Drag reduction by suction of the boundary layer separated behind shock wave formation at high mach numbers

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NATIONIaL ADVISORY COOLO ITTEA FOR AE10AUTICS


TECHNICAL E\MORAVDUL No. 1163


DRAG ?EDUCTIOi BY SUCTIGH OF TH E;OUlnaY LiYE;iE

SEPAn;LTED EEFIHD CHOCII aVE FOPJRATIO;

AT HIGH MACH N7B.ERS*

By B. RecQnfschvit


SUI.U.IARY:


CONTENTS:


With an aprroach of the velocity of flight of
a ship to the velocit'- of s und, there occurs
a considerable increas--e of' the drag. The
reason for this i-ust bs found in the boundary-
laVer .3eparatoln c3i.iased by form. Lion of
shock waves. It v:'.il b-e fnde,...vor.:-d to reduce
the drae incroas-e b'r jucticn of the boundary
ayer.

Exporimental results showed tt drag increase
may be conSidrabl i red'Jced by thIls method.
It was, also, observed that, by suction,
the position of shoOl: wavess can be altered
to a cjonsis rablne 1-:tanL.

T. Introduction
II. Method of .e.asure'encs, odel and
Spei1'men-..e1 iProcedure
III. Evaluation of M'easue'e.Ment Results
IV. Test Resiults
V. ConcliSio. .
VI. Appendix
VII. References


I. INTRODUCTION


Drag coefficient of a wing with an ordinary cross
section has a tendency to increase considerably when

*"Versuche zur Widerstandsverringerung eines Flugels
bel hoher I'achscher-Zahl lurch Absaugung der hinter dem
Gebiet unstetiger V'Lrdichtung abgelb'osten Grenzschicht."
Zentrale fur wissenschaftliches Berichtswesen der Luft-
fahrtforschung des Generalluft-zeu-igrneisters (Z.'B) Berlin-
Adlershof, Forachungsb-rLcht Nr. 1L 24, Julyl 1, 1941.









2 NACA TM No. 1l68


the velocity of the air flow approaches that of sound.
The reason for this .increase is !.-n':.rstandable. During
a very fast flight, there appears on the surface of the
wing profile certain local velocities which exceed the
velocity of sound. (This phenomenon may occur ev'n then,
when the lift coefficient ca is equal to zorG, and
may be entirely due to the displacement of the air).
In its further flow, the necessary air-flow retardation
(the theoretical limit of velocity must be equal to
V = 0 on the trailing edge of the wing) becomes
discontinuous, ..hich is in contrast with the usually
continuous air-flow phenomena in incompressible air.

The discontinuity of retardation causes an
.appearance of a series of shock waves, creating, a
condition of a sudden decrease of velocity in a small
interval of distance traveled, vihich in its turn causes
a sudden change in density and pressure. These ranori-ena
are, -of course, not free from wasting of energy. This
loss, however, does not constitute the principal cause of
noticeable c.-ag increase; rather it must be seen in a
sudden increase of pressure (due to a forr.iaticj of
unstable shock waves) which.forces a separatica of the
boundary layer from the wing's surface.


II. ARRA1TS :TT FOiR :A2'CUT LITT, MODELS,

AND TE2T PROCEDTUIE


The high-speed wind tunnel of the AVA (oren-jet
wind tunnel) was at disposal for the measurements. It
has a test cross section 110 by 110 mill'tmetera.
0. 7.Yalchner (1) gave a description of such a wvind
tunnel with a sl.1'itly smaller ijet cross section. A
low pressure chamber of 1[0-meter volume which was
connected with the suction slot of the wing by a duct
was used for increasing the suction quantity. The flow
observations were carried out by means of the v.well-known
method of schlieren optics (2).

The wake behind the winf section was mrea-ured wi th
the aid of a Prindtl tube in order to deter.^:ine the
drai. The total te t arr'an-'_ 1 nt is shown in figure 1.









NACA TM No. 1168


The model wings had for wing sectiu-n a digonous
circular-arc section of 17 percent, thickness with
rounded nose.

