Drag reduction of turbulent boundary layers by means of grooved surfaces Citation for published version (APA): Pulles, C. J. A. (1988). Drag reduction of turbulent boundary layers by means of grooved surfaces. Eindhoven: Technische Universiteit Eindhoven. https://doi.org/10.6100/IR280307 DOI: 10.6100/IR280307 Document status and date: Published: 01/01/1988 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected]providing details and we will investigate your claim. Download date: 26. Jan. 2020
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Drag reduction of turbulent boundary layers by means ofgrooved surfacesCitation for published version (APA):Pulles, C. J. A. (1988). Drag reduction of turbulent boundary layers by means of grooved surfaces. Eindhoven:Technische Universiteit Eindhoven. https://doi.org/10.6100/IR280307
DOI:10.6100/IR280307
Document status and date:Published: 01/01/1988
Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication
General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:
www.tue.nl/taverne
Take down policyIf you believe that this document breaches copyright please contact us at:
september 1987, the first "International Conference on turbulent drag
Reduction by passive Means" took pi ace in London. About half of the
presentations considered the use of microgrooves.
As fuel consumption is a major operational cost of supertankers
and surface drag is a large part of the total drag experienced by the
ship ploughing through the sea, microgrooved hulls could be of certain
importance. It remains to be established, however, whether it is possi
bIe to maintain the quality of the grooves for longer periods of time
under the adverse conditions at sea. And of course, in a world in
which the value of currency can change by 50% or more, 5% drag reduc
tion will only be a major factor determining economie success or fail
ure of an application in very special cases.
In the present study we will not pay further attent ion to sharks
and economie benefits of microgrooves. Instead we wil! approach the
problem from a different angle. Drag reduction by means of micro
grooves is not only interesting because of possible technica I applica
tions , but i t provides also an opportuni ty to refine and test the
theories of anormal smooth wall boundary layer as weIl. We will try
to illuminate the mechanism responsible for drag reduction. By doing
this we will have scrutinized simultaneously the mechanisms for
momentum transfer in a no rma I boundary layer. We will do this mainly
wi th experimental means as opposed to theoretical and mathematical
approaches. This has two reasons . Firstly, much experimental data
needed to conceive a coherent intui tive picture of the influence of
those grooves on the flow are still lacking and secondly a theoretical
approach seems less prom,l.sing, because no theory exists today which
can predict drag in a normal turbulent boundary layer with an accuracy
of a few per cent without the help of empirically determined
constants.
It is probably wise to regard this thesis as a reconnaissance
study in which the feasibility of studying micro grooved induced drag
reduction at 10w Reynolds numbers is demonstrated. During the last
four years the instrUments needed for the experiments (the water chan
nel, the drag balance, the laser-doppler anemometer (LDA) and the
computerized visualisation) were developed and checked out. These are
no scientific resul ts on their own but i t was very necessary and i t
took its time to do it. Further resarch wil I prof it from these funda
mental achievements.
...
§ 1.2 Short description of smoöth wall turbulent boundary layer.
From the existing I iterature about a turbulent boundary layer.
the theories and the experimental data the following description of a
turbulent boundary layer can be distilled [see e.g. Hinze 1975].
Generally a turbulent boundary layer can be separated into four
distinctly different parts. They can be characterized by the proper
ties of the mean velocity profile or by the observed flow structures.
For the properties of the mean velocity profile some theoretical jus
tification can be given but theories describing and predicting the
flow structure are very incomplete and the subject of much contempora
ry resarch. The distinctive regions are:
I y + < 5 The viscous sublayer. Very close to the wall exists a
reg ion in which the viscous forces dominate the momentum transport.
The vertical velocity component is strongly damped and the flow is
near ly two dimensional. In this region the mean veloei ty is a
linear function of the distance from the surface.
11 5 < y+ < 50. The buffer layer. Somewhat higher from the wall
the momentum transport by vlscous forces is gradually replaced by
transport by convective means. Very long and narrow low speed
reglons are visible and in these reglons is the vertical velocity
component positive (fluid flows away from the wall). They are
commonly called "low speed streaks". Further away from the wal! the
.b
Flgure 1.3 Model of near wall turbulent boundary layer from Blackwelder [1978]. a: Counter-rotating streamwise vortices wlth the resul ting low speed streak; b: Localized shearlayer instability between an incoming sweep and low speed streak.
