Theoretical investigation of drag reduction in maintaining the laminar boundary layer by suction

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Title:
Theoretical investigation of drag reduction in maintaining the laminar boundary layer by suction
Series Title:
NACA TM
Physical Description:
30 25 p. : ill ; 27 cm.
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English
Creator:
Ulrich, A
United States -- National Advisory Committee for Aeronautics
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NACA
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Washington, D.C
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Subjects / Keywords:
Drag (Aerodynamics)   ( lcsh )
Laminar boundary layer   ( lcsh )
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federal government publication   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
Maintenance of a laminar boundary layer by suction was suggested recently to decrease the friction drag of an immersed body, in particular an airfoil section 1. The present treatise makes a theoretical contribution to this question in which, for several cases of suction and blowing, the stability of the laminar velocity profile is investigated. Estimates of the minimum suction quantities for maintaining the laminar boundary layer and estimates of drag reduction are thereby obtained.
Funding:
Sponsored by National Advisory Committee for Aeronautics
Statement of Responsibility:
by A. Ulrich.
General Note:
"Report date June 1947."
General Note:
"Translation of "Theoretische untersuchungen über die widerstandsersparnis durch laminarhaltung mit absaugung" Aerodynamisches Institut der Technischen Hochschule Braunschweig Bericht Nr. 44/8."

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University of Florida
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tnA- W 2







f 00 3 : -' -'" -



NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


TECHNICAL MEMORAiDUM NO. 1121

THEORETICAL INVESTIGATION OF DRAG REDUCTION BY MAINTAINING

THE LAMINAR BOUNDARY LAYER BY SUCTIOI;'

By A. Ulrich

ABSTRACT

Maintenance of a laminar boundary layer by suction
was suggested recently to decrease the friction drag of
an immersed body, in particular an airfoil section 111.
The present treatise makes a theoretical contribution to
this Question in which, for several cases of suction and
blowing, the stability of the laminar velocity profile is
investigated. Estimates of the minimum suction quantities
for maintaining the laminar boundary lay-er and estimates
of drag reduction are tnhreby obtained.

OUTLINE

I. Statement of the Problem

II. Symbols

III. Exam-nation of the Stability of Laminar Velocity
Profiles

(a) The flat plate with suction and blowing
vo(x) k 1/

(b) The flat plate with uniform suction

(c) The flat plate with an impinging jet

IV. Stability Calculations

V. ApplicaL.on of the Results to Drag Reduction by
Maintaining the Laminar Boundary Layer
*"Theoretische Untersuchungen Uber die Widerstandser-
sparnis durch Lami.narhaltung mit Absaug-ung." Aerodynamisches
Institute der Technischen Hochschule Braunsch-weig, Bericht
Nr. 44/8, March 20, 1944.







2 NACA- TM No. 1121


VI. Measurements of the Velocity Distribution in the
Laminar Boundary Layer with Suction

VII. Summary

VIII. Bibliography


I. STATEMENT OF TIE PRO7'LE.1


Recent investigations established the fact that the
drag on a wing may be reduced by maintaining a la..inar
boundary layer. The first method to obtain a large region
of laminar flow is to select a profile which has the
minimum pressure position as far back as possible. Suction
of the boundary layer as indicated by Betz [1] is another
means to move the transition point from laminar to turbulent
flow as far back as possible. The present investigation
makes a theoretical contribution to the problem of
transition laninar/turbulent in the bounia-y layer under
suction and blowing conditions. To this end an examination
of the stability of the laminar boundary layer with
suction was made.

Suction always has a stabilizing effect on the laminar
layer, that is, the transition point is moved downstream;
whereas blowing has destabilizing effect. The stabilizing
effect of the suction results from: first, a reduction
of the boundary layer thickness (a thin boundary layer
is less inclined to become turbulent than a thicker one,
other conditions being equal); and second, changes in
the shape of the laminar velocity distribution and
therefore: an increase in the critical Reynolds number
of the boundary layer (U6*/'U)ri (U = velocity outside
crit
the boundary layer, 6" = displacement thickness, see
chapter II, v = kinematic viscosity). In both cases there
is an analogy to the influence of a negative pressure
gradient on the boundary layer.

Th-oretical calculation of the transition
laminar/turbulent must be based on Lnowledge of the
laminar velocity distribution and requires considerable
accuracy. H. Schlichting and K. Bssima~ [5] and R. Iglisch
[4] gave exact solutions of the boundary layer with suction
and blowing and these solutions are suitable for an








IAGC, TM Ho. 1121


exCLAin_.ti.n of stc.bility. The follo.'inc c:.ses were
invei3 t i '- C. d :

(1) Th'Ie boundqr?'- larrer on th.3 fl Ct plate in
long-. r i.:tn filon with .suction rndri b, owing distri-buted
accordin- to v (x) i//:- (. = distance alon, the
plato.)

(2) The- :.undar;,- layer on the f.s t .late in
Icnl itudin'i flw wit u.nifor -: 1 C t :, : = c:,nst.,
starting ; t the front e~e of tle .iat e.

() The b.iuniar,-l yie r for aflEt -l:.t3 with an ImpTngfng
jet uithi-I unjifo'ri! suc i on or uni fon or* .owi.:-

Cnii tihe r-.S iits Cf i.n'-t .1- -ti io n Tf stobi iit 7
of a. a in.-.. b t-,,iA.nd :'r- la)r "n-i fl t _l -,tr in lon-itudi inal
flow and -n th uni for, ,i Ln are at .resent avai label ,
For this ca:s a, the thici n':n s oc the- cound-,liy layer i..
cons' L nt i 9 l 1 ~ 4iist nce fri:i t.:. '_le .din. n : ,d r'-o f
the pPr.-

6 = L ( 1)


prThe v lisety deistriutio n yf this as. ,pt otic suction
profile is de,-n.nent un y onn ,-, at,. is, -,rc.:odlng to
IH. chlic'hting ['] aT follows:

;-Z
I.y
iJTh =T 10- ; v(:.:,'r t s= const. )



p'rofil, i'. : c cor-,di. to K. Bu.srsminn and H. M'.LCn.z [2]
(U6i. -)corit = :.00. Since for the ..lst in lonituirinal
-low th "C uct i t I-.., tn T ),.,
flow *'ithcrT suction (U'L o) = 5'i., the suction
in this case inc v. se3 s the critical Reynolds nu-imber bj,
a factor of &bot .t 100.

Fror.: the known Reynolds numibe;r with suction, the
minimumr suction quantity n'cLssary rfcr miri ntsining tie
laminsr boundary layer can be determined immediately
(since C"I 5 i t
crit







NACA TM No. 1121


Uo0 I Uo -vo "' Uo6 -
-
U -vo crit


Then from equ-tion (1) -vo6*/i = 1, the minimum suction
quantity is:


crt o > 1 0.14 x 10-4 (3)
q crit Uo 70,000

Since the quantity is small the maintenance of a laminar
boundary layer by suction seeiis rather promising; therefore
further investigations of the stability for the boundary
layer with suction were carried out in this report.
The minimilu suction quantity for maintaining the l.'-r.-Ii.r
boundary layer and the cdru reduction. shall be ststb'lihei.



