C^.,. ) and p l o t t e d against log C (Fig. 17)
^' Cj = 0
'^
it is found that, for each incidence, a straight line is obtained the slope
increasing with incidence indicating that the incidence effect and jet
effect are additive and that
G
N
^N. . ~ ^ï ^ 1 ^ " )
vAiere n is a constant depending upon the incidence ct, and g. ( K ) is
zero when n = 0 .
I t i s n o t i c e d t h a t , for incidences considered, n/sin^a i s a constant
and equal t o 1,55 approximately,
- 15
a
n
i^sin a
n/V s i n cc
2°
0.290
0,1868
1.55
5°
0.455
0,2953
1.54
10°
0.640
0.4166
1.54
15°
0 . 7 9 2 '
0.5058
1.56
Ylhen log(C, - C. ) i s s i m i l a r l y p l o t t e d (Pig. I8) i t i s again seen
^ ^C-, = 0
t h a t C. - C. i s proportional t o C^. g_( a). The value of n i s 0,58
^ ^"Cj = 0 -^ ^
approximately and appears t o be independent of incidence,
Ylhlle t h e normal force coefficient for t h e conical afterbody does obey
a law of the form
°N " °N
Cj = 0
cJ
g^{ a )
irhe r e l a t i o n between n and a cannot be s t a t e d as p r e c i s e l y as for t h e
bluff afterbody. To v/ithin 20^ acciJracy the r e l a t i o n n
T- = 4.7
sin^cc
covers the experimental p o i n t s . The a x i a l force on the conical afterbody
i s predominantly dependent upon incidence; t h e experimental evidence i s
not s u f f i c i e n t to deduce a functional r e l a t i o n s h i p between a x i a l force and
j e t moment\:im c o e f f i c i e n t .
l6
-7. Conclusions
(i) The presence of a jet issuing from the afterbody at incidence
significantly increases the magnit-udc of the normal force, drag and pitching
moment on a bluff cylindrical afterbody and a conical afterbody. This
effer't is in addition to the normal jet reaction.
(ii) On the bluff cylindrical afterbody the effect of the jet is comparable
in magnitude to the effect of incidence. The effect of the jet on the conical
afterbody is secondary to the effect of incidence,
(iii) Typical magnitudes of these effects on the cylindrical afterbody are
as follows
:-At 15 incidence the normal force coefficient v/as raised from 0,27 at
C = 0 to 0.73 at C = 40. The base drag coefficient was raised from
0,31 to 1,38 for the same increase in C.^ but the increment in drag coefficient
is roughly independent of incidence,
(iv) On the conical afterbody the maximum effect was experienced at 15
incidence v,ti.ere the axial force coefficient v/a^ raised from 0,8l to 0,97
by increasing C from 0 to 40. The correspondi.ng values for a = 0 are
0,11 and 0,13. The normal force coefficient at 15 incidence changed from
-0,46 to -0,59 for the same range of 0^..
(v) The pitching moment on the bluff afterbody v/as predominantly due to
the pressiorc variations on the base v/hereas on the conica.1 afterbody it
vra-S sensibly independent of jet interference,
8, References
17
-1, Craven, A,H,
2, Craven, A.H,
3 , Spence, D.A,
4, S t r a t f o r d , B,S.
5, Craven, A.H.
6, Dimmock, N.A,
7, Davidson, I ,
The i n t e r f e r e n c e of a rearward facing j e t
on t h e flow over thi'ee r e p r e s e n t a t i v e
afterbody shiapes in a uniform subsonic flov/,
College of Aeronautics Note N0.6O, April,1957.
The effect of j e t d e f l e c t i o n on t h e
interference of a rearv/ard facing j e t vd.th
the flow over an afterbody i n a uniform
subsonic flow.
College of Aeronautics Note No. 70, October,1 957,
Treatment of the j e t flap by t h i n a e r o f o i l
the ory.
R,.A.E. Report Aero. 2568. November, 1955.
Mixing and t h e j e t f l a p .
Aero. Quarterly, Vol,7, Aug\.ist, I956.
A p o t e n t i a l flov/ model for the flov/ about
a n a c e l l e v/ith j e t .
College of Aeronautics Report No, 101,
March, 1956.
An experimental introduction to t h e j e t
f l a p , N,G,T.E. Report R.I75, and
Somxe further j e t f l a p experiments.
N. G. T. E. Memorandum M, 255.
The j e t f l a p .
J o u r n a l of t h e Royal Aeronautical Society,
January, 1956.
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