Figures 2 and 5 show the investigated wing sections.
Suction slots in the direction of the flow were provided
for a irtir.' wing (4) acco--dlr',:n to Professor Betz'
suggestion.
The invest:i.:xtic-3 were carried ou.t for only one
anrle of atc.ck (a = 00), but for different i.'ach-
numbers soi suction q2antitIes. The first part of the
investigation msn limited' Lo thl-e observation of the
suction eff-ct in the 3chl5 ?er .hoto.'.rph. The
suction 2lot v.was cut ia onl, ; t1- side which was to
be cbsc.rvsd for this part of t.; i. vest .igition. In
the second part the wake b-5.r.' tl.e :winr was measured
point by point '),7y means3 of A. P- ndtl buoce How the
suction slots were contrived on roth uide.l

III. EVALUTATIOii OF TH-T RESULTS OITAIiuD Y 57:EASIREiEiTS

Velocity of the oir flow u and its ratio to the

velocity of sound a Q.Kach numrbe'r = were obtained
in the usual r.anner (1), (3). T'he evaluation of results
obtained by measurements of the wcU:-: was done with the
use of formula:



,,-p K-pi1? -
K-1 / E-1
N --. JD -l




PPp 7p d

giving all necessary data for calculation of drag
coefficient.









NACA TM No. 1168


The derivation of this formula is given in the
appendix.

The symbols encountered in the formula signify the
following quantities:

gD total pressure behind the nozzle outlet

PD total pressure behind the nozzle outlets

gP total pressure measured in the Prandtl tube

pp static pressure measured in the Prandtl tube

A correction of values obtained with the use of the
Prarn-0.1 tube was not nec-s!.rT because, as it was
prove-d. by 0. \alchncr (1), the 3orors due to suction
pressure indicatorwere very sr-mall for the condition of
yaw anrgle m = 0, even when Ll.e '.aoh nunberwas as high
as f-i = 0,9. C-'t' rA.3 rsrei-.ents were rath er rough.

For more accurate measureimnits, the suction
apparuus was provided with a slL-:e valve calibrated to
register the ch"anp f r,.-re'su:, aue to the suction of
ths air pir second. 'V'ith this ajStmrient of the slide
va he pressure 1i.-Kinutic'n in th.: ulction box was
det'-rir.2ned for a Dricc o' aac'ut 30 s conds. It was
four.Jd that, during t-i period, the pressure was
di:-.inic.hed by 1 to 2 pZrcont of the initiDl suction
pr s ure.

The volurrie of suc;;ed out air s.'as found to bs equal

to = 40t whic,- ccro'enzonds to the following inmeasured
values s

40O voluile of Ltihe suction c :oxX eipr-ssed in cubic
rmaiers, ii h a suctio oressure b = 760 rmm Hg

760 normal atrmcisph-.ric pressure in r~mi Hg = 10.555 m H2 0


This is an obvious error in the: German original; as
p indicates static pressure, pD = static pressure
behind the nozzle outlet.









IACA T- No. 1168 5


p increase of pressure no a t`irne unit, in
.?iiUlimeter of mercury

t tiIe, in ser.cnds

The obta-ined Q value was used for determination
of the velocity of tho air flow and for 'th-t of
c.--coefficient on the -.,ing .iu-rfacoe.


IV. RESULTS OF ElPB I-I"T.11TION


E;:;erirents connected w-ith the sa-udy of the air
flow shc.;ed that boundary -layer ca-, b'-e :Influenced ve-ry
strongly b-7 suctiLon.

Figures 1 an. c illusce.te the phenomena of the
air flow.

Locations of suction 3l1 cs are shoan cy arro-s.
Only o1.e side :-f the wing) is sho'n, the ocher is covered
by suction appar'at us.

Figra r5 sows the re.:ulU. observed with a suction
slit ctt out on the TC-p'Erc:ent point of the .ing chord.
ifhen sucti.on is aot used (3 % 0), t-he first shock wave
appears at thi-- 5O-percen-t oi.J-it of th chord length
(approxi.a.bely); at 70-pe rcent -oint, there ben;ins
anotihvr shioc.: ave, whose direc o2 *o.'oses slightly
that of the air flow. at S3-percert poin-:, a third
shocc.: wav.'e is seen.

