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Access and use of this website and the material on it are subject to the Terms and Conditions set forth at The use of vortex generators to delay boundary layer separation: theoretical discussion supported by tests on a CF-100 aircraft Gould, D. G.
LABORATORY REPORT LR -183
THE USE OF VORTEX GENERATORS TO DELAY
BOUNDARY LAYER SEPARATION
THEORETICAL DISCUSSION SUPPORTED BY TESTS
ON A CF -100 AIRCRAFT
IATIOIIAL ~tp-c•or. c~ FEB 21 1957 VPLAJ..uS L d .ARY BY D.G. GOULDCLASSIFIED DOCUMENT • CONDITIONS OF RILEASE
I . THIS INPOIINATIOJI II DISC:LMID roa THil OI'PJCIAL USI. IJI CANADA OIILY, OP 1111
oaeAJIIZATIOJI AND SUCH OP ITS ITAI'P AI IIAY II AU1110aJZID UJIDia IIAL OP . . .
AN UJIAUTHOaiZilD PUION WOULD II A IUACH toYIRN.IJIT OF CANADA.
OTTAWA
LABORATORY REPORT Flight Research Section
- Preface - 12 - G - - . - 0
----'-'
.=-:.g-..:res Text -44
App. 6 1 48 _ :::-: Internal CONFIDE NTIAL Laboratory Report: LR-1 83 Date: 19 December 1956 Lab. Order: NAE - 383 File: BM49-7-133-::.-:: ~e ct: THE USE OF VORTEX GENERATORS TO DELAY BOUNDARY LAYER SEPARATION. THEORETICAL DISCUSSION SUPPORTED BY TESTS ON A CF- 100 AIRCRAFT
?~~ared by: D.G. Gould
~-::.~=itted by: A.D. Wood Head
Flight Research Section .. -;:;:!'oved by: J. H. Parkin
Director
This report gives the results of a limited theoretical
-~7estigation undertaken t o establish vortex generator design
~~axete rs and presents the findings of an experi mental
investi-=~~~on on a CF-100 aircraft of the effectiveness of vortex
ge~erator arrangements in delaying the onset of buffet to higher
::.=~ coefficients.
The theoretical analysis is based on the definition of e -o rtex generator effectiveness parameter related to the transfer
-=
=omentum across surfaces parallel to the wal l induced by the~~~ling vortex. The effectiveness was found to be a functi on of
~-e clade height, b oundary laye r height, blade lift coefficient ,
blades were co-rotating or counter-rotating. The change in effectiveness associated .with movement of and dissipation of
the vortex cores with downstream distance is discussed. An analysis of the design criteria of an installation to give minimum drag f or a given effectiveness is made; · Suggestions
are made to minimize the adverse effect of the vortex generators on the b oundary layer in the vicinity of the blades.
The results of the tests on t he CF-100 aircraft were in qualit ative agreement with the theoretical analysis. Recom-mendations for the design of vortex g enerator configurations for application in s uppressing boundary layer separation on
aircraft wings, i n ducts and in the corners of ducts or corners forme d by wing-fuselage or wing-nacelle junctions are made.
1. 0
2 .0
3 .0
_
...
SUMMARY LIST OF ILLUSTRATIONS ::.IST OF SYMBOLS INTRODUCTION TABLE OF CONTENTSTYPICAL VORTEX GENERATOR CONFIGURATIONS
THEORETICAL DISCUSSION OF PRINCIPLES AND DESIGN OF VORTEX GENERATOR CONFIGURATIONS
3.1 E~~ectiveness o~ Vortex Generators in Controlling Boundary Layer Separation 3.1.1 Ef~ectiveness of a Single Vortex
3~1.2 The Effectiveness o~ a Single Vortex Generator Blade
3.1.3 Effectiveness per Vortex for a Row of Vortices ( i) (iv) (ix) 1
3
4
5
6 9 11 3.2 Paths of Vortex Filaments from a Row of VortexGenerator Blades 14
3.3 Dissipation of Vorticity 17
3 .4 Effect of Vortex Generators on the Boundary
Layer in the Vicinity of the Blades 19 3.4.1
3.4. 2
3.4.3
Lifting Vortex Bow Shock Wave
Row of Counter-Rotating Vortex Generators
3.5
Drag Due to a Vortex Generator Installation3.5.1
3.5.2
3.5.3
Spanwise Spacing
Blade Lift to Drag Ratio Blade Height EXPERIMENTAL DATA 4 .1 ~ .2
4.3
4.4
MethodInstrumentation and Accuracy of Measurements Vortex Generator Configurations
Results of Tests 20 21 24 24
25
26 27 28 29 2931
32
-4. -4.1
4. 4. 2
4. 4. 3
TABLE OF CONTENTS (Cont'd)
Ini tial Tests with Vortex Generators on the Basic Aircraft
Tests with Vortex Generators on Aircraft with Wing Flap Deflected 10 Degrees
Drag Increment Due to Vortex Generator Installations
5 . 0 RECOMMENDATIONS FOR DESIGN 5.1
5.2 5.3
5.4
5.5
Blade Plan For.m and Incidence Blade Height
Spanwise Spacing
Choice of Counter-Rotating or Co-Rotating Configurations
Arrangements in the Corner of a Cha~nel or Corner Formed by Wing-Fuselage or Wing-Nacelle Junction
6. 0 CONCLUSI ONS 7 . 0 REFERENCES
TABLE I: Det ails of CF-100 Mk IVa Aircraft APPENDIX A: Devices Related to Vortex Generators APPENDIX B: Paths of Vortex Filaments for
Counter-Rotating Vortices APPENDIX C: Tuft Studies
LIST OF ILLUSTRATIONS
Typ ical Co-Rotating and Counter-Rotating Vortex
33 35 38
39
39
40
4041
41
42
44
Figure Generator Arrangements 1Photographs of Vortex Generator Ins tallations on
an Aircraft 2a-c
Typi cal Arrangement of St aggered Counter-Rotating
Vortex Generator Blades 3
LIST OF ILLUSTRATIONS (Cont'd)
Figure
-~~ation of Effectiveness with
h/o
for aS~~le Vortex Generator 5
-~~a~ion of Effectiveness per Vortex Generator ~th h/b and ~ for Rows of Equally Spaced
o-Rotating and Counter-Rotating Vortices 6
-~~ati on of Effectiveness per Unit Span with Sp anuise Spacing for Rows of Co-Rotating and
Gaunter-Rotating Vortices 7
2 ow of Counter-Rotating Vortices 8
?a~hs of Vortex Filaments for Counter-Rotating
7ortices, D = 2?\h'0 9
7 ariation of Effectiveness per Unit Span with
Jistance Downstream 10
-ariation of Radius of Vortex Filament with