II. S'"T-OLS


x, y rectanlr coordinates parallel
and perpendicular to the wvall;
x = y = 0 at the leading
edge of the plate, or the stag-
nation point (figs. 1, 4, and 7)

]. len t of plate
'b width of plote

U(x) potential flow outside of lthe
boundary layer; 5 = ulx
for the plane stagnation
flow U = Uo .for the flat
plate in longitudinal flc-.'

Uo freo-strnam velocity
u, v components of velocity in the
boundary layer parallel and perpen-
dicular to the wall, respectively








MACA TM No. 1121


V,(x)


To
0
o* =/ (i


0


- dy


I


CQ = -
zb x U


U'Tv
o = 0



-o\ 2- Uo : = 2
= KU "- x "-"

-V0
Co -


cf =
b L U o2
2 0


prescribed normal velocity
at the wall; vo > 0
blow-ing, vo < 0 suction


shesr stress at the rall

displacement thickness of the
boundary layer

moiintuim thickness of the
boundary layer

total suction quantity and
blowing quantity, respectively,
for he late In longi-
tud.in.l flow; Q < 0
auction, Q > 0 blm~inPg


nondimensional quantity rate
of flow coefficient for th3
flat plate' f)r tle plate
..with uriforrm suction tiis
coefficient becomes
--v
c =- (v = ccnst);
'I U
o
c- 0 suction, c- <: '
blowing

reducE flow coefficient f.or
the flat plate with the
:-;.tion distributed. as
V (x) 1./,

nondimensionol extent of
laminar flow for the pl'-ite
flow ith uniform sucti-n

reduced flow coeffici,=nt for
the plane stagnation flov

friction drag coefficient for
the flat polte in longi-
tudinal flow (plate wetted
on one side)








NACA TN No. 1121


III. EXAMINATION OF THE STABILITY

OF LAMINAR VELOCITY PROFILES


(a) Flat plate with suction and blowing according
to vo = 1/'.

The first series of the investigated velocity pro-
files concerns the flat plate in longitudinal flow with
continuous suction where the suction velocity is distribu-
ted according to vo 1/VI (fig. 1). Schlichting and
Bussmann [5] gave exact solutions of the differential
equations for the boundary layer with. suction and blowing
for this case. It is a characteristic of this case that
6ach velocity profile along the -plate is related to a
prescribed mass flow coefficient. The reduced flow
coefficient
C = c i = 'e'~= 7,


appears decisive. Herein


c = O/Z b Uo


stands for the ordinary flow coefficient for the plate
of the length and the width b, and Re = Uot/u
for the Reynolds number of the plate. Positive flow
coefficients correspond to suction, negative ones to
blowing. For this case all the blowing profiles have
a point of inflection.

The velocity profiles for the flow coefficients

C = -; 1 and -,that i., on.eblowing roIfile with a nolnt
of inflection and three suction profiles were selected
for the investigations of stability. These profiles
together with the -)rofile for C = 0 (flat plate without
suction) are -iven in terms of y/'"' in figure 2. The
second derivatives of these velocity distributions, which
are essential for the calculation of stability, are








HIACA TL. IO0. 1121


dres'n in figure Tsble 5 shows the connection between
"6: and the r' mt-:on of the lmIrrnar flow x.

(b) Fl1t r-,i3te with uniform suction: V = const.

The' second osries of velocity r-Profiles iaong LIe
plate ;re i: o the c,,,se of uniL orL suctl.in (v- = cons.: L )
these r: ';fil. s were csci.ulsatd ex;--tly b'I I tlisch [ L .
Figure lich '.va tr.e flow ?lon- tI.h:- flt lacx with
uniform sue..t io-, which wc irnv. t i g-t Ili iaoh,
and f iuAre 5 represents Lhe ei;:?::in': e!r- cit-. rrofiles.
The vye' c ity p: f. 1les it c i-nc rea.r n,


S'r x .- ,



starting. at t.: oi f ror:,m :f the B3lsius -o .file &at C0,
graduially -i -,.,prc. the a;,rrpCt tjo c suction ..,rofi l accord- ingi
to equs..:. in (2) [E5]. The second Jt. i-;-ti .ves of t.er"S
velocity t r.,-f ls ae dr:wn -in fi .,-ire D. A11 the
velocity 7rcf.. les -a&ve nzw-'ative cIur',atre th-.ouhout
(62i' .'< 0). J1 'ih incrrazinp the .:soliut vs lae3 o
6 u/.7- ncro:.'c ra-idly. F'-i.ur en t 7 r. t:~'~lr es't-nt
the Iion:.li iional optP.net- c f th, o n :;.r y lr i4er,
na.miel- t, di- iisj cement rhici:nr Ts '- /, :c I t
thickne.:s 0 shear str-:. T, /iU and sh~:' E
parnrteter F'/ -.: functions o't ,'- c ccrdin;. t
Ili ch's c ld1.-' I : -.s L)] Six r file with' t he
pa--";.,::-te. = .-.'."5; C .02" .Od; O .1l"- 0.32 5 :1 0.5 were-
ex-:,rinedl v.'it h ce se .ct to state it The r es uts for
6 = 0 .n-C. -= n.ro !:noPn fr-m [2 .

(c) Flat oa t e with an is rin Tin j "w :i h unifo rm,
sacticn.

As a third siies several s ta.nat L n int pr ofiles
from those c.lc''lat.i cd ex ctly 'by Schlichtin S nd
Eussmann [5] were a:-. The ootential flow i s in thli .a.c2e ( co.'i1:,a, fig. 7)


ULi x) = uI x; V(y) = -v. y








8 NACA TM No. 1121


Figure 8 shows this plane stagnation flow. Figure 9 shows
the velocity profiless which were investigated. Their
shape changes with the flow coefficient

-v
Co (5)



Positive values of C correspond to suction and negative
values of Co to blowing. The profile with Co = 0 is
Hiemenz' profile of the boundary layer; this profile
results from the first term in the power series starting
at the stagnation noint for the boundary layer of the
circular cylinder.

The velocity profiles with the flow coefficients
Co = -3,1905; -1.198; 0; 0.5; 1.095 and 1.9265, tht is,
two blowing profiles, the profile with an impermeable
wall Co = 0 and three suction profiles were selected
for the stability investigations. Figure 10 shows the
second derivatives of these velocity profiles which
have negative values throughout. T'ble 7 shows the
corresponding boundary-layer oaramieters.