When auction is used, a consei:-r'.'lc change in the
schlieren '-cturo cf thc. i loli Is cwite noticeable,
even 'when su sucked-out air q.-antitv coefficient
cQE is as small as cE -= 0.0024. (The sub3script E
indicates that suction is usd. an?'.. on one side of the
't-.CA v.hen iu. is used on both sides c,,-sr.Tol is used,
and is a.pryxiiat.ely equal to c = o.oob. when c is
QEI
equal to 0.0021.) In this c-se, *.he firzt shock wave does
not begin on the wing's surface, but is formed in the
free air flow above. The boundur1 layer ,which has been
definitely 3e-arated whe- c4i wa:- equal bto zaro (c- = 0),
now adheres to the ,!inn's surface t.) the very suction slit.
The second shock wave is alriost v-ertical, and the third is
defined very feebly.








ITACA T:. 1io. 116G


When coefficient cQE reaches 0(009-9value, the
first shock wave is very weak; the second wave is
noticeably moved aft from the suction slit and is bent
in the direction of the air flow; the third wave
practically disappeared. The boundary layer is visible;
in the neighborhood of the slit it becomes gradually
thinner, as it is sucked out.

Figure 6 is a study of the air-flow conditions when
the suction slit is cut out ahead of the shock waves.
In this case, the slit was made at the 30-percent point
of the wing's chord. When suction is not used, two
distinctly outlined shock waves appear along the wing
surface. The first, at approximatelyl) the 50-percent
point of the chord length, is caused by the interference
of the suction slit. The second viave appears automatically
at (approximately) the 60-percent point of the chord.
Ahead of the second shock wave a feeble third wave is
formed. Between the first and the second waves there
is a definitely thick boundary layer.

When suction is used, the first shock wave recedes
to the trailing edge of the slit and. is very sharply
outlined. Over the slit, there occurs a change in the
bending of the first shock wave. The second shot: wave
is also more pronouncedly bent in the direction of The
air flow and, which is very noticeable, is displaced aft.
The distances by which the begi-in. of the second shock
wave was shifted on the surface of the profile when
suction was applied is shown inL figure 6.

The boundary layer between the first and the
second shock waves became much thinner. A very feeble
condensation line is seen between the top of the first
shock wave and the bottom of the second.

A comparison between fi'u-' s 5 and 6 gives an
impression that the position of the shock waves is more
definite in the last case. Furthermore, boundary-layer
separation, as seen in figure 5, without the use of
suction, does not appear in figure 6, which h was taken
when suction was applied.

Measurements of the wake were taken with the use of
two diagonally cut slits and one slit cut in the direction










1TACA T HIo. 1163


of the wing's length. The -esults of these measurements
sre shcwn in figures 7 iand A sla.itinr slit at
70-percent of -ch wing chor-d was found to be superior
to two czhr arrangemrents for 'uah nui-ber =0.9.
When c- was as l1v. as.O0L, the drag diminution
bec-sre apparent,

A .':;ing with- a s-lanting zlit at c8-percent of the
chord had`. s lightly greater dra th.i the wing with a
slit c.t out at 75--percent '.f ti. ch.rdl, when tach
nu;oer e was e':._.al co 0.9 (L 0z.)), and CQ = 0.
The curves repre.neritin,. the 'Lia fir both arrangements
(slir. cut cut at 55-r.ircent on-. 70-1ercent points of
the chord ) arce s i'ilar when a; ion is used (c,q = 0);
the i-Liarity bEginis with a r;i.ier larger quantity of
suckel-ou1 air.

.Tleasure.-L-nLs with a slit cut out in the lorn.g tudcinal
diretionE-enrall~r sDea!:iJj
direction r, nerally sp-i:ir, I oTvnient for larger
drag r1value. In this case, a trU.: Cr2 value could not
h meae n.a7ue. In oroier- to ohtlji a a.Cr :D Crratel ,
cor-rect .r v alue, the drCUg s -oulQ b' Tesasured in many
points .long *h- ing sran, anid t-n avc-rage of the
results tjP:en. Cur :.ixverij rtAa. .r.rn:rAtus was nrLe
adatet f' cr- such a process o ii-. azurie nent

it appears that a :int 5ec0in ''ith a very high drac
hadl bee-n chosen for thi s e;ceS W:i ni.L-ion.