Jistance Downstream 11
~epresentat ion of Blade of Vortex Generator by a
~ine Vortex 12
~ecrease in Fl ow Velocit y Along Line z
=
o,
y=
h Induced by a Lifting Line Vortex A= 0°, 60°,8~. 3° at M
=
0 13=~~uence of Mach Number on Decrease of Flow Velocity 14
~aximum Decrease of Velocity as Influenced by Sweep
and Mach Nuniber 15
~epresentation of Vortex Generator with Leading
Edge Sweep as a Cone 16
";edge and Cone Semi-Angles for Attached Shock Wave 17 l .'edge and Cone Angles for Shock Waves of Equal
Strength 18
L IST OF ILLUSTRATIONS (Cont ' d)
Figure
Photograph of Test Aircraft 20
Error in St at ic Pressure Sensing Head Installation
on Test Aircraft 21
Types of Vortex Generators Tested 22
Buffet Boundary of Basic Aircraft 23
Buffe t Boundary of Aircraft with Outboard Flap
Deflected 10 Degrees
24
Buffet Boundary with Configuration A Vortex
Generators at 30 Percent Chord 25
Buffet Boundary with Configuration B Vortex
Generators at 30 Pe rcent Chord 26
Buffet Boundary with Configuration B Vortex Generators on Wing Panel Only and on S ide of Nacelle and Inboard 27 Percent of Wing Panel
Onl y (at 30 Percent Chord) 27
Buffet Bo~~dary with Configuration B Vortex
Generators at 15 Pe rcent Chord Position
Showing Effect of Corner Arrangement 28
Buffet Bound~ry with Configuration B Vortex
Generators at the 9 Perce nt Chord Position 29
Comparison of Effe ctiveness of Configuration B Vort ex Generators at 30, 15 and 9 Percent
Chord Positions 30
Buffet Boundary of Aircraft with 10 Degrees Outboard Flap Deflection and Configuration B
Vortex Generators at 9 Percent Chord 3 1
Buffet Boundar y of Aircraft with 10 Degrees Outboard Flap Deflection and Configuration C
LIST OF ILLUSTRATIONS (Cont 'd)
Compa rison of Effectiveness of Co-Rotating Configuration C with Counter-Rotating Configuration B Vortex Generators at
9
Percent Chord on Aircraft with 10 DegreesFigure
Outboard Flap Deflection 33
Buffet Boundary of Aircraft with 10 Degrees Outboard Flap Deflection, Configuration C Vortex Generators at 9 Percent Chord and Configuration F Vortex Generators at
Leading Edge
34
Buffet Boundary of Aircraft with 10 Degrees Outboard Flap Deflection and Configurat ion F
Vortex Generators at Leading Edge
35
Buffet Boundary of Aircraft with 10 Degrees Outboard Flap Deflecti on and Configuration D
Vortex Generators at 9 Percent Chord 36
Comparison of Effectiveness of Configuration C Vortex Generators (0 Degrees Leading Edge Sweep) with Effectiveness of Configuration D Vortex
Generators (60 Degrees Leading Edge Sweep) 37
Buffet Boundary of Aircraft with 10 Deg rees Outboard Flap Deflection and Configuration E
Vortex Generators at
9
Percent Chord 38 Comparison of Effectiveness of Configurat ion Eand Configuration D Vortex Generators
(9 Pe rcent Chord) 39
Drag Increment Due to Vortex Generator
Configurations D and E as a Functi on of Mach
Numbe r at Constant Altitude
40
Drag Increment Due to Vort ex Generator
Configurations D and E as a Function of Lift
Coefficient 41
LIST OF ILLUSTRATIONS (Cont'd)
Leading Edge Discontinuities Boundary Layer Fences
Wing Le ading Edge Fairing
Schematic Drawing Showing Tuf'ted Region, Camera Positions and Location of' Pressure Sensing Heads Regions of' Flow Separ ation at Onset of' Buf'f'et
Leading Edge of' Separation Re g ion on Wing at Ons et of' Buf'f'et
Figure 43
44
4546
47a - h 48a A c
-
c d ::>0 g h LIST OF SYMBOLSpropo r tionality constant (Section 3.3)
aspect ratio of vortex generator blade and its image
effective aspect ratio of vortex generator blade and its im age in the presence of a bo~~dary layer on the fluid c ontaining surface
const ant dependent on spanwise load distribution on vortex generator blade (Secti on 3.1.2)
local chord of vortex generator blade
standard mean chord of vortex generator blade standard mean chord of aircraft wing
drag coefficient of vortex generator b l ade
local lift coefficient of vortex generator blade lift coefficient of vortex generator blade
aircraft normal force c oeffici ent
indicated ai rcr aft n orma l force c oe f f i ci ent
lateral s pac ing between vort ices ad j acent to hi gh energy ch a~~el fo r c ounter-rot at i ng vortices
(Fi g . 8)
l ater al sp aci ng b etwee n blade p airs of c oun ter-rot ating vortex gen erators (Fi g . 8)
dr ag per unit sp an of vortex generator install ation vortex generat o r effectiveness parameter
ef fect i veness per unit s pan of vortex g ener ator install at :i on
acceleration due to gravity
d is t ance of tip of vortex ge nerator b l ade f rom f luid c ontaining surface
H H
M
n
LIST OF SYMBOLS (Cont'd)
distance of vortex filament from fluid containing surface
boundary l ayer shape parameter (Section 3.1) total pressure (Section 4)
Mach number of flow at vortex generator position (Section 3.4)
Mach number of aircraft (Section 4) indicated aircraft Mach number
index defining velocity profile in the boundary l ayer (Section 3.1)
lateral spaci~ between vortex filaments (Section 3.1.3)
static pressure (Section 4) indicated static pressure dynamic pressure
indicated dynamic pressure
radial distance from centre of vortex core radius of vortex core
aircraft wing area time
velocity component in x direction
velocity in stream outside of boundary layer in the absence of a vortex
velocity component in y direction velocity component in z direction aircraft weight
X z
ou
~0 T)e
a
K A~ . E.