IV. STABILITY CALCULATIONS


The examination of stability for these laminar
velocity profiles was carried out according to the r!thod
of small vibrations in the same way as previously liv'en
in detail by W. Tollmien [10] and H. Schlichting [ol .
A plane disturbance motion in the form of a wave motion
progressing in the direction of the flow is superimpniosed
over the basic flow. It is essential that the basic flow
U(y) be assumed dependent on the coordinate y only.
Then the amplitude distribution of the basic flow also
is a function of y only. The equation


( -, v'
(U V6 I x
by 6x


*(x,y) = c(y) eia(x ot)


(6)









NACA TM io. 1121


is valid for thi flow function j(x,y) of the snperirmo:-.-
disturba.nc-.- motor (u', v' ). i real and ,ives t:.he
wave length X of the disturbance :notion, X = 2n/u.
c = cr + ici is complex; Cr represents the wave ve3ocO- r
of transmission and c, positi-e or negative, the
excit ci.:n or da-mrping, respectively. '(y) = -,r() + ic ()
gives the complex amplitude function. The ordinary
linear differenuial equation of the fourc.h order

T -i
(Ti cJ (" -a2 2a + a-) (7
CLA


with the bou-ndar' conditions


S= .: = .',,' = 'r : = -.,: '-= ,P' = o (2)


is obtained i .,r that fincti..n fr.im ila-oier-St:ke=' eiqu3tiros.
In equate. .c-l i(7) all values arred rcnle rndimnension:.1
with as .uiabl. boundary-layer tiickne.c u and the
potential velccity U. R =',/ .l/ stands for- the Reynl..:"ds
nurber; si-:niflis differenti-atiton ith respect to
y/o. The boundar.-layer cbnditlnns result from the
disappearance of the normal rand: tangential ccmponent
of the cdistr'ii-ncc velocity at the w ll and outside c"f
the boLundar.r.layeer (7 = c"). The e-camijnat.on of sta'-ili]...-
of the prescribe.. tasic flow Ui (y) is a ci.racceristic
value .-robler! of that diffsrenti-i e-iuaticn in the
follo'.7in0 ser.se, since U(y) the tia,- lenlsth = 2T//a
and the R.eynclds number U/i, are prescribed. The
corrle:-. characteristic value c = C + icI is requir'..T'
for every t..o cc:responding values a, t; from the
real part of c results the velocity of transmission cf
the supr i-. llp .sed_ disturbance; ti!e irmaginar"y part of c
is decisive for the stability. DiZturbance occurrir.
for the condition of neutral st.':, i lity (ci = 0) are
especially interesting, and lie ,on a curve (neutral
stability curve) in the a, t plane. The neutral
stability curve separates the stable disturbances from
the unsctrlle ones. '.-e figs. 1- to 1( )Tihe tangent to
the neutral stability curve parallel to the a-a;is gives
the smallest Key-nolds number at .ich a neutrally stab-le
disturbance is still possible. This number is the critical
Re-nu-bcr of the basic flow.









JNCA TM No. 1121


In examining the stability of the suction profiles,
the boundary conditions of equation (8) were held the
same as in the case of the impermeable wall; that is,
disarpearance of the normal and tangential disturbance
velocities at the wall is required for the boundary
layer with suction also, although the normal co-mronant of
the basic flow at the wall is different from zero.

The numerical solution of the characteristic value
problem then takes exactly the same course as indicated
by W. Tollien [10] and ,. Schlichting [6] and needs,
therefore, no further explanation here. For the stability
calculation, the velocity profiles are approximated by
parabolas in the form:


= 1 p (a y/)n


with


6 = 56*


The constants p, a, and n for tho three investi,?ted
series of profiles are enuLmrated in table 1. The closest
agreement with the exact velocity profiles near the .aell
was important. (Figs. 2, 5, and 3.) The polar di. griis
for the examined velocity profiles are given in fig-.-rs 11
to 1$ as an intermediate result of the stability calcu-
tation. The neutral stability curves were obtained from
these dialcrams and a6 is plotted against Uo0 /, in
figures 14 to 16 and corresponding values are tabul:t;d
in tables 2 to 4. These curves show that the stability
is greatly increased by suction while blowing decreases it.

Figure 14 shows in detail that in the plate flow
with continuous suction the neutral stability curves
for positive flow coefficients C lie between those
for the flat plate without suction and those for tho
asymptotic suction profile, which were calculated
previously by Bussmai- and :.:hn [2] The case of

blowing with C = demonstrates clearly the enlargement
of the region of instability.









NACA TM Nce. 1121


As to the flow along the plate, figure 15 shows that
the neutral stability curves for the values of u used
here also lie between the curves for = 0 (flat plate
without suction) and r = a (asym).totic suction profile).
For increasing E the region of instability diminishes
and at : o = 0.5 the neutral stability curve a-. ears to
aporoacn the curve of the asymptotic suction profile.

The stability in the stagnation flow also is rr't-tly
increased by suction; with increasing flow coefficient
Co the neutral stability curves (fig. lo) a,:.,roach the
curve of the asymptotic sucti'-n profile for the flat
late. It is of interest that the neutral stability crves
for the investigated cases of blowing still lie inside
the curve for the irper;neable flat plate.

The critical R:ynolds number (Uo-:/ )crit is
the tangent parallel to the ordinate of the neutral stability
curves. Tna critical Reynolds numbers for the three
series of stability examinations -are enumerated in
table 5.

The following detailed result was obtained for the
plate flow with continuous sucuion

(Vo ~ 1/): (Uo1( /'Ujcrit = 24 for the blowing
profile (C =--\ and therefore is far below the critical

Reynolds number 575 for the iimoermeable flat .'late.
WVith suction the Peynolda tnitlber inir-reases rapidly and

reaches for C =-- the value of 19,100, thus evidently
aonroach ing the critical Reynolds number 70p003 for the
asynmptotic suction profile Ieter-nined by Bussinann-
?'!unz [2]. Figure 17 shows how th? t-ransition .-oint on
the 3-.ate is shifted backward w ith increasing suction.
The Re.nolds numbers formed by the disnlacemennt thick-ness
are, for different flow coefficients C, plotted against
the Re numbers formed front the distance (x) measured
along the .-late in this figure 17 ind also figure 13,
and values are tabulated in table 5. The stability limit
of the imnermeable wall (Uox/u)cn]it = 1.1 x 105; but
for a flow coefficient C = 1 critical Re :-xc'eds 107








12 NACA TM No. 1121


and therefore reaches the Re-number region of todayts
large and fast airplanes.1 Figure 19 shows the
dependency of the critical Reynolds number on the sha-ie
parameter 5*/ .

Flow along the plate with uniform suction (vo = const.),
the critical Reynolds-numbers for different /, compiled
in table 5 lie between the critical Reynolds numbers 575
for the impermeable wall and 70p00 for the .":'-. totic
suction profile. Figure 20 shows the result of the
stability calculation in which the critical R:;,'rolids
numbers (Tor'/U)crit are represented as functions of
the non.'iiE.1r.i.nonal. flow distance \/s. In figure 21 .he
onset of instability is ascertained. Here both the
stability limit (Uc /'-/uI according to figure 20
and the nondimension'.l r.-:, n..1J.i..,; -I :e. c- er'L. i -ss_ Uo,: '/!
plotted against \ e lw ,", c '-lc nrit 2
CQ = vo/ T are sh i,'wn. Th. l.' :- .-i y-lA:;er ti'ickne-s
is obtained from


(lci)
-(o0


the values of -v 6:'/ n function: :.f are
given in figure 7. SIt3ce i 1r -':- -Ve":'."r = 1, the
separate curves have t.-e asymr-totes

___ ,_V,D
t ,'- n)

The point of tr.nsrit io^nis -iven bt thle :.rters.ction
of a curve Uo / it" th' st */iUi t- lrim t (;U,, '/ ) c.it*



1 1 means c, = thi ,'ith io"

c, = 5.16 x 10-4.