5
shape of these regions becomes more irregular. On top of these low
speed streaks vortices are generated. The ends of the vortices are
heavily sheared and appear as longitudinal vortices along the
streaks. These structures are cal led horse-shoe vortices. The low
speed streak sometimes ends abruptly and fluid is then replaced by
faster moving fluid from higher up in the boundary layer. At y+ of
about 50 the turbulent momentum transport reaches a rather broad
maximum. In figure 1.3 a somewhat different view is pictured by
Blackwelder [1978]. + -
III y > 50. U < .8 Uro The logarithmic region. From that height to
the height where the mean flow veloei ty ij is about . B times the
free stream veloei ty the transport slowly decreases again. Flow
structures in this region are layers of vortices inclined at 45
degrees. This reg ion is characterized by a logarithmic dependenee
of the mean velocity on the height. and is therefore called the
logarithmic region. It is generally assumed that up to this height
the wall shear stress is the main parameter which controls the flow
and consequently all physical quantities can be made dimensionless
with the shear stress and the properties of the flow medium.
IV .8 U < ij. The outer layer. Above the logarithmic region the ro
outer layer is situated. Here the flow is determined by the
pressure gradient and the upstream hlstory of the boundary layer.
The flow is intermittently turbulent and laminar. Physical
quanti ties tend to scale on boundary layer thickness. I t can be
shown from dimensional analysis that the existence of the viscous
sublayer and the outer layer imply the existence of a reg ion where
the mean velocity follows a logarithmic curve. The precise shape of
the velocity profile depends on the pressure gradient. but the
velocity tends smoothly and asymptotically to the free stream
velocity.
The layers. however. do not exist independently. Extreme dP pressure gradients cen cause relaminarisation Cdx < 0) or separation
C: ) 0). thus affecting the boundary layer as a whole but under
normal conditions the individual layer only provides the boundary
conditions for its neighbours.
It is only fair to note that the description of the turbulent
6
boundary layer in tenns of coherent structures is subject to much
debate. As yet no complete consensus has been reached. Al though the
structures here described are detected by many observers, discussion
centers around their relevance to momentum transport or their
relevance as building blocks of turbulence. As long as no firm picture
of a smooth wall turbulent boundary layer emerges, backed by a more or
less solid mathematical theory the interpretation of changes in the
boundary layer above microgrooves can only be tentative.
§ 1.3 Structure of this thesis.
The basic idea used in this thesis about the mechanism behind
the microgrooved drag reduction is: the grooves influence in some way
the convers ion of viscous to turbulent momentum transport thus
hindering the momentum transfer as a whoie. This affects particularly
the viscous sublayer and the buffer layer. It is expected but yet to
be proven. tha t the logar i thrnic layer merely adjusts itself to the
lower momentum flux passed by the layer below. The outer layer should
remain entirely unaffected by the microgrooves and alternatively.
except under very extreme situations, the outer layer eannot affect
the drag reduction mechanism of the microgrooves.
The details of the dragreducing meehanisms are unclear but
microgroove drag reduction itself is confirmed by several experiments
[Saviii & Rhyrning 1987] . From the optimal size of the grooves. experi
mental studies (particularly flow visualisation. for instance Offen
and Kline [1973]). and theoretical considerations we can conclude that
the behaviour of the total turbulent layer is detennined to a large
extent by the viseous sublayer and the bufferlayer. The theories could
be developed along several ideas. which are discussed in chapter 2.
In our experiments we will thus pay close attention to the flow
layer very close to the wall. In the present study we will show that
the turbulent boundary layer maintains largely its structure above a
drag reducing grooved wal!. For instance. the logari thrnic veloei ty
profile is still present and near the wall low speed streaks are still
diseernible. When looked at in more detail. however. some small
quantitative changes can be found. The aim of the present study is to
highlight the differenees and to compare them against the incomplete
7
ideas offered about the subject of mlcrogroove drag reduction. .
The general outline of the experimental equipment is discussed
in chapter 3. The measurementsthemselves can he roughly divided into
three categories:
I Point measurements (chapter 4), which give accurate information
on the physical quantities in the flow at a single point.
II Visualisation studies (chapter 5), which provide less accurate
information over a more extended area of the flow .
111 Direct drag measurements (chapter 6) which give the yardstick
for scaling the different boundary layers.
Ihis subdivision cannot be made too strict because sometimes it
is just the combination of the information provided by the different
methods which is particularly valuable. If this occurs we will try to
point out this explicitly.
Ihe implications of the experimental results will be discussed
in"chapter 7.