LIST OF SYMBOLS (Cont 'd)
coordinate in direction of vortex filament coordinate in direction normal to vortex
filament and parallel to fluid containing surface coordinate in direction normal to vortex filament and normal to fluid containing surface
angle of attack of vortex generator blade maximum semi-cone angle for an attached bow
shock wave in supersonic flow
maximum semi-wedge angle for an attached bow shock wave in supersonic flow
boundary layer thickness
boundary layer displacement thickness
decrease in velocity in x direction due to bound lifting vortex
excess thrust
=
thrust minus dragp. - p l.
eddy viscosity
vorticity component in direction of vortex filament
2?Cd/2 D
bo~~dary layer momentum thicknes~ (Section 3.1)
2
~x
(Appendix B)
circulation about trailing vortex filament sweepback angle of lifting line vortex sweepback angle of leading edge of vortex generator blade
v
p
LIST OF SYMBOLS (Cont'd)
kinematic viscosity
21th t
r r
o/h'
density
flux of momentum through a surface parallel to the fluid containing surface
-::=
~? VORTEX GENERATORS TO DELAY BOUNDARY LAYER SEPARATION.~-~=:CAL DISCUSSION SUPPORTED BY TESTS ON A CF-100 AIRCRAFT
:Y30DUCTI ON
Control of boundary layer separation in fluid flows
-~c ~s , wind tunnels and over aircraft surfaces has long been of engineering importance . Phenomena such as wing buffeting , control oscillation or loss of
effective-3e~=, :ongitudinal trim changes, and loss of longitudinal
~--~:i~y on aircraft are usually associated with boundary
~=~ separation. Separation of the boundary layer in wind
~: diffusers or in jet engine intake ducts results in a _ s~ ~~total pressure with a corresponding loss in efficiency
-- ~he ind tunne l or engine o
Se veral methods of controlling the boundary layer ---: ~een developed experimentally with the aid of theoretical
-2~~erations. One of these methods consists of supplying
~~~onal momentum to the retarded fluid particles near the ___ ace in the boundary layer by dis charging fluid from the -=-e r1or of the body through a slot~ or in deri ving momentum
--r=c~ly from the main stream, as in the case of the familiar
_e~~g edge slot. In another method the retarded fluid
=-~c: es are removed from the boundary layer before they are
~-=~ a chance to cause separati on by providing a suitable
---~=6ement of suction slits or continuous porous suction. The conditions under which boundary layer separation occur at flight Reynolds number are not always predictable
--~er from theory or from model tests9 particularly for the
-
~= of aircraft wings at hi gh angles of attack at hi ghsub---
_._ .... Mach numbe rs , where the presence of shock waves h a s a influence on separation . A simple device effective forsuppression of boundary layer separation is, therefore,
extremely useful. Vortex generators are particularly simple devices that have proved to be effective in allowing boundary layers to sustain large adverse pressure gradients without
separation.
Vortex generators are devices, placed on or near the surface on which the boundary layer is to be controlled, which generate vortices whose filaments extend downstream
approximately in the direction of the flow. The vortices
induce a transfer of momentum through surfaces parallel to the wall and by so doing affect the bo~~dary layer in a manner
such that it can sustain larger adverse pressure gradients without separation. Vortex generators were originally pro-posed by Bruynes (Ref. 1) and since that time have been
successfully applied to the control of boundary layers in ducts, wind tunnels and over aircraft surfaces. Particular success has been achieved in the control of separation on the upper surface of aircraft wings at high subsonic Mach numbers.
The fluid mixing action provided by vortex generators is also potentially useful in the mixing of fluids in chemical flow processes.
A series of flight and wind tunnel tests on counter-r otati ng vocounter-rtex genecounter-ratocounter-r acounter-rcounter-rangements wecounter-re made counter-recently at thi s establishment by Dr. B.G. Newman (Ref.
9).
The effective-ness of various counter-rotating vortex generator arrangements i n de l aying the onset of aileron buzz on a T-33 jet aircraft was determined in these tests. The present report gives the r esults of a limited theoretical investigation undertaken to establish vortex generator design parameters and presents the f indings of an experimental investigation on a CF-100 aircraft of the effectiveness of various vortex generator arrangements in del aying the onset of aircraft buffet to hi gher normal force coefficients.e
s
t
e
:.o
TYPICAL VORTEX GENERATOR CONFIGURATIONSTypically, vortex generat or configurations consist
~ rows of small blades attached to the surface containing the
~uid and having their span essentially normal to the surface. Each blade is set at an angle to the flow direction in order
~o generate lift and thereby cause a vortex filament to extend :=wnstream from the tip of the blade.
Common configurations of vortex generators can be
se?arated int o two main classes. In one9 the blades are mounted
-~ a single row with their angles of attack alternately positive
=~r. negative, so that the circulation about the adjacent trailing ort ices induced by the bl ades is of opposite sense. In the
s econd class, the angles of the blades to the stream direction
~-e all positive (or all negative) so that the circul ation about
£1:
of the trailing vortices is of the same sense. If the sense~ the circulation about adjacent trailing vortices is opposite,
~~e arrangement of vortex generators is usually referred to as
-:~ter-rotating. If the sense of the circulation is the same E: out al l of the trailing vortices , the arrangement is usually
~:ed co-rotating. Typical co ~ ro tat ing and counter- rotating
To~~e x generator configurations are shown in Figure 1 and photo-g:aphs of installations on an aircraft are shown in Figure 2.
Multiple rows of vortex generators may also be
~loyed . A configuration of interest and Which Will be discussed
~n Section
3
is one in whi ch two rows of co-rotating vortexge~erators are arranged so t hat the b l ades in the second row
pro-~~~e vortices of opposite sense to those produced by the first row,
-~e blades being staggered with respect to the stream direction.
-~s type of arrangement produces counter- rotating trailing
-~tices and is shown schematically in Figure
3.
Considerable variation in pl an fo rm of the blades of
and leading edge sweep angle of the blade.
The above description of vortex gene rator arrange-ments covers the configurations normally encountered in
engineering applications and Will serve as a basis for the theoretical and experimental analyses of vortex gener ators.
A number of devices used for the prevention of boundary layer separation are related to vortex gener ators
through similarity of action on the flow. These related devices - ramps, wedges, wing leading edge discontinuities, boundary layer fences, and wing fuselage leading edge fairings, achieve a part of their effectiveness through the action of a vortex filament trailing downstream from the device in the same ma~ner as vortex generators. A discussion of these
related devices is given in Appendix A since a recognition of the similarities with vortex generators should be helpful in the design and testing of these devices.
3.0 THEORETICAL DISCUSSION OF PRINCIPLES AND DESIGN OF VORTEX GENERATOR CONFIGURATIONS
Vortex generators achieve effectiveness in controlling boundary layer separation through the action of the vortex
filaments which trail from them approximately in the stream direction. The trailing vortices induce velocities normal to the stream direction and cause a transfer of momentum through surfaces parallel to the wall. A discussion of the principles
and design of vortex generators must include a definition of the effectiveness of the trailing vortices in suppressing boundary layer separation. The trailing vortices must be generated in an efficient manner and in such a way that the adverse effect on the boundary layer in the vicinity of the vortex-producing devices is small. The effectiveness of the trailing vortices
s,
;:onfigurations- consisting of small blades attached to the wall
~~d having their span essentially normal to the wall are
dis-~ussed in the following section.
3. 1 Effectiveness of Vortex Generators in Controlling Boundary Layer Separation
The susceptibility of a boundary layer to separation in the presence of a given adverse pressure gradient is primarily a function of the distribution of ve~ocity within the layer
( for example, the familiar boundary layer shape parameter, H
=
o*/9).