NACA TM No. 1121


The onset of instability occurs before V = 0.1 for
Vo 1 1 1
the flow coefficients 70,000' 20,000' ,00
on the other hand, there is no intersection for
Vo 1
U, 8500
Flow coefficients

c1it = 1.18 x 0"- (12)
cWit 8500
are, therefore, sufficient for mPr.ntainin the laminar
boundary layer for the entire preliminary laminar flow
region. This value is to be compared with the value
Qcrit = 7000 = 0 1 x 10 determined by Bussmann and
CQcrit 70000
Munz (reference 2) for the asympototic suction profile.
The minimum flow coefficient necessary for maintaining
the laminar boundary layer is, therefore, increased by
about the factor 10, if the preliminary laminar flow
region is taken into consideration. The earlier investiga-
tion had already led to this presumption. The minimum
suction quantity2 found herewith is Q t = 1.18 x 10-4;


2One could consider the possibility of reducing
the total suction quantity still further than
CQcrit = 1/S500. One would have to select such a
distribution of -vo(x) as to make the curve Uo6--/,
in figure 20 remain ever,.here just underneath the
stability liniit (Uo6:/u) rit. The necessary distri-
bution [-vo(x)/Uo]c is given to a first approximation
crit
by the intersections of the curves Uo6 /v for different
-vo/Uo with the stability limit (fig. 21). One then
obtains up to about 0/ = 0.1 an increasing local flow
coefficient [-Vo(x)/Uo]ci; the maximum is reached
with 1/8500 at about V = 0.1; for higher Vi there is
again a decrease down to the constant asymptote
(-vo/Uo) = 1/70000. The total suction quantity, however,
would hardly be reduced under the constant value
CQcrit = 1/8500 for practical purposes if such an
"optimum" nonuniform distribution of suction were selected:
For a plate with the Reynolds number Uol/u = 10' and







NACA TM No. 1121


this quantity is still so small that the maintaining
of the laminar boundary layer by suction appears quite
promising. We mention, for comparison with experimental
results, that the necessary suction quantities in
Holstein's [7] measurements on the supporting wing are
cQ = 1.1 x 10"4 to 2.8 x 10-4. This value is, however,
not exactly comparable to the thoeretical one since the
suction in the measurements. was produced through slots.

Figure 19 represents the critical Re-number
(Uo 6*/U)rit as a function of the shape parameter
6*-s/& Simult3aneously, the results of the stability
calc.lat:_cn for the velocity profiles of the flat plate
with continuous suction vo 1/Vi are drawn into this
diagram One ccn see that the critical Reynolds numbers
of the two stability calculations.. lie on the same curve.
Hence it is concluded that the critical Reynolds number
(Uo6/:1)criit is dependent on the shape parameter 6-:-/
only.
Plane stagnation flow.- The critical Reynolds number
(U o-::-U)rit for the impermeable wall (C. = 0) is 12,500;
for the suction quantity (Co = 1.9265) this figure
increases to 38,000 (fig. 22). .ith blowing the critical
Rey;-olds number decreases slowly; the value of 707 is
reached at C, = -5.1905 (table 5). These critical
Reynolds numbers also are given as functions of 6:-/
in figure 19; one can s'e that they ta!:e a course
similar co the flow along the -'late although they lie
somewhat underneath this curve.



o/U 10", 4 = -0.5.; therefore the

region where oQ can be considerably smaller than
1/8500 is still far beyond the end of the'plate.







NACA TM No. 1121


V. APPLICATION OF THE RESULTS TO DRAG :ZDUCTION

BY MAINITAIIIING THE LAKIITHAR BOUITD.I-Y LAYER


The drag coefficient cf is plotted against the
Reynolds number in figure 23 for the laminar and
turbulent flow in the boundary layer of the flat
plate with continuous suction vo ~ 1lx. The drag-
coefficient curves from reference [33 for different
quantities of suction and blowing C also are shown
in the figure []J in this diagram; the coefficients
Cf increase with increasing suction quantities.3
Drag may be reduced by suction in the region between
the curve for the laiiinar flow of the flat plate
(C = 0) and the fully turbulent curve, if the laminar
boundary layer car be maintained there by suction. The
result of the stability calculation given in figure 18,
that is, the critical Reynolds number (Uox/u)crit as a
function of the mass coefficient C, was transferred
to this diagram and yields the curve denoted "stability
limit." This curve signifies that for conditions (C, Re)
above this limit the suction quantity is sufficient to
maintain the lamiinar boundary layer at tne respective
Reynolds number.

The drag reduction by maintaining the laminar
boundary layer for different Reynolds numbers can be
specified immediately by neans of this diagram. The
minimum suction quantity cQ crit = Ccrit/V- necessary
for maintaining the laminar boundary layer is determined
for a given Reynolds number; then the drag coefficient
Cf for the fully turbulent and laminar flow with
suction is read off the ordinate. This calculation is
carried out for the most interesting Reynolds numbers
6 Q
from 2 x 10 to 10 in table 6. One can see that for
instance for Re = 107 a drag reduction of more than
70 percent can be obtained. This statement, however,
does not yet make allowance for the power required


3The frictional drag coefficients represent in the
present case of continuous suction the total drag, because
there is no additional sink drag of the suction quantity
since the-parts sucked off spent their x-impulse fully in
the boundary layer already. Compare Schlichting C8].






NACA TM No. 1121


for the suction blower. But this power is not excessive,
since only very small suction quantities'are needed here.

Figure 23 was concerned with the plate flow with
continuous suction; in a similar way, in figure 24
the laminar frictional drag coefficient cy (determined
according to Iglisch's C[] calculations) for the plate
flow with uniform suction is plotted against the
Reynolds.number Uol/u with the flow coefficient
q = -vo/Uo as parameter. For very small Reynolds
numbers, all curves converge to the curve of the plate
without suction. cf becomes constant with the value
cfj = -2vo/Uo for high Reynolds numbers where the
larger part of the plate lies within the region of the
asymptotic solution with constant boundary layer. The curve

c crit = = 1.18 x 1 0" named "stability limit"
U0
was drawn into the diagran (fig. 21) as the result of the
stability calculation. Figure 25 represe-nts the same
condition again; but, different from figure 21, cf is
given on the crdinate in ordinary scale. Both represen-
tations show thit for instance at Re = 107 a drag
reduction of 380 percent of the fully turbulent TF~itional
drag can be achieved. Figure 25 compares the drag
reductions by maintaining the laminar boundary layer and
the critical suction quantities for the two cases
uniform suction and vo ~ 1/VX.