B
Chapter 2 Summary ofexisting ideas, theories and experiments.
§ 2.1 Survey of different means of obtaining dragreduction.
There are many ways in which turbulence can he influenced and
most modifications have in principle the potential to achieve drag
reduction . We can split these attempts in two categories: the use of
active or passive devices. Active devices are those which use a sensor
to detect a particular event (eg separation or a turbulent burst) and
trigger an actuator to act upon the flow. This feedback is absent in
passive devices.
Due to the large number of parameters and absence of useful
theories, active devices (moving needles, loudspeakers) are only
occasionally considered in experiments. See for instance Papathanasiou
& Nagel [1986], who discuss a method depicted in figure 2.1. They
measured the instantaneous flow velocity upstream of a large eddy .
breakup device (LEBU for short, is known to produce some drag
reduction as will be described later). If the sensor detects a large
eddy it activates an acoustic driver. This influences the large eddy
cancellation of the LEBU, according to the authors. They obtained an
addi tional drag reduction of 7 to 15%.
Most ideas about drag reduction are based upon the assumption
that there exist regularities (for instance coherent structures) in a
a
"'/ - ....... , ,/ _\, .5.~ __ _ _ /' J ,' / n,/.-o .. ,- ·1 I ~' .J LEO" ------1 , -- o.e1' HOT FILM ACOU ST 1 C~ _ _
SENSOR WAVES _
b 8
E E
• LEBU conllll"r'1101I l<:oll.lIe.llr ,u;lI.d
• LEBU c:o"II"", •• lon no . ~ c:It.llon
• ~ 0 ~. 100,OOO/m
3 x' m4 Flgure 2.1 The effect of boundary layer control by active means [Papathanasiou 1986]. a: Schematic representation of the acoustic excitation mechanism; b: momentum thickness 9 versus axial distance x for various flow configurations.
9
, turbulent boundary layer which can be modified to advantage.
Bushnell [1984] reviews a number of drag reduction methods with
passive means. Apart from drag ' reduction by means of microgrooves a
number of other methods are mentioned by him. Passive devices include
polymer solutions in liquids (50% drag reduction [Virk 1971]. see
figure 2.2). injecting micro air bubbles in wall layers [Madavan ea
1985] (also only applicable to liquids. see figure 2.3). the classical
method of delaying the transition to turbulence by blowing or applying
a favourable pressure gradient.
60 '
50
20
Viscous 10 sublaycr
'-101 10' 10'
Flgure 2.2 The effect of polymeric drag reduction [Virk 1971].
Flgure 2.6 Resistance formula of sand-roughened plate; local skin friction coefficient. A: experiment with balance in waterchannel (§6.6) B: experiment with balance in windtunnel (§6.2).
13
· the smooth wall behaviour and the behaviour at high velocity .
Consequently complex behaviour can be expected. Even anormal sand
roughened plate shows a dip in the value of the skin friction
coeffient in this region. In the case of the microgrooved walls this
dip, apparently, is deep enough to cause some drag reduction.
It is for this reason that classical theories and empirical
relations can not be applied without some reservations. Apart from the
empirical fact that turbulence can be readily influenced no indication
of a potential drag reducing surface could be derived from them.
The classical, statistical theory of turbulent flow does not
provide much indication for the possibility of drag reduction either.
Central to the statistical theory of turbulence is the concept of
mixing length ~ as introduced by Prandtl [1925] and in a somewhat
different context by von Karman [1931]. In the boundary layer we can
consider the mixing length as the distance (height) over which the
turbulent momentum exchange takes place. It is strongly dependent on
the distance from the wall. It is clear that a decrease of mixing
length will lead to a lower turbulent momentum transport and thus to a
lower drag. A phenomenological definition of mixing length is:
~ ~
I ~ ~ I and an accepted fonnula in boundary layer modelling is [Van Driest
1956]:
* ~ ~ K Y ( 1 _ e A v ) A 26, K 0.41
rhe exponential term describes the diminished role of turbulent
exchange near the wall; the measurement of the mixing length above the
grooved wall will enable us to think more clearly about the behaviour
of the stress transporting turbulent structures near the wall. A word
of caution, however is necessary.
14
The Van Driest formu!a. combined 'with the equa!!y accepted
Spa!ding formula for the velocity profile yields:
+ 2 + 3 + 4 ~-~-~)
2 6 24
This is in conflict with the assumption of constant stress in the
layer near the wall:
au -p ( v 8y - uv ) constant.