A boundary layer with a velocity profile such that the momentum of the particles near the surface is large will sustain a larger adverse pressure gradient without separation t han one in which the particles near the surface have a low momentum. To be effective, therefore, the trailing vortices must increase the momentum of the retarded fluid particles near the surface.The trailing vortices produced by vortex generators mix particles having high momentum from the free stream with
particles having a low momentum within the boundary layer.
Momentum in this description refers to the momentum of the fluid particles in the stream direction. In the presence of a trailing vortex the fluid particles take up a helical path about the
filament of the trailing vortex. Particles of fluid in the free s tream having a high momentum are continuously being swept into the boundary layer on one side of the vortex. Similarly, fluid p articles are being swept out of the boundary l ayer on the other side of the vortex . The turbulent mixing process within the boundary layer mixes the particles of high momentum swept into
~he boundary layer with the particles having a lower momentum, with the result that the mean momentum of the fluid particles in
are very complex and are not amenable to a rigorous mathematical analysis . It seems plaus i b le, however, that the increase in momentum of the fluid particles in the b oundary layer is related to the momentum transferred per unit time towards the wall across surfaces parallel to the wall within the b oundar y layer.
The flux of momentum across a surface parallel to the wall induced by a vortex is a fUnction of the distance of the surface from the wall fo r a vortex of given strength with its filament a given distance from the wall. The efficacy of the trailing vortex was taken somewhat arbitrarily, therefore, as being proporti onal to the average flux of momentum towards the wall across a ll surf aces within the boundary layer.
3.1 .1 Effectiveness of a Single Vortex
The system of coordinates (x , y , z) was chosen with the wall as the x- y plane and with the x- z plane containing the vorte x filament and its image. The x coordinate was taken in the direction of the vortex filament , with the coordinates of the vortex filament and its image taken as (x, o, h' ) and
(x, o, - h ' ) respectively . The vortex and its image were
assumed to be two-dimensional and the slope of the path of the vortex filament relative to the stream direction was assumed to be small . The component of velocity in the x direction was taken
as the free stream velocity,
u,
outside of the boundary layer (z ~ o) and was taken as u = u(z) inside the boundary layer(z ~
o).
It was fUrthermore assumed that the velocity component in the u direction was not affected by the presence of thevortices.
The flux of x momentum ( pu) through an e lemental area of dimension dy in the y direc tion and of unit dimension in the x direction is given by
ical a ted cross 'the to taken nent rea the where is the by the toward K [ 1 1 ]
w
y z h' - - - y -( ' ' ) - 211: y 2 + ( ' h -z ) 2 y 2 + ( ' h +Z ) 2velocity induced in the direction normal to the wall vortex and its image. The average flux of x momentum the wall through all the surfaces within the boundary layer is
A. --
-;:1 /0
/00
'~' v puw dy 1 dz
Z=O Y=O
A non-dimensional vortex effectiveness parameter, E, was defined as
6
f
0Jm
puw dy dz Z=O Y=OThe denominator in this expression for E represents the flux of x momentum through a surface normal to .x of unit width in the y direction within the boundary layer with a uniform vel ocity distribution u
=
U within the boundary layer.The effectiveness parameter, E, as defined, is a :Unction of the circulation around the vortex, K, the ~atio
of the height of the core of the vortex above the surface to
~he height of the edge of the boundary layer above the surface,
~·;o , and the velocity profile in the boundary layer u
=
u(z).:t
is desirable, from the point of view of general design criteri a , that the choice of h'/o and K to give maximumprofile of the boundary layer that is to be controlled. The dependence of the choice of h'/o and K on the boundary layer
velocity profile was demonstrated by assuming that the velocity profile was of the form u
=
U(z/o) 1/n and computing E as afunction of K and h'/6 for the two c ases of n = oo and n
=
1.The case of n
=
oo corresponds to a uniform velocity in theboundary layer, u
=
U; while the case of n=
1 corresponds t o a linear decrease in velocity from u = U at z=
o to u=
0 at z=
0. The usual types of boundary layer profiles encountered will correspond approximately to values of n between 1 and oo;for example, the velocity profile for a turbulent boundary layer on a flat plate with zero pressure gradient may be approximated very closely by taking n
=
6.
The expressions for E for asingle vorte x for values of n
=
1 and n=
oo areEll=1 K
1 h t
[1
1
[h'2
1]
log (h'Lo
+1)j
=
27CU ob
4h'/o 02 h'/o - 1E n:oo
=
21lU K 0 1~1
log(h'LO
+~
h ' /6~)2
+1
lL
log(h'
2
Lo
2
-
1)j
'2' o h,2
162 E is proportional to K/U and inversely proportional to the boundary layer thickness, o. E 0
~
is plotted as a function of h'/o in Figure 4 for the two cases of n = 1 andn
=
oo . The effectiveness for a given value of~U
increaseswith increasing h'/o to a value of h'/o between 0.7 and 0.8, dependent on the value of n, and then decreases with increasing h'/o . The ~alue of h'/o for maximum effectiveness is seen to be not very dependent on the boundary layer velocity profile as it only increases from 0.7 for n
=
oo to 0.8 for n=
1. Maximum effectiveness for a given value of~
should be obtained for thety d yer ed ng as the
usual types of boundary layer velocity profiles encountered, therefore, by choosing the ratio of h'/o to be about
0.75.
3.1.2 The Effectiveness of a Single Vortex Generator Blade For vortex generator configurations consisting of small blades normal to the surface, the blade is in many respects similar to a wing. The similarity between a vortex generator blade and a wing becomes evident when it is recog-nized that the surface to which the blade is attached is
aerodynamically equivalent to a plane of symmetry in the absence of a boundary layer. The vortex generator blade is then equivalent to the wing formed by the blade and the image of the blade in the plane of symmetry. The use of wing theory i s useful, therefore, in the calculation of the vortex strength ?roduced by the blade.
In wing theories the assumption is made that the flow !s uniform. Such is not the case for flow about a vortex
6enerator blade attached to a surface having a boundary layer ! n that the flow velocity near the surface is retarded. If the
~l ade hei ght is more than four times the boundary layer height, experiment has shown that the effect of the boundary layer can :e al lowed for by taking the effective plane of symmetry at the
~ei ght of the boundary layer displacement thickness. This ratio
o ~ b lade hei ght to boundary layer height is typical for most - ortex generator configurations. Relatively smaller blade
_ei ghts are often encountered in practice but test data are not
~7ailable for these cases. It is suggested that when the
~oundary layer height is less than the blade span, the influence
=~ the boundary layer may be allowed for with sufficient accuracy
~7 taking the blade height as the actual blade height less the boundary layer displacement thickness.