V. C :UOLUSI:'I


rhe problem of the pres et r-ecrt consistCed in
prov-ng that the dr;i4 1-f thi- in- rc :ile appearing
with high vel city of th- z-a. le.' c:!n be diminished by
the u3s of suction prod.ucinj 2.?Vces

E::pc rinients performed '.t1 sii 1:. impalements
showed thiiat ..'ith a larger quAnt:ty 01 sucked-out air,
there occt:.rrd a considerable di .injtion of the drag.
Among dirif.;rant arr&angrmnentso a' ctir: anparatus, the
most favorable vas that having the- suction slit at the
70-pe-ce-nt roint of the wing chord (u.71 ). From
schliJr.-en photographs of the air flow, it may be
assumed that suction- slit placed ahead of the region









NACA TM No. 1168


of shock wave formation is also not entirely ineffective
with regard to drag diminution. Such arrangement was not
used for testing the wake; an arran s.nt having one
suction slit before and the other behind the region of
shock wave formation-was not used also. During the
performance of the experiment efficiency of suction
apparatus was very high with respect to the quantity
of sucked-out air and the losses in the suction conduits.
Therefore, a direct use of results obtained in this
work should not be entirely possible in the airplane
technique.

Further experiments must be performed for an investi-
gation of this interesting physical phenomenon. This
research will, perhaps, provide the possibility of
obtaining such results which could be used in actual
practice.

I should like to thank "L--. Lud'ieg for his valuable
assistance in performance of this work.




Translated by N. S. Medvedeff
Goodyear Aircraft Corporation








NACA Tr No. 1168


VI. APFT TI

DERItP..XTIC OF FOR!UL.. F'T DT:ni':.-.IC'I OF DdG FPfi!

M.ExS.SIRETENTS OP WE:E AQ T-IGi VELC'ITIBS

Z F WE AI r LO:

A formula for *rar V:lu3Y:Jn 7 .5 jeri'vdj on the
basis :4' equations ,.iven by KIr-.er ci--'j Doetsch on the
one !c"'c., and Jones 0.on t'E t-i L%., (: ) (t )

A*cc -"linr t c these e;u; ti'.::


W = b V 1 (uO-2) 1r.
r- n _


I.ilogrunms


where: UI and p1 cre, respeccivel-., die velocity
and thr-e .e50sit in th'e cres:s e33 .1.i ii rn-jr csci-erat"icn,
U0 Is thc r.'iai veloci ty .i ;..:.1 cf tcc, '.it, and
Up is :he a::nd ve oc'l;' c1 ..:- ving, b is tL
spsn i`avth c-: tinhe 1 fiAv.

In the wind tunrel the f;ll.. i. co:':vditions dere


v.'ind velocity dir-..l-. i:h :i the nozzle

:Mnt' velocity reisu:**ed :.:- b .Prnrtl tube
dire-ctl: behiLnd th? ".-*in


7'r the evasluatior. :of the rl: t;:- of the ir flow,
the cIl. ri ng r =:r.atons 'rtc 1i -:.'i" ar(: transform ring
the Sai5nt-Venarn r.ati cosi.O


/ 2K f2 .
T = / v- v.'here: t = total pressure
.* K- static ,
I K-1

\D 1 (&K ) ]j 9;l p = static pressure


cre-arLa.::
Uo = '
UO= UD
-1 T-








10 NACA TM No. 1168


U2 can be calculated from Up-equation assuming
that there is no loss of energy between the two points
of observation, and that the density Is changing
adiabatically with the static pressure. Assuming that
the pressure at the point 2 is equal to PD, we obtain:


Up2 K P U 2 K
P-+ K P + D
2 K 1 Pp 2 K 1 P2

(P \ 1/K
p2 = p l/K
'2 PP


U2 =I


LF

L2


Therefore, the drag is:


K-1

d'b 2K2 b\ K 2.
t) I p( P
dN pp ,, P)


. K-1

Dp-1


1/ K /P, K
-p p(^ P/
vp j









NACA TM A o. l 68 11

p
WVe must noe. find an exproz.:; ion for the ratio -.
P>
K)
'ith'. a constAn a ir 1 :Ivi i.p:ce! '.r. the dra..g but
dvoidC oF. the loss of .at, h Lae i rg; tr- e .ainis
unchLngeu. SIr t ti. of :-.dIs sirtato-'-n c, fi.tm .-. there
occurs it? LTr!inrjr.%s.i'; a r`. tacuit i -: s f the ai
along. the suf'fIace of the wing pCro.uceZ a transfornmticu
of energ=.,- o r-oti o- int.or he-it.