As indicated in the formuia the total stress consists of a viscous
part Tl and a turbulent part Tt' The total shear stress derived from
the Spalding profile and the Van Driest mixing length predict a
maximum stress that is 20% higher than the wall valueat some distance
away from the wall. See figure 2.7. The assumption of constant stress
as ~ ..... ...
1.2
1.1
1
O.G
0.8
0.7
0.8
0.6
0 .•
0.3
0.2
0.1
0 0 20 60 80 100 120 180
y+
Flgure 2.7 Tota! (D) and viscous (+) shear stress versus height according empirica! formulas of Spalding. Van Driest and Prandtl. Va!ue of the constants (see text): K = .41. B = 5.5. A = 26.
15
180
· is relatively weIl founded theoretically [Townsend 1976] and velocity
profiles are accurately rneasured with relative ease. Although the
necessity to differentiate the velocity profile can add sorne
inaccuracy to the results,this is considered insufficient to explain
the discrepancy between the theory and the Van Driest empirical
formula. The lesson is that this kind of rough modelling is inadequate
to explain the working of the microgrooves which change the wall shear
stress by only about 5 percent.
The currently most popular model to calculate turbulent flow is
the k-é model [Patankar 1980]. This is not applicable to our problem
because it is mainly an extension of the mixing length model. Moreover
in the standard formulation the flow in the viscous sublayer is not
calculated but modelled with a simple empirical relation of the type
described above.
Perhaps i t is possible to borrow some ideas from other and
earl ier discovered dragreducing methods, for example polymer addition.
The last method has been studied for a relatively long time and leads
to drag reduction up to 50 percent. Virk [1971] proposes the idea that
the elastic polymer molecules extract kinetic turbulent energy from
the flow and thus affect turbulent mixing. He showed that the velocity
profiles tend to a l1miting profile in the case of maximum shear
stress reduction: a profile characterized by a logarithmic region with
different constants, compared with the classical smooth wall profile.
In contrast wi th the normalrough wal!, not only the offset, but also
the slope of the profile is different (figure 2.2). This indicates a
turbulent energy transport to the smaller scales different from a
normal fluid. If this is true then polymer drag reduction wil 1 be
essentially different from micro groove drag reduction. This is also
substantiated by the applicability of the Clauser chart method in the
case of microgroove drag reduction as was mentioned by Sawyer and
Winter [1987] . This rnethod is based on the assumption of the universa 1
nature of the Von Karman constant which prescribes the slope of the
velocity profi-le in the logarithmlc region. There are also some
analogies between the resul ts of polymer addl tion and the use of
microgrooves. Both seem to have the same effect on the turbulent
intenslty very near thewall. In the case of polymer addition thls Is
attributed to the assumption that the smalles,t lengthscale eddies
16
disappear near the wall thus effectively thickening the viscous
sublayer. This constitutes actually a second idea about the mechanism
of polymer drag reduction.
A test of this idea could he the measurement of accurate spectra
in the viscous sublayer: the higher frequencies should be attenuated.
A second, more indirect way of testing this hypothesis is measuring
the bursting rate near the wal I. A thicker, more stabie viscous
sublayer leads to a lower bursting rate. Ihe lat ter effect has indeed
been observed, both in the case of polymerie drag reduction and micro
groove induced drag reduction.
In this context the surface renewal model of a turbulent
boundary layer should be mentioned [Einstein & L1 1956]. Ihe basic
idea of this model is that the wall layer is periodically replaced by
fluid from the buffer region. This fluid will be slowed down by
viscous forces and forms a new wall layer. Ihis process is described
in the model by a simplified x-momentum equation:
Ut(x, t) ; u Uyy(x, t)
The boundary and initial conditions are:
U(O, t) = 0
U(y, 0) ; Uo ; constant
The solution of this equation is described using the errorfunction:
U( y, t); Uo erf [-y--] J;;;
Z
erf(Z) ~
J e-z2dz
-()Q
The mean wall shear stress and several other quanti ties ' can be
calculated by averaging over one period. One easily obtains the result
that the mean wall shear stress is proportional to the square root of
the time between two renewals (the so called "bursts"), so a 5%
decrease in drag is associated with a 10% decrease in burst frequency,
according to this model.