Wing theory shows that the strength of the circulation
gi ven by
[ ( o•)
1 + A/2 ]h 1 - -h -1 + Ae/2
where B is a constant whose value is given by (01
~)
at the CL ceffective plane of symmetry of the blade. In this expression CL is the lift coefficient of the blade if it were in a uniform stream, A is based on the actual geometric properties of the bl ade, while Ae is based on the dimensions of the equivalent wing having semi-span equal to h - o•. The height of the v ortex filament above the surface is ( Ref. 2)
h '
=
hBo• + o•=
R
+ o•(1 - 1/B)For the particular case of elliptic spanwise load distribution on the blade, B
=
4/~. The boundary layer displacement thick-ness for a boundary layer whose velocity profile may be approxi-mated by u = U(z/o) 1/n is given byo•
=o ( -
1+n 1 )A typical value of the ratio
o•jo
is 1/7 so that for h/o > 2and
h' :::::
h/B
rm
n
xi-With these substitutions for K/U, h' and 6* into the equations for the vortex effectiveness given in Section 3.1.1, the effectiveness of a single vortex generator blade may be computed. For a given value of h/6 and a given boundary layer velocity profile, E for a single blade is proportional to the ratio of CL/A of the blade. E
~
for a single vortex generatorL
blade is plotted as a function of h/6 in Figure 5 for boundary
layer velocity profiles given by n = oo (u = U) and n = 1
(u
= U~)·
The effectiveness is maximum for h/6 ~ 1.2 and the value of h/6 for maximum effectiveness is not very dependent on the form of the boundary layer velocity profile. If h/6 is decreased from a value of 1. 2, the effectiveness decreases rapidly to zero. As h/6 is increased from 1.2, however, the effectiveness only decreases to about
65
percent of its peak value and remainsapp roximately constant for values of h/6 > 3.
3 .1. 3 Effectiveness per Vortex for a Row of Vortices The effectiveness per vortex of a number of two dimensional vortices in a row in the y-z plane is usually re-duced because of the velocities inre-duced by adjacent vortices. The effectiveness per vortex becomes a function of the spanwise spa cing of the vortex cores and depends upon whether the vor-t ices are co-rovor-tavor-ting or counvor-ter-rovor-tavor-ting. The velocity induced normal to the wall,
w,
is• = K
I
(y+rp) [ (y+rp)2 12?t
+ (h'-z)2 r=O, ± 1 ' •••:or equally spaced co-rotating vortices, and
( - 1)r ( y+rp) [ 2 1
(y+rp) + (h'-z)2
for equally spaced counter-rotating vortices, where p is the spanwise spacing between the vortices. The effectiveness per vortex for a uniform velocity distribution in the bo~~dary
layer (u = U) is E K 1 }::"1
=
2?tU6 ""
r=O, ±1, ±2 !J. 1 2 r2 + ( 1 +~ I ) 2 2 1 2 2 !1.' (~+r) + (1-~1 )J
22 2 !.l.'r + (1-~')(~r)
2 - !.l.'r tan- 1for equally spaced vortices, where~'= 6/h', !.~.'
=
p/h' and i = 1 for co-rotating vortices and i=
-1 for counter-rotating vortices.The effectiveness per vortex generator blade (for elliptic spanwise load distribution on the blade) has been computed for rows of egually spaced co-rotating and
-_ .,
_
...:;er
spacing parameter~= p/h of
3.92, 2.36,
1~57 and0.79.
The above values of~ correspond to values of~· of5, 3,
2 and 1, respectively. The results are compared with the effectiveness of a single vortex generator hlade in Figure6.
The effectiveness per unit span, E/~, for rows of
equally spaced co-rotating and counter-rotating vortices divided by the effectiveness of a single vortex generator blade is given as a function of 1.1. in Figure
7
for values of h/o =1. 27 (
hYo =1. 0 ),
~o =
2.0
(h'/6 =1.57)
and h/0 =10.
For co-rotating vortices~he effectiveness per ~~it span increases as the spanwise spacing
~s decreased to a value of 1.1. between 2 and
3,
depending on theyalue of h/6. For counter-rotating vortices the effectiveness
~e r unit span increases as the spanwise spacing is decreased to a value of 1.1. between 1 and
1.5,
again depending on the value of~o. The effectiveness per unit span of counter-rotating
vor-~ices can be made almost double that for co-rotating vortices.
~e effectiveness per unit span is almost independent of h/o for 7Slues of h/o > 2 (see also Fig.
6).
The results of Figure
7
would be somewhat modified if:~e loss of momentum in the boundary layer due to the profile
~ag of the vortex generator blades were included in the
~e:initi on of effectiveness9 particularly as the spanwise spacing
:5 decreased. For example, for h/o = 1.27 , ~ = 10, the
effective-~ess per unit span is approximately
0.079
GilA
for bothco--=~ating and counter- rotating vort ices. If the spanwise spacing
~;de creased to~=
1.0
for counter-rotating vortices, the=~~e ctiveness per unit span is increased by only
6.8
times while~~ momentum losses per unit span due to the profile drag of the =:srles will be increased 10 times. Similarly, for co-rotating
-:~i ces, if the spanwise spacing is decreased to ~ = 2, the
e~~ect iveness per unit span is increased by
3.7
times while theblades would be increased by 5 times. It would not be expected, therefore, that the effectiveness would increase as rapidly with decreasing spanwise spacing as is indicated by the curves of Figure
7.
Furthermore, the value of ~ for maximum effectiveness per unit span would probably be greater than that shown inFigure 7.
3.2 Paths of Vortex Filaments from a Row of Vortex Generator Blades
The computations made in the preceding section showed t hat the effectiveness of a trailing vortex for a given value of the circulation, K, decreased rapidly if the ratio of the height of the vortex filament to the height of the edge of the boundary l ayer was increased (Fig.
4).
When the vortex filaments are arranged initially in rows in the y-z plane, the positions of the filaments relative to each other and relative to the wall may change with increasing distance downstream. Hence, theeffectiveness may become a function of downstream distance. The general form of the path of any vortex filament of the system can be determined qualitatively by considering the velocities induced at the filament by one or two adjacent vortices whose influence is predominant.
If the vortices are co-rotating the only motion of the filaments is parallel to the wall and the height of the filaments above the wall and the relative spanwise spacing of the filaments remain fixed . The path of the filaments in the x- y plane makes an angle with the stream direction equal to
tan-1 [
.JL
2Up coth?C~'
J
If this angle is not large the motion of the filaments parallel to the wall wi ll not influence the vortex effectiveness. For
1 J j D E n f T ( t t d c a C t
s e the ents ents l el r
typical co-rotating vortex generator arrangements this angle is less than 15 degrees.
If the vortices are counter-rotating the relative spanwise spacing of the vortex filaments and the height of the filaments above the wall change with downstream distance. An analytic method of determining the paths of the filaments
for counter-rotating vortices is given in Reference
3.
This method assumes that the vortices are two-dimensional and that the component of the velocity in the x direction is uniform and equal to the free stream velocity, U. The details of the method for calculation of the paths of the vortex filaments for typical counter-rotating vortex generator configurations are given in Appendix B.The coordinate system chosen is shown in Figure 8.