A comparison of the results obtained under the
assumption of uniform suction vo = constant with the
results based on the suction rule vo l/VT demon-
strates the following: The critical suction quantity
cQ crit for continuous suction vo -3/x is variable
with Re = UoZ/u and is for all Re< 7 x 107 larger
than the suction quantity for uniform suction which is
constant cq crit = 1.18 x 104. The drag reduction
for uniform suction also is larger in the considered
region of Reynolds numbers than for vo 1/VS; for
instance, the drag reduction at Re = 107 is 80 percent
against 75 percent. Therefore, the uniform suction is-
at any rate preferable to the suction with vo ~ 1/yx
for the whole region 5 x 106 < Re < 108 that is, the
main region of interest for practical purposes.









IICha Tir. Ho. 1121


At h!ixh Re-numbers (ever ,10') only the suction
accordin- t to the rule v,,(x'l 1/' shov:s sm allr
critical -ucticn quantities and higher drayg reduction
than uniform suctir-n. Table 6 and fi__ure 23 .'ive a
corrm::.ario.n -f t-ih3 critical su.ction. quanttities and th-2
drag reductions for" the two vucti-.n rules.


VI. I'.EASLUFEIT TS OfIF T':E VELOCITY DIST'-ITBUTI':D

IF- THE LAM.ITAP 30U1IDARY L -.' .TTF S'TCTION


Finally, 9 few results of e-.l rimr=nts about thiG
bound ary 15s,.7r with suction s-all b ;-*.':, n. In figl
27 two nmieas, r .d '-.locit:i distr-ibjtions v.ith- tLe
asymps:.tic suction ro.i-:file [5] a;i t-i- -lasiu:- i profilel
for thJ- L Iie an lat. j'n lon'itui din::1 ilow .itlhout sucri'n
are co.,iear,- d. Th.- first !ie .3u.-erii;. nt f' ,*.*arri.d out
by Holstein 1[] on a wing with the i.rofile ITACA 0u12-o1;
the tit ksur.-ms nt wi:-. tak'-.r at x/7 = t0.9 ( 7 = wind chord)
of the w.ir-i ce-nter sect:,.on on th.e si- ct.:n side (a = O ),
with six suction slots ,of- th e suction side o,..-ned. The
valocit-7 distribution which .:s c-nv.-crted il.to the dlis-
placeri, nt t:icknccs conforms .'-..th. r we ll with the asyJin:t otic
suction .rofiil of the flat -lite .'.with uniform suction
while differing ,r.;tly from the l.:,aius profit~ -aith
imoermoable ws.ll.

The second rmeqsuranent was te!:on by Ackeret [9] ; [ .
suction c-hannel with n.umn.rous narrow. sl-ots :? short
diRst:!nco behind thc: suction length '- S iLs us.d. This
ve:-locity .iistr:'.tution -lso ts.:.es course similar tc
the as:ymtoLic su.ct.I on -rcfile. Thi- r.fore, 1: fw
existin g ricosurcrm-nts show hoocd a .-r.;ement :wir.h the
theory as .to the fnrm of laminar velocity distrib utLon with
End v:ithout zs.ction ,r3s'ectiv; 1.y.


VII. 3SU',." ARY


Stability calculations vr-wre carried out on three
series of exactly calculated velocity profiles for the
laminanr boundary layer with suction: (a) on the'i flat
plate ith continuous suction according. to tho rule
vo 1/7, (b) on the flat plate with uniform suction









NACA TM 11W. 1121


vo = const., (c) on the flat plate with an irmpin3 .ig
jet with uniform suction. It became obvious that the
stability of the boundary layer is greatly incr,-aszd
by suction, on the other hand greatly reduced by blowing.
While the suction quantities are increased slightly,
the critical Reynolds number increases greatly arid
approaches the value found by Bussmann-j%.Infi
(UoS/u)crit = 70p00 for the asymptotic sucticn profile.
Then the minimum suction quantities necessary for
maintaining the laminar boundary layer were det=rriIined;
they were c Q= 1.1 x 10- to 2.8 x 10'- for ti- plate
with continuous suction and 1.18 x 10-4 for the -19te
with uniform suction. The drag reduction obtained by
maintaining the laminar boundary layer at Re 10i is
80 percent of the turbulent drag without suction.



Translated by Miary L. Mahler
National Advisory Committee
for Aeronautics








IIACA Tri1 N?. 1121


VIII. BIBLIOGRAPHY


1. A. Betz: Besinflussung. der Reituncsschicht und ihre
r -rakiis che Verwertunc. Sci-rift-sn der DeuLtchien
Akademile ,der Luftfatnrtforschauni, Heft Lv9 (1i L);
v-1l. inch J-~hrbuch der Deutschen a !kelemnit der
Lftr'fi;thrtforscrLung 19'9/K0, 3. 246.

2. K. B.s':',nn u. H. iKrinz: Die Std'bilitit Jder laminaren
e.ibi.:.rn Cschichu ilit Ab Ut-i.IT.ni. j,To.lrochl 19k2 der
Deut-Lchen LJ'Ctfcjlhrtforecha .mc, 3. I 36.

5. !-. Schlichting u. }:. BusEr.u nn EXAl:t Lsunre- n fr'r
die larr.intpne ( iGen S'.sc'.icht rnit AbsauLArung r Und
Ausblacen. cohriftzn der Deutschien Akade.le
der T-iftfahr,-tf'or.schun BF:. T-, 19' ie t 2.

S. R. Iglisch: Ex-kte Losungein 'Lir lie 1m-jinare
Grenzschicht .n der l1i.n,.sane stin--iten ebenen
letter 'it lioriogener Absn-: _iir,-. Berir cht
',/2 de ? Aernodyn. Instiluts tder T. H. Br-Aunschweig.


5' H. SchIlci-ting7: Die Grenzschicht mit Absaul un,-- uLind
Ausblasen. Luftf hrtforsciun' 1942, S. 179.

6. H. Schlichting: Ueber die th-roretische Ber'eci-inunl der
kritischen Reynolsschern 'Zahli inner ri3ibunrsschicht
in beschlE.unigter und verzogernterr Str;mung.
Jthtrbuch 194i' der deutsc hen Luritfahrtfor crsc hung,
S. I '?7.

7. H. Holstein- Hiessunpen zi.c Lsmi.nqrlhaltung der
Grenzschicht duirc Absaugiun.- 9nn einem Trawfl'.xuel
mint 0r0ofil 1 ACA 0012/4 .- Bericht der
Aerodvnamischen Versuchicsanstalt Gotr.inren.
F3 1S, (19:42).

8. H. Schlichtin:: Die Beeinflussun_- der iGrenzsc.hicht
durch Absaugi-~ng und Ausbiasen. Jahrbuch 19 j/441
der Deutschen Ak:.:ademiie der Luftfahr-tforschiung.

9. J. Ackeret, li. Ras, W. Pfeningir: Verhinderung des
Turbul'entwerdens einer Orenzschicht durch Absaugung.
Nlaturwissenscheften Bd. 29 (191), S. u22.








20 NACA TM No. 1121


10, W. Tollmien: Ueber die Entstehung der Turbulenz.
Nachr. Ges. ..Lss. G6ttingen, Math. 2hys. Klasse
1929.