17
Bechert ea [1986] introduced the term protrusion height of the
riblets. rhey show that the protrusion height by given riblet spacing
is limited. rhe most effective riblets are those with the highest
protrusion helght, because they maximlze the lnfluence on the boundary
layer. rhe optimal spacing of the riblet is derived by the following
argument. lang ea [1984] calculated that the most persistent
perturbation mode in a turbulent boundary layer consists of
longi tudinal counterrotating vortices spaced 90 vlscous units
pairwise. rhe region where the flow has a vertical velocity component
coincides with the position of the observed low speed streaks .
Apparently obstacles interactlng wl th this mode must be spaeed much
less than 45 viscous units, because then every vortex is blocked by
one rib . Bechert also proposes a three dimensional fin instead of an
inf ini te groove ",hich has a much higher protrusion height and must
consequently give a larger .drag reduction.
The calculation of the penetration depth for a longi tudinal
grooveproceeds as follows. For a first approximation we will assurne
the flow independent of the streamwise coordinate x, incompressible,
stationary and with a constant pressure gradient ~. rhe Navier-Stokes
equations reduce to:
v + W 0 Y z
p VU +WU
x (U + Uzz) - -- + v
Y z P yy P
VV +WV - --1-+v (V + Vzz) Y z P yy
P VW +ww z v (W + W ) - --+
Y z P yy zz
Before we proceed, we will normalize the variables on the
* * v P U + u + u p+ = P
x andu + viscous units Y = -v- y, z = -- z, tG v x p * p u u
For convenience we drop the superscripts.
We will not allow secondary flow and so we assurne : V 0 and W
O. rhe equations reduce now to the very simple form :
18
u + u P yy zz p
rhe boundary conditions are (see flgure 2.8):
Along curve AD, y = h(z): U(h(z), z) = 0
Along AB:
Along CD:
and along BC:
Uz(y, 0) = 0
Uz(y, ZJ = 0
U(O, z) = constant = Uo
rhe function h(z) describes the roughness. To simplify the
discussion we can separate two components of h:
A
h(z) = h + hmaoh(z)
h is the ave rage height of the domain, hma is the maximum height of A
the roughness and h(z) is the function describing the shape of the A
roughness ( f h dz = 0, maximum of h is 1). The total height htt of
the roughness is of course somewhat larger than hma , as is shown in
figure 2.8.
In order to assess the influence of the grooves, we can compute
the mass flux Q or the momentum flux M through the surface ABCD and
compare it with the va lues (~u and Muu respectively) in the case of a
smooth wal!. The solution for the velocity above a smooth wal! is au
independent of z. Due to the definition of u*, uu (h) must be equal ay
Figure 2.8 Geometry of the problem discussed in text.
19
' to 1. And of course the no slip condition u (h) uu
satisfied. This leads to the solution:
u (y) = (h - y) + 1 P (h _ y)2 uu 2 p
We note that Uo cannot be choosen freely, but must satisfy:
- 1 -2 Ua = Uuu(O) = h'+ 2 Pp h
o must be
We are now able to derive the expressions for the mass and momentum
flux:
M uu
h o = z f U (y)dy uu uu
o h
Z h2 ( 1 + 1 P h) 2 6 p
f 2 -a 1 1 - 1 -?-2 = Z U (y)dy = Z h (3 + 4 Px h + 20 r; h )
o These expressions can be used to normal1ze the resul ts for grooved
wal Is. An ave rage normalized shear stress coefficient Cf can also be
calculated. With the help of Gauss' theorem we can replace the
necessary integral along AD, by the more easily evaluated integral
along Be. This leads to the formula:
Z f aU(O,
o ay z) dz + P h
p
It is also possible to calculate an offset in height needed to
recover the smooth wall value of the shear stress. The groove height
minus this offset is the protrusion height. With some thought one can
derive the relation:
h = h - iï (1 __ 1_ ) p ma Cf
Bechert ea used the method of conformal mapping to obtain exact
solutions. The net result of this procedure is equivalent to moving
the upper boundary to infinity (h -) co) and matching the upper
boundary condition to the smooth wall solution U(y) = y. The method of
conformal mapping can only be appl1ed when the pressure gradient is
20
zero. Ooly with special groove geometries one can derive closed
formula for the solution of U and the protrusion height. But the
resul ts indicate that the protrusion height divided by the width of
the grooves tends to a limiting value even if the height of the
grooves is increased (see figure 2.9 for a typical result). Bechert's
resoning does not provide a direct estimate of the amount of drag
reductionwhich can be obtained.