The coordinates of a particular filament were designated as ( x, d/2, h') and the initial position of the filament was taken as (o, d0/2, h'0) . The results of the computation for
the case of D
=
2~h'0
and D/d0=
2, 2.5, 3 and4
are shown in Figure9
in the form of d/d0 and h'/h'0 as functions of theCL
downstream distance parameter,
-f-
Jr·
For e qually spacedh 0
counter-rotating vortices (D/d0
=
2) the vortex filaments move away from the surface and the relative spanwise spacing d/d0 increases as the downstream distance is increased. For values of D/d0 > 2 the vortex filaments approach nearer the surface ini tially and then move away from the surface. The minimum value of h'/h'0 decreases with increasing D/d0 and the final rate at which the vortices leave the surface increases with D/d0• The rate of increase of the relative spanwise spacingd/d0 increases with increasing D/d0•
The initial downward movement of the vortex filaments can be used to increase the effectiveness of the vortices over
a limited distance downstream. If the initial blade height is chosen such that h' . /6
=
0.7 (the value of h'/o such thatUo
m1nE
1f
is maximum, see Fig. 4), K would be larger and hence E l arger over a limited downstream distance than it would be if h'ofo were chosen to be equal to 0.7. This is illustrated by t he curves of Figure 10 showing the effectiveness per unit span of counter-rotating vortex generators as a function of down-stream distance for the case of D=
2?Ch'0 and D/d0=
2, 2.5, 3 and 4 . The effectiveness per ~~it span for values of D/d0 > 2 was assumed to be equal that of equally spaced counter-rotating vortices having a spanwise spacing p=
D/2 . The initial blade hei ght was chosen so that h'minlo=
0.7 . The effectiveness per unit span of co-rot ating blades having spanwise spacings of~ = 3 and 4 is also shown in Figure 10 for comparison with the e·ffectiveness of the counter-rotating arrangements.
These results show that counter-rotating arrangements should be more effective than the co-rotating configurations for values of x / h · CL/A less than about 12 and that the effectiveness in this region of x /h · CL/A increases with in-creasing D/ d0• Typically, the value of CL/A for
counter-rotating arrangements is about 1.4 so that they would only be more effective than co-rot ating vortex generators for distances downstream less than about 8 times the blade hei ght and for lar ger distances downstream co- rotating blades would be more effective.
Three dimensional effects were not considered in the analytic analysis of the paths of the vortex filaments . The major portion of the movement of the filaments toward the wall occurs during the first one or two blade heights downstream (Fig .
9).
In this region three-dimensional effects would be significant and it may be argued qualitatively that the three-dimensional effects would reduce the motion toward the surface .Fj tl Tl .p • .I.] ::c tl ti a :nc :nE we cc -de tc
an 3 2 .ng le
L-Firstly, the trailing vortices are semi-infinite starting at the bound vortex representing the lifting line of the blade. The velocity toward the surface at
x
= 0 induced at thef ilament by the adjacent vortex would only be one-half that
f or the two-dimensional vortex assumed in the theory. Secondly, t he bound vortex induces a velocity at the filament of the
t railing vortex tending to make it move parallel to the wall in a directi on away from the trailing vortex that is inducing
motion toward the wall so that the resultant downward motion is further reduced.
It would not be expected, therefore, that the improve-me nt in effectiveness with increasing D/d0 as shown in Figure 10 would be fully realized. The loss in effectiveness of the
counter- rotating configurations shown in Figure 10 for distances downstream greater than about 10 blade heights would be expected t o be essentially correct, in that at this distance downstream t he assumption that the vortices are two-dimensional is not appreciably in error and the effect of the bound vortex is negligible.
3 . 3 Diss i p ati on of Vorticity
~es The effects of viscosi ty were not considered in t he
ll
di scussions of vortex generator effectiveness in the previous secti on s . One of the more obvious effects of viscosi ty is the dis sip ation of t he vortices with distance downstream. App r
oxi-~t e calcu l ations may b e made to show that the dissipation of
~ he vortices may have a ma rked effect on the downstream
e~fectiveness of the vortex generators .
The dissipation of the kinetic energy of the vortex
~nt o heat energy due to the viscous forces in the fluid may be
~nt erpreted in the simplest case as the rate of growth of the <ortex filament with time or downstream distan c e . The rate of
growth of the vortex core in turbulent flow is discussed in Reference
4.
For the simple case of a single two-dimensional vortex whose filament is in the x direction and with r taken as the radial distance from the filament, the mean vorticity component in the x direction is given by3.3.1
i f e is assumed independent of t. In this expression K is
the circulation at infinity, v is the kinematic viscosity and
e is the eddy viscosity . The assumption is made in Reference
4
that the eddy viscosity can be approximated by e=
aK where a is a constant. If the edge of the vortex core is arbitrarily defined as the radius r0 at which ~
0
is 0.05 of the value of~
0
at r = 0, then equation 3. 3. 1 may be used to determine an expression for the radius of the core, r0•
r 2 = 12(v+aK)t
0
In most cases v can be neglected compared to aK.
3.3.2
For the case of elliptic spanwise load distribution on the vortex generator blade and t
=
x/U the expression for the core size becomes r 2 0 h2=
CL x a -A hThe value of the constant, a, is unknown. It was arbitrarily chosen as a
=
10-3 in the example given inReference
4.
An approximate value of a was deduced from the results of some unpublished tests . These tests covered at'on
la£
range of Reynolds numbers from 1.94 x 105 to 10.1 x 105 based on the vortex generator chord (the blade was of rectangular plan form with the chord
4
times the blade height). Thisrange of Reynolds numbers is typical for most vortex generator applications. These results showed that a was less than
5
x 10-4. The variation of rclh with CL/A · x/h for a=
5
x 10-4 is given in Figure 11 .The effectiveness of a vortex will be reduced if the vortex filament grows sufficiently with downstream distance such that r
0 becomes greater than (h'-o). For some applications,
then, the height of the vortex generator blade will be primarily determined on the basis of the required downstream effectiveness. For example, for a configuration of co-rotating vortex generators having CL/A
=
1 that must give maximum effectiveness for a dis -tance downstream equal to 50 blade heights, the value of h would have to be chosen such that it was6
times the height of the boundary layer at a distance 50 blade heights downstream. In practice the height of the vortex generator blade to give thedesired downstream effectiveness must be determined experimentall~
The above analysis may serve as a guide in selecting approximate values of h .
3.4
Effect of Vortex Generators on the Boundary Layer in the Vici nity of the BladesAt subsonic speeds vortex generators increase the local flow velocity in the region adjacent to the low pressure side of the blade and decrease the local flow velocity in the region adjacent to the high pressure side of the blade. At supersonic speeds the local flow velocity at the vortex generator position is further reduced as a result of the bow shock wave that will form forward of the hlades. On the low pressure side of the
blades the increased local flow velocities induced in the vicinity of the blades will have a favourable effect on the boundary layer
in this region. The adverse pressure gradient on the high pressure side of the blade, however, may be sufficient to
cause a local separation or a rapid thickening of the boundary layer in this region. Unde~ such conditions, the strength of the trailing vortices may be appreciably reduced and the
effectiveness of the vortex generators in suppressing separation reduced . The bow shock wave at supersonic speeds will have a further, and possibly much larger, adverse effect on the
boundary layer at the blade position.