N..CA TM No. 1121

TABLE 1

A~' OXI'"ATIIO] OF THE VELOCIfTY ROFCILZS F'O: VArIOUS

C, \C AND Cc, O TH'IE T'iREE IiVESTIGAT ED FLO.vS
u Iyn
ACCORDIiG T'O EQUATION (9): = 1 a -


C p a n


Fl-st plte with
conti nuioi s.ect ion
V0 I/:


-0.25


10
1
1.5


Sp a n


Flat .::.i te withh
uniform suction
vo = c-onst,


.005
.02
S13
.52
.5
W


Plan3 stargn tiion flow
with uniform suction


.0707

L ,



-.141


5
.707



o


-5.190'5
-1.19 ;
0
.50
i100
1.- 0


1. ~C'u

* 1Z)3


i. :0o
i. 'o ',
1. OLh 2
1. 042


.13.5



Si
'0254


P


1. 0550
.100
.1375
* i


0.95 2
1.015 2

i.6 2 L
L~ 14


.0 15



i .oo0
. 5 3

.1JO
1.66 7

lc54
4 .05o


.r4
1.642
1. 33
1.622


2
2
2
2


4
4


n






22 11CA TM to. 1121

TABLE 2
:;UI'E.ITCAL VALUES OF TIIE NEUTE..L STABILITY CURVES CF
THE PLATE FLOW WITH CONTINUOUS SUCTiOi vo I/

C c/U0o y
c c/Uo YK/6 a-: i x 10-3


] 0.20 0.587 0.092 3.5
4 .25 .483 .0 1.75
.568 .696 ., I .341
.Lo .756 .37 i. +98
Asymptote .6 .6 5
.45 64
5 .846 .27 .217
7 .879 '5 .567

0.05 0.084 .J.)3 857
.05 .084 .0. 1920
.10 .150 .- 5-
.10 .150 s 206
.15 228 .11 105
.15 i228 1 1.5.3
1 .20 .312 .1 26.2
2 .20 .512 .3 15.7
.25 .390 55 15.5
.25 .90 .1)1 6.14
.50 .774 .1- 5.50
.50 .47 .-. 5.53
.51 .9 70 5.6
_______ ~ ~ -__ 49__ u__ ___


0.05
.05
.10
.10
.15
.15
.20
.20
.25


0.069
.o69
.158
.158
.207
.207
.280
.280
.357


0.038
.021
.071
:or
.050
0cJ0
.1531


500
2764

115
55.2
) .92
9.9d


0.05 0.022 0.0:7 1150n
.05 .022 .017 5770
_ .10 .044 .o77 571
2 .10 .oJ 1055 505
S .15 i .' .7 ..-, 102
.15i .067 .055 6.2
.20 .0 .ll. 32.1
.20 .090 .22.5









NACA TM io. 1121 2

;-.LE 3

--.ERICL VALUES O'F THE NEUT''.AL STH-:ILL.TY OTJU.rES OF
THE O0Pil30IID PLATE FLOJ WITH UITIFpI J. SUCTIOII


a o x. 10'-3
U '
0

0 3.10 0.056 1S
-

.20 .077 7.20

.20 .1!9 57.7

.25 .101 35.01

.25 .133 12.0

.129 1.53

.-0 .225 ,.61

:1 5 -5 ;. ; .l1
.55 .2 23. _

.35 .159 .89.

.55 .252 2.0

.575 *181 .S

.375 .26- 1.42
.LO .2 05 .653

.1o .274 1.02

.L2 .259 .,105
.42 .275 .713








24 NACA TM No. 1121


TABLE 3 Continued
NUTTERICAL VALUES OF THE NEUTRAL STABILITY CURVES OF
THE Oi-COi"-iG PLATE FLO' 7ITH UTIiFOR,; SUCTION -'Continued


i rc YK Zr Ui"
0 -x103
o 6" D

0.005 0.10 0.055 0.076 630
.10 .055 .0365 131
.20 .114 .157 22.7
.20 .114 .085 7.9
.50 .175 .224 3.
.50 .173 .145 1.86
.35 .205 .237 1.51
.55 .196 1.16
.02 .10 .053 .074 778
.10 .055 .0o5 198.5
.20 .108 .14 28.9
.20 .108 .074 12.8
.25 .138 .176 9.5
.25 .153 .108 5.06
.50 .167 .200 5.85
.30 .167 .14 2.59
.08 .10 .050 .075 543
.10 .050 .05LL 204
.20 .100 .15. 26.6
.20 .100 .o8o 15.5
.25 .127 .160 9.67
.25 .127 .il 6.65
.275 .105 .163 6.17
.275 .1405 .152 4.67
.295 .151 .165 5.95








NACATiM Loc. 1121 2Z


TIBLE3 Concluded

IHJ1'" ~IC' ,.'-VL'M' S 07' -i" iIFUTRAL ,0' 1"-i P IR'/l S 0'n.

THI C .(, : IlU1 .A.TL FLO\. ..Il U.H' I AL. Li Ol Concl i

c U 8"w
> b:: O" o" i
c I 10-*




1 i
0.1i 0.10 0.047 '.07 '0?.
.10 .017 S,.u 89.7
2 .0 o 1.2"5 20. '
-.10 .L .0.- lu.

.2 1 I1 i .

2 C.05- 0.02:. C.017 12250
.03 ,0'2"I 5 .010 4217-
1 i5 .00 0- 'o .'i
.15 .06.2 .O:', 0o.2

0., .0,2 .0 i '2.0

.5 0.0 O. 1064
5e. .0o2,, .. ,N-7 O .r4
1, .066 .*0"'4 i017.0*
.15 .Oco6 .'056 o
.20 .0.0;' .111 51.'
.20 .O8;:; .0.1i 2n..9


0.0 0'
.0 2'
.09
. 09
.15.
.15
.175


.051,

. I0 7
* 1 ,,

. I: ,3


0.0176
n. O
.000
.0526
.00 5
.OYQ5


L 1200
104i00
1500
70C
147
115
70








26 NACA TM ie. 11u1


TABLE 4

TUCTERICAL VALTUS OF THE .iEUT~RAL STABILITY CUV.'E ,.'

THE pLT.A STA.ITATION FLOW WITH UNIFORM S'CTIT iT


C a,6 xo6* 10
o UO


.15

.20
.50
.50
.35

.10
.10
.15
.15
.20
.20
.25
.25
.29
.05
.05
.10
.10
.15
.15
.20
.20
.23
.235


0.109
.054

.079
.207
.'15
.2357
.200

.071
.07,
,106

.0 5



.039
.oi6
.125

.016

.0534
.098
.055
.119
.082
.125
.102


77.6
25.1
20.7
8.6
5.70
2.02
1.58
1.12

655
218
107

27.4
14.5
9.65
0.