.itLhout 9.iLn. a:rou cn-*.a KrsbJ.e er'or it may be
assured chla ther-- di:n nor. *.' any loss of het.
Thriefors, t'.e enr'er nl'. 1e::;ecn ect> .ions D -nd P
crar; be u:rittc thu..:

2 c -- 2
UD, K 4f ._ *> K,
J_+ JL^- -J T''LE
2 .-l PrT 2 K-1 Pp
ul'P


The refoi'i-re:


+ -+ _
P2 = E-1" + -
'-2D ) 2
P + J
2 E-1
8 -1


p 1 +P
i-.-

/''4 :;
pt") -- 1+p.


T--1



(g p p p
PDr iP








12 NACA TM No. 1163

When this value is introduced into the formula
for drag we obtain:
__________ C- _____ ^ --
K- 1 K-1 K-1

= bJ \ K 21 \
Pp^A/ VDv 'P/


/ K-1 1


-P
Drag coefficient can be then determined frorn tne
dynamic pressure for any given velocity U- and area
of the wing F = bl. by formula



K D
YI PD
Lb DD -12









NACA TM No. 1168


REFERENCES


1. Walchner, 0.: The Effect of Compressibility on the
Pressure Reading of a Prandtl Pitoc Tube at Subsonic
Flow Velocity. NAGA TM Ho. 917, 1939.

2. Prandtl, L.: Abriss der Stromungslehre, p. 195,
Verlag Friedr. V).eveg und Sohn, Braunschweig 1935.

3. Betz, A.: HITtte Band I, Gasdynamik, p. 413.

4. Doetsch, H.: Erganzende Mi.tteilungen zum Bericht
Profilviderstandsmessungen im groasen Yindkanal
der DVL, Lufo Bd. 14, 1937, Heft 7, p. 367.

5. Jones, B. M.: Measurements of Profile Drag by the
Pitot Traverse Method. ARC Rep. Nr. 1698, London 1936.































































































t






NACA TIA No. 1168 Fig. 1


(,
0









7 7 0
..4 J






ba,
*B~ ~~ ~ .--- ^II, ...












90
4-1




^ -b_:- ^...'- -.-J
-(.~~Ir U2-^ ^^



^Li~~ L s -^^







0











e-1
IID
I' '-I -*- U (
xi
7F___14
^ | II 1 h
^7 \ C
^ / \ N h
^ :/ \ > ^
V CD __ ___ __ \ '&


^~\r =\--- ^W
C 3> > I

r *o or^ -. L
p; ^ sC

^ ^1-------- <-t


^^=1lP 4





Figs. 2-4 NACA TM No. 1168


Suction slit at 70% of the chord.






Suction slit at 30% of the chord.





Figure 2.- Cross-section of the wing used for air-flow observations.




Suction slit at 70% of the chord.






Suction slit at 85% of the chord.





Figure 3.- Wing cross-section for measuring wake.








76
I


Figure 4.- Wing with longitudinal slits.




NACA TLI Io. 1163 Fig. 5


C E












CE


= .0024












=.0049


air flow direction -




Figure 5.- Wing with a suction slit at 70% of the chord, M = 95.
The suction refers only to one side of the profile. An arrow
on the picture shows the position of the suction-slit.




NACA TMI ITo. 1168


C =0
QE

















C E =.0049


air flow direction -





Figure 6.- Wing with a suction slit at 30% of the chord, M = 95.
The suction refers only to one side of the wing. Arrow on
Schlieren picture indicates the position of the slit. Distance
S indicates the shift of the second shock wave produced by
suction.


Fig. 6






NACA TM No. 1168 Figs. 7,8









M = 0.9



wing with slanting sliBs at 0.85


wing with slanting silLts at 0.70 1

wing with longitudinal sills


Figures 7 and 8.



Variation of drag coefficient with different position of suction slit.

*Translator's note: *1 is the length of the wing-chord.










UNIVERSITY OF FLORIDA
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