In view of the possible large adverse effects of the vortex generators on the boundary layer at the blade position it would appear to be desirable to eliminate as much as possible any effects of the vortex producing devices on the boundary
layer in their vicinity. These effects can be appreciably re-duced by using large angles of leading edge sweepback on the vortex generator blades. The effects of sweepback are illus-trat ed in the following sections by assuming that the flow about the blades may be computed using wing theories.
3.4.1 Lifting Vortex
Lifting line theory is the simplest form of wing t heory and was used to demonstrate the favourable effect of l eading e dge sweepback for vortex generator blades. The blade of the vortex generator was represented by a bound line vortex and its image in the plane of symmetry (Fig. 12). A decrease in flow velocity in the reg ion on the high pressure side of the blade is caused by the lifting line vortex.
The e ffecti veness of the vortex generator blade is dependent on the circulation, K, and the hei ght of the blade, h, so that the effect of sweepback of the lifting vortex was com-puted for constant values of h and K. The decrease in flow velocity at a p oint x
on
e
t
'
sweep angl e of the lifting vortex, A. The decrease in flow velocity induced by the lifting vortex along a line defined by
z
=
0, y=
h, is given in Figure 13 for values ofA
of 0, 60 and 84.3 degrees. As A is increased the peak velocity decreaseis decreased and the velocity g radients in the stream direction, auja x, are decreased. Hence, the adverse pressure gradient
imp ressed on the boundary layer by the line vortex may be
app reciably reduced by the use of large angles of leading edge sweep back.
The influence of Mach number was illustrated using an appl ication of the Prandtl-Glauert relationship. If the sweep angl e and semi-span of the bound vortex at a Mach number M were gi ven by A and h, then the velocity induced at a point
x0 , y
0 , z
=
0) at a Mach number M by the bound vortex was~aken to equal 1/~1-M2, the ve l ocity induced at a point ( x0,
~1-M
2 y0 , z = 0) in incompressible flow due to a bound
vortex having a sweep angle e qual to tan-1
( tanA;f~1-M
2)
and a semi-span equal to~1-M
2 h . The effect of Mach numbe r is illustrated in Figure 14 for v alues of A=
0 and 60 degrees.~he unfavourable effects of high Mach numbers are gre atly re-iuced by usi ng large angles of sweepback of the lifting line •ortex.
The magnitude of the peak velocit y decrease due to
~he lifting vortex is gi ven as a fUnction of the sweepback angle
of the lifting vortex in Figure 15 for Mach numbers of 0, 0 .866 and
0.944.
3.4.2 Bow Shock Wave
An important characteristic of the flow over a vortex ;enerator blade at supe rsonic speeds is the shock wave that =orms at or ahead of the leading e dge of the blade. It is
desirable tha t the decrease in velocity that occurs across this s h ock wave should be small. A small decrease of velocity c an be achieved by a proper choice of blade angle of attack or l eading edge swe epback. Since the blade angle of attack is determined by the requirements for vortex generator effective-ness, a useful desi gn parameter is the leading edge sweepback.
I n the ab sence of a simp le exact theory f or t he in-f luence oin-f le ading ~dge sweepb ack on t he f low over the blade of a vo r t ex g enera tor a t l a r ge angles of a tt a ck, t h e flo w over t he blade was considered to be an a logous to the f low over a wedge when the leading edge sweepb ack angle was zero, and a n al ogous to t he flo w over a cone when t he le ading edg e sweepback angle was lar ge. The flow chara cteristics for small and medium
angl e s of s weepback were assumed to lie between the flows for the above two c ases.
A crite rion chosen to illustr ate the f a vourable
effe c t s of swee pb ack was th at of determini ng the r ange of angle of att a ck of the vorte x ge ne r a t or blade a s a functi on of Mach numbe r such th at the b ow shock wa ve rema ined a tt a ched. I f the bow shoc k wave is attached it b elongs to the weak f amily of shock waves and when i t becomes detached it changes t o one
belonging to th e st rong family of waves. The veloci ty de c r e as e t hr ough the shock wave i s appreciabl y l ess if t h e s hock belongs to the we ak f ami l y than if i t belongs to the strong family s o that it is des i r abl e t o h ave the bow shock wave at t ached to the leading ed ge o f t he vortex gene r a tor blade.
For t h e c a s e of zero leading edge s weepback the b l ade angl e of att ack wa s t ake n to b e analog ous to t he s emi- angle of a we dge, a nd t he maxi mum we dge semi-angles, ~' for a~ attached s hock wave were c ompu ted. f3w is gi v en as a functi o!l o~ Mach number i n Figure 17. The allowable blade angles o~ attack f or
numbers (1.2 < M < 1.5) if the leading edge sweepback angle is zero.
For the case of large angles of leading edge sweep-back the analogous cone was taken as one whose axis was in
the flow direction and whose surface contained the leading edge of the blade . An illustration of the assumed cone is given in Figure 16. Using this analogy, the angle of attack
of the blade, a, is related to the semi-cone angle, ~C' and the leading edge sweepback angle, AL.E. by
-1
a
=
cos(
~OS ~C
)s 1n J\.E.
For ~ .E. large, sin ~.E. ~ 1 and a ~ ~C
The maximum cone angle, ~C' for an attached shock wave is given as a function of Mach number in Figure 17. The allowable cone angles and hence angles of attack for vortex generator blades having large leading edge sweepback are appreciably greater than the allowable angles of attack for zero sweepback1 particularly at low supersonic Mach numbers.
At the higher supersonic Mach numbers, the decrease in flow-velocity through the bow shock wave, even when
attached, may be large. A criterion based on the ratio of the Mach number leaving the shock to the Mach number entering the shock is shown in Figure 18 to illustrate the favourable effects of leading edge sweepback. This plot is essentially one giving wedge and cone angles as a function of Mach number for equal strength shock waves such that the Mach number
leaving the wave, M2~ is equal to 0.9 ti me s the Mach number entering the wave, M1 • The cone angles are from
4
to8
times larger than the corresponding wedge angles.3.4.3
Row of Counter-Rotating Vortex GeneratorsFor a row of counter-rotating vortex generator blades, the adverse effects of the lifting line vortex and the bow shock wave are additive in the channel formed between the high pressure sides of two adjacent blades. Thus the
adverse effects of the vortex generator blades on the boundary layer in the vicinity of the blades is likely to be mo re severe for a row of counter-rotating blades than for a row of
co-rotating blades.