14 7 0
lG7o
711
292
114

51
18.1
14.8
13.8


4 ________________- --


-5.1905







-1.198







0








INACA TM No. 1121 7
-7


TA.LE 14 Corc.luded

liUTzr' IC, L V, LiES n' 0 -'FE !IEUTR'L ra2T LITY CURVES *'~'

THE ?L..,A. T ".GtL.TT ICli FLOR/ Yi"'H UiiIFORi'l &UCTTOII C,.c,.o 'ded

c U,-,'u _
," a6' -- x 1i0-
.o 1'D0


.-^, .CO ii7 D :

.10* *'13 '' ^0
1* C. ;-,1 .1 F L
15 1 -
.2:' 1 p, 7 ?- 7l '
.2 .1 .
-, _- |' *.7 '*
.-* .1 1 ..


I ,, .01 '2'

10 *.',


1* L
1i .' 1 0
.io .-1 ? .0

1.'-\ 5 ..' .i 1'; 21 '1
.0 .014 L1 0
.10 *(4 71*
15 -1 124

175 lI.l 5Q 5
.175 *-''T7 49.7
S. 19 *lr-1 7^


~







NACA TM No. 1121


TABLE 5

z0 CRITICAL REYNOLDS NUMBERS AS FPrUiCTIONS OF C, ,

AYD Co FOR THE T7ERT INVESTIGATED FLOWS


oC
U =


- \/U cr
* /c rit


oU i
a .- c it


Flat late -0.25 2.77 204 1.03 x 10
with con- 0 2.59 575 1.10 x 10?
tinuous .5 2.1 2986 525 x 10
suction 1 2.29 9550 8.1 x 10A
vo- ~ 1/ 1.5 2.22 19100 4.90 x 100
Asymptotic 2 70000 ---
suction
profile


Flat plate
with uni-
form suc-
tion
vo = const.


-v lU-x
; 0


.0707
.141
.285

.566
.707
"; 5


2.59
2.553
2.47
2.39
2.51
2.25
2.21
2


/U 6
U c rit


I i


575
1122
1820
3935
7590
13500
21900
70000


v 4iul- y \" rit


,lane stag- -3.1905 2.538 707
nation flow -1.198 2.552 460
with uni- 0 2.21 12300
form .5 2.172 17360
suction 1.095 2.126 27700
1.9265 2.088 38000















thCA TM :Io. 1121


C'-4




C, 4-'
r-







r-




A
r-i
















.j+
r.
'-4 L
iJ + *


'r-
"< ----

"I r-

o -l





--r




0
)k

j


--- I1~


4- i


Lr-c


Lr',
r"I c; -"


l-'








~J. ) c-.


-i --




0 iJ C3 ]. J-

O -


L ,' .L- '
--- LC. CO C' 0



,0 ,0 [- [-- D '- .X ,

-- r- r- r-l -- r-4

X X XX

lry L CJIL1


,- I
C.,
7 c
E 0
C >


'0 -i o O \0
* 3 [ (- .0 CO Cjj 3)
0


UL. l.


L.-\ L, 3

*t r-





-^~~~ -r 4^ "j '


3 0' E' C- 0- 0
C-7 0000
r-I r -4 r- 4 r e- ,I r-i

x x x

,\I LP. CJ LP,

-A-!



D H OD
.4; 4 -


c-, ? >


*r














I



44:






i


SII

i-
2 r-O


-+--


- a c~ :


- --- ------t- ----- ---- ---


CmI









NACA TM No, 1121

TABLE 7

THE CHARACTERISTIC BOUNDARY-LAYER PARAMETERS OF THE

ITVESTIGI.TED LAMIN-AR VELOCITY PROFILES :.ITH SUCTION


C = C


*"o
1-xp


v0)x


ToO
lUo


Flat plate -0.25 2.010 0.7L0 2.77 0.500
with con- 1.721 .66 2.59 .53
tinuous .5 1.5 2.41 .682
suction 1 1.047 .458 2.29 .765
o ~ 1/V7 1.5 .863 .590' 2.22 .818


Flat plate
with
uniform
suction
v = const.
0


Plane s; ag-
nation flow
wi t~h
uni for-
suct i r.il


77 = /U0x


.0707
.141
.212
.28d
.554
.L24
.495

.656
.707






-5.1905
-1.193

.5
1.095
1.9265


-v u
-


-v
v


4 4 +


.211

.5'-'1

.51


*'. v J


l.C'1J


.6.

. :. 'J ;''
.^.*F)


.125

.192
.221
.27j3

.2'95
.515
.5

u-


2.59

2:4,

2.59
2.3'5
2.51

2.23
2.25

2.21
2


oT
0


0.571
.607
.631
.671
.699
.726

.773
94

.8o50
1

T 0
0


0.772

.292
.250
.209
.167


2.54
2.55
2.22
2.17
2.15
2.09


0.608


.917
.917





NACA TM No. 1121


o -
> "^ hi c ^H6
y jO X-y^


Figure 1. Explanatory chart: Boundary layer at the plate in longitudinal flow with
continuous suction according to the rule vo (x) = --- y Uo
x


=3
L 2


Figure 2. Velocity distributions u/Uo against y/S for various flow coefficients C
of the flow from Fig.l; WP = point of inflection. Comparison with the approximation
of equation (9).


Figs. 1,2






NACA TM No. 1121


Figure 3. The second derivatives of the velocity distributions from Fig. 2. (C= flow
coefficient).


Fig. 3






NACA TM No. 1121 Fig. 4










-3

0
.0


o




0
-'

3


/S4



i 0I /
S ,"/ // -"
', ',r'),y 4




/ / / / .










CM
0











rc.





Fig. 5 NACA TM No. 1121







<---- .--.----i_ _.--,,___I

U 45 05










vii ---""-y'











Figure 5. Velocity distributions u/Uo against y/& for different according to
Iglisch [41 ; comparisons with the approximation of equation (9).
S- Uo_-x
Uo ( )2
0 qo







NACA TM No. 1121


Figure 6. The second derivatives of the velocity distributions of Fig. 5, according
to Iglisch [4 .


Fig. 6






NACA TM No. 1121


__ VI o
fs uI


Figure 7. The boundary layer parameters for the plate with uniform suction:


-Vo o J*and
yv 7 ,


f against
n V5


according


to Iglisch [4].


(Flow Fig.4).


i suction V0 = onst i
suction VQ=const.


Figure 8. Explanatory chart: Boundary layer of the
suction vo= const.


plane stagnation flow with uniform


Figs. 7,8




NACA TM No. 1121


Figure 9. Velocity distribution u/Uo against y/j* for different Co, according to
Schlichting-Bussrann [3] ; comparison with the approximation of equation (9).


Fig. 9





NACA TM No. 1121


0 / 2 3 5 J 6



Figure 10. The second derivatives of the velocity distributions from Fig.8
according to Schlichting-Bussmann [3] .


Fig. 10







NACA TM No. 1121 Fig. 11










_,, /, I /. <.,

.--
'.-' y,, ,


^ -/7-. ,--I
.' 'a / I;



E. -.





/ -,


1 ,J 'I/ ,L

I 1' : / '0 -'

I / .
,, E lE.I i o
,,I, l I. I .
.F- /* .In .








't ,'" ,' -. _
.n, Ci









Si.-I
'.1 If L4 0






U I .

> 0
.4. 1%.
.o Cx.