A method of generating counter-rotating vortices · with an adverse effect on the boundary layer in the vicinity of the blades that is not greater than that from co-rotating blades is shown in Figure
3.
This method employs two rows ofc o- rotating blades arranged so that the blades in the second r ow produce trailing vortices of opposite sense to those pro-duced from the blades of the f i rst row. The blade positions i n the two rows are staggered with respect to the stream di rection to give the desired ratio of D/d
0 (Section
3.3) .
3. 5
Drag Due to a Vortex Generator InstallationVortex generator installations on an aircraft ge ne r all y i ncrease the aircraft drag at l i ft coefficients
below that at which boundary layer separati on occurs. In some i ns t ances the drag increment may be sufficiently large to cause an apprec i able reduction in aircraft perfor mance, and i t becomes necessary t o consider means of reducing the drag increment due to the vortex generator installation with a minimum loss of effectiveness.
It has been assumed for the purposes of analysis that t he major portion of the drag increment due to a vor t ex generator installation is that associated with the blades and t hat the drag i ncrease c an then be comput ed using wing theory. ~~e drag of the
rat or drag
f the
installation per unit of span thus becomes h
=
4q
~·
CnfAThe effectiveness of the installation per unit of span, E
0 , is proportional to
where the function f(h/o,~) is defined in Section
3.1.3.
The form of f(h/o, ~)when plotted against J.L for constant values of h/o is that given in Figure7.
For values of h/o > 2, the dependence of f(h/o,~) on the value of h/o is small. It wasshown in Section
3.3
that in gene ral for applications of vortex generators on aircraft wings where downstream effectiveness is require d that h/o must be greater than 2 owing to dissipation of the vortex. The function f(h/o, ~) then becomes a function of J.L only, say g(~). The ratio of the drag per unit span to the effectiveness per unit span for values of h/o > 2 is pro-portional toD 0 h/J.L • CD/A
Eo a CL/A • g(~)
=
The mimimum drag for a given effectiveness should be achieved , therefore, by keeping the spanwise spacing parameter, J.Lg(J.L), large, the blade height, h, small, a~d the
c
1;cD
ratio of the vortex generator blade large.3.5 .1
Spanwise SpacingThe variation of the spanwise spacing parameter
co-rotating and counter-rotating arra~gements. For co-rotating vortex generat ors the spanwise spacing should not be less than about
4
times the height or the drag for a given effectiveness will become very large. For counter-rotating vortex generators the spanwise spacing should be greater than about 2 times the~lade height.
3.5.2
Blade Lift to Drag RatioThe minimum drag for a given effectiveness should be obtained by choosing the blade geometry and incidence such that t he blade is operating at its maximum lift to drag ratio. In general , for wings of low thickness chord r atio, the maximum lift to drag ratio increases approximately proportional to the square root of the aspect ratio (Ref.
5).
At lift coefficients well above that for maximum lift to drag ratio, the lift to drag ratio is approximately proportional to the aspect ratio. Within limits, therefore, it is desirable to use a blade havinga high aspect ratio in order to reduce the drag for a given effectiveness .
The lift coefficient for maximum lift to drag rat i o is equal t o ~~eCD
0
and typical values are in the range of lift coeffi cient around 0.2. At lift coefficients above that for maximum l i ft to drag ratio, the lift to drag ratio decreasesr apidly wi th increasing lift coefficient . For a low installa-t i on drag for a given effecinstalla-tiveness, installa-therefore, installa-the blade in-c idenin-ce should not be apprein-ciably greater than that whi in-ch gives maximum lift to drag ratio.
Both of thes e requirements conflict with the require -ment for maximum effectiveness per blade discussed in
Section 3 .1. 3 . It was shown there that the effective~ess per b lade was proport ional to CL/A. The definition o~ e~ective
ness neglected the loss of momentum introduced i~~o ~~e
f
1
boundary layer due to the profile or wake drag of the vortex generator blade. If this were taken into account maximum effectiveness for a given installation would occur where the ratio of the induced drag to the profile or wake drag was
~aximum. This would occur at a lift coefficient somewhat below the maximum for the blade such that the profile drag of
~he blade would be just beginning to increase rapidly with increasing lift coefficient. Similarly, the minimum drag for a given effectiveness would occur at a lift coefficient
some-hat larger than tsome-hat for maximum lift to drag ratio.
The blade taper ratio and the blade section may be chosen to give large values of lift to drag ratio without
con-~icting with the requirement for maximum effectiveness. ?ractically, it is difficult to use other than flat plate =lades because of the small scale of the vortex generators . •r-t transonic and low supersonic Mach numbers the lift to drag
~atio for const~~t aspect ratio thin wings is maximum for a
~aper ratio of about 0.1 (Ref.
5).
At low Mach numbers,-ambe r of the blade section may be used to increase the lift oefficient at which the maximum lift to drag ratio occurs.
:~e effect of cambe r at transonic speeds is almost negligible
~or thin wings if the percent camber is not large .
A typical vortex generator configuration designed -o reduce the drag due to the installation is shown in
:~gure 2(c) and the geometric properties are given in Figure 22
:onfiguration E). The results of tests with this configura tion ere given in Section
4.
; . 5. 3
Blade HeightThe drag of geometrically similar vortex generator
-~tal lations for a given effectiveness is proportional to the :ade h e i ght, so that it is desirable to keep the blade height
as small as possible and still maintain effectiveness. If the boundary layer hei ght is accurately known it was shown in
Secti on 3.1 .2 that the ratio of blade hei ght to boundary layer height for maximum effectiveness is about 1.2. For applications
on ai rcraft wings the b oundary layer height and separation position are not normally fixed and the requirement for effec-tiveness at large distances downstream from the blade usually r equires a large value of
h/o
(Section 3.3). The minimumblade height for such an installation usually must be determined experimentally on the basis of the required downstream effective-ness. Typical blade height s are in the neighbourhood of one percent of the wing chord.
4.0 EXPERIMENTAL DATA
'
A series of flight tests on a CF-100 Mk.IVa aircraft was undert aken at t he Flight Research Section to investigate possibilities f or i mproving the buffet manoeuvre boundary of the aircraft at high sub sonic Mach numbers. Tuft studies were made in an effort to determine the probable origin of buffeting
cf the aircraft. The tuft observations showed that the buffet
was caused by a shock wave induced "bounda r~ layer separation on t he aircraft wi ng (se e Appendix
c).
Vortex generators were us ed to suppress t he separation to h i gher lift coefficients . The increase in the lift coefficient at Which buffet occurr e d for a given Mach number was taken as a measure of the effective-ness of the vorte x generators . Th e increase in drag due to t wo of t he vortex generator configurations was determined. Adescription of the t ests and the results of tests with various vortex generator configurati ons are given in this secti on.
Pe rtinent details of the CF-100 aircraft are given i n Table I and a phot ograph of the t est air craft is shown in