Fig. 12 NACA TM No. 1121










S' '
I,

I awl p I a C.)
Qu I. "



S, I 77 -
./ / J '.



I' I


S' / / C







N..4. II_, 0


m I C4
i i ". I ,









o- cd Z




lc / / 0 5


^ ii ^4$ 0)
r -I
I I .














,, i t I 1 I I*ll s.; ;. C.4
I I,
v I






/ _t.I If __I_,,,_____ >'. d
S .' I /I I I1 .



/ I 0 -








1 I l -" C0
-- ,,, a I V
j I I\I Y ^/R O'O







S.~I IL~e







NACA TM No. 1121 Fig. 13









,,1 /q
own :, : L4
I I I _I, | '" 0"



1 4
,- ^ /- -


Uz 7 /C:
l-{"-7,,' I-:-,a "


I ,'9 1 / i





y I
/ i
'I C / i c







4 I : I .) .
/(\/ 8/ 1- / I-

0 110


n / cd
Q, 11 ..
I I
I /r1 0 (1

0-. / 11 0. 1 0




c Lu
c1 cn
4 / .-
/ ,- l I s I I- l i






-i % Ll




-, -
*- -

-^^ 1
$ s 85 a-- o




Fig. 14 NACA TM No. 1121








SStable






(-0 plane plate










C= o
7 without suction












asymptotic
suction profile
o- I \- --"....







o-








0 1 01 10 I I 5




Figure 14. Result of the stability calculation for the flat plate in
longitudinal flow with vo-1/\. The neutral stability curves
Os* against US* /rfor various flow coefficients C.






NACA TM No. 1121


0,3


0,2








0,.


O
l 02


0o 4


/5


i6 6W* t 7
IV


Figure 15. Result of the stability calculation for the plate in
longitudinal flow with uniform suction: The neutral stability
curveso6&* against U */V' for various ; V= 'o 2 Uox
= 0: Plate without suction (Blasius)
=oo: Asymptotic suction profile.


Fig. 15






NACA TM No. 1121


0,2
\ Stable
















II I I Iuctio









-v
f02 5 6 7



Figure 16. Result of the stability calculation for the plane stagnation flow
with uniform suction: The neutral stability curvescxS-*against US* /ij'
for various flow coefficients c =
Ul r


Fig. 16








NACA TM No. 1121


S01 '1













I k

_O l
___ _______

- ---------4--

















Shill I


[aVI


Fig. 17


a,
e 8

0r
E-1
4
1-i *4


bo




No z






0- 1


o o
o 0


N-S
s0


t o
f


'-S*


Li







,--
0,

(1o





cdi
-i




o ,
,-i-


-I .I







Fig. 18 NACA TM No. 1121









0







4-1
















o


EO
-_| I o



















a 0










0 0
It 0




C .0
---V ---- uL
































to C-*







4)
S 4 0,
--4
rx.
--- II cc
\ ^t c





<- \ 0 0
l"^ "" ^ "" t i
^ ^ ^ ^1 p- *
I '^1 I C Q)







NACA TM No. 1121


5

2



5

2
3

5

2
O8


2


2,4
I?


Figure 19. The critical Re-number (Uo S/y )crit as a

function of the shape parameter S */1 for the plate

in longitudinal flow with vo l/ /Y and vo- const.
and the plane stagnation flow.


760 0 asymptotic suction profile


1

\\ ,






5751(plate without suction)
PlaTeu u-- ut T
o Plate with uniform suction o=co nst .r
= continuous v ? ~
a Plane stagnation flow
I I I


Fig. 19






NACA TM No. 1121


f5
O

5

2


52

2




2

10


/,4 0,6S

VII @r,


Figure 20. The critical Re-number
function of -0;o 0
u 0 ; V


(UoS'/i,)crit as a
for the flat plate


in longitudinal flow with uniform suction.


70000 (asymptotic suction profile)




----- -
/_ e___t u___t_




5775 (plate without suction)


Fig. 20


r






NACA TM No. 1121


f05


5



2


10"


5



2


0 o,2 0,9 6 08 o



Figure 21. Ascertaining of the critical flow coefficient c9 for main-
taining the laminar flow for the plate in longitudinal flow with
uniform suction.


Uo r
Asymptotes: (
"T-


Uo 1

oc
-vo Ce


Fig. 21






NACA TM No. 1121


-3 -2 -f 0 1 2
Slowing S uetion




Uo0
Figure 22. The critical Reynolds number (crit as a function
of the flow coefficient Co for the plane stagnation flow with uni-
form suction.


Fig. 22






NACA TM No. 1121 Fig. 23









/ 0
/ ik
I ----- I--- H-17-.--n / H-
1 / /// I


_



N c&
.I -







--l I I Y + -I i



t / I/ / *
_: ,, l




/Z 0
ii i t /

/ /" / / I

.r L4 0;
ii > c C1








NACA TM No. 1121


Z,



'-4








a-




<^ I I
O C

bo








0>


04 0
to
I I I
4-3








443 c






CD



C c


i=C4 o I
Ca L o
-, -



00 (



+i 0 U





4 *a La
3
-I 3
C|.


+3 3 C








Iftlr tic t
-rl3 U


Fig. 24








NACA TM No. 1121 Fig. 25








er I.



4 6-


.. / C -






0 U 2
a l e











C >



S -.-I
a -0 -0

O

o--. .,



c1















L ,O
+3 0
z" .9 =-I ed













'i IA / ,.
/ / = _i













Io n
jC4L4 r -
II
-ioiC- W- 8L
G -7 -. C- o b.. o
'4.' 3 3








--*"~~~~" /-^O' t U 3
.-' ~ ~ ~ ~ ~ r ^-* I,-RC. i>
---^- ~ ~ ~ ~ ~ ~ ~ ~ ~ *^- '' __ __ __ __3 g J>^.
^^:' ~~ ~ q -- -- S8- 3 y
-- -- -- -- -- ^ S 5
--- __ __ __ __ ___^ o ) i L
---~ ~ ~ ~ ~~- -- ----r 3
L? mo c S






-- -- -- -- __ __ s <
10 ) M^.Q






NACA TM No. 1121


FiL. 26


+cct.1o,

32

2,+

f6

48


I I I -I I I I I 10
10' 2 3 5 7 VO7 2 3 5 7 fo

U =- Re
VJ


A Cf
Figure 26. The relative drag reduction ) f t and the minimum
(cf) fully turb.
suction quantity necessary for maintaining the laminar boundary
layer CQ crit as a function of Re = Uol/!r for the plate in
longitudinal flow with uniform suction (vo-0const) and with
Vo 1/ fX. Cf= (Cf) -(cf)
fully turb. laminar with suction









NACA TM No. 1121 Fig. 27






















\ e a d e a C
i A s V
-- 0 -


o .o ac o0
I I a "_ a) a
-1 .-



m \ -. u o

*o -. o o -
.aooa

1 ii







I I0



\ .-N I.. \
\ ,, O ,_ 0




0 0
\- 0 1
-o
CU















S o S (
I I To

















ai C; ( k7-' caW d












i







UNIVERSITY OF FLORIDA


3 1262 08106 301 7




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