Some other hypothetical mechanisms center around the influence
of the grooves on the observed coherent structures. A possible
mechanism is the resonance with low speed streaks. It is assumed that
coherent structures carry a major part of the momentum transport from
the wall to the flow. A kind of wall attached structure is the low
* * speed streak. Ihis is a long (1000 y ), narrow (lOy ) area where the
veloci ty component in the direction of the free stream is markedly
lower than its ave rage value. These streaks are spaced at 100 viscous
units. As a working hypothesis one could assume that grooves hinder
their formation or decrease their intens i ty if formed. Iwo problems
occur immediately:
I Ihe best dragreducing walls have grooves spaced 20 viscous
uni ts, which seems too narrow for direct interaction wi th those
streaks.
II Even if one sees some influence of the grooves on the streaks,
one still has to prove that the modified streak transports less
momentum.
Apart from performing a visualisation experiment which visualizes all
types of structures, a measurement of the mixing length would yield
some insight whether a turbulent structure whichs transports momentum
near the wall, is affected. A test of the influence of the grooves on
the turbulent structures would be the measurement of the spanwise
correlation of the velocity fluctuations. As normally all near wall
* lengthscales scale on viscous units (v/u ), drag reduction without
change in structures would lead to larger lengthscale and thus to a
broader correlation curve in absolute units. If, loosely speaking, the
grooves somehow cut the structures in pieces thls would lead to a
narrower correlation curve.
And lastly one could suggest that the grooves are able to
suppress the meandering of the low speed steaks.The streaks meander
21
L h rI
r h L
...;:. r
-Sj -
:). 'I.. J< Y-:. :.x 'I.. J< hp
Î { \ { \ { \ t u-veloctly and nuid .hear force distribution of the vi.eaus flo. on a blad. rtblet. Burf.ce. Blad. hehrht h/B = 0.25.
rf~ Ff ~p;tP(rf~ Blade riblet, helght hl. = 0.5.
r-s~
Figure 2.9 Protrusion height h versus element height h. with . p
constant separation s [Bechert 1986].
22
slowly over the smooth plate. Suppression of this meandering could
reduce the drag (in this case the form drag of the low speed streak to
the rest of the flow). In the extreme case this could be observed as
an attachment of the streak to the grooves. But the two objections of
the former point are still applicable.
§ 2.3 Experimental results from literature concerning drag reduction
with microgrooves.
In the last few years several experiments have been performed
which give information about the nature of the drag reduction attained
with microgrooves.
Reif and Dinkelacker [1982] drew attention to the fact that
sharks and several other fish had smaillongitudinal riblets on their
skin (see figure 2.10).
Liu ea [1966] investigated the effects of small longitudinal
fins on turbulent bursts in the boundary layer. They found a clear
reduction of turbulent burst frequency (figure 2.11) even with a very
wide spacing between the fins (s+ = 100).
Walsh ea [1978] were the first to pay attent ion to microgrooves
in a direct application to drag reduction. They used a dragbalance to
measure the drag directly in a windtunnel at a Reynoldsnumber of about 6 10 . They tested a large number of different grooved walls (see figure
2.12. the best walis). They found a maximum of 7% reduction in drag.
on a grooved plate with a dimensionless groove height h+ of 13 and a
dimensionless width s+of 18. They also observed that the sharpness of
the groove peaks is of importance . Their data imply that the
dimensionless width of the grooves is the proper scaling parameter.
Nitschke [1984] studied the flow in pipes with grooved walis.
The drag was indicated by the pressure drop in a fully developed
turbulent pipe flow. The conclusions were only partly in line with
those of Walsh. She found a maximum drag reduction of about 4% with + + grooves of a height h of 12 and a width s = 10 (figure 2.13).
. + + Reduction occurred in the range of 6 < s < 20. A different groove (s
23
a b c Flgure 2.10 Riblets on shark skin [Reif 1982]. a: riblets on an embryo shark .37 m long. 3Ox. b: riblet profiles on an adult blue shark 2.34 m long, 13Ox, c: riblet profiles on an adult shark, 2.3 m long, looking from tail to head, 64x.
Flgure 2.11 Longitudinal fins and burst rate [Liu ea 1966]. fs: burst rate above smooth plate. 0: h = 6."1 DIR, A: h = 9.5 DIR.
0: h = 15.9 mmo
2"1
1.2 ~QQlJ. t!l.!!!!!!l. llmi!l!. 1!.~.lt1~:h o UR 0.41 O. dJ II 0 o 1).\\ Q29 0.47 9.l 0 o 7'<\ Q08 " IB 6.1 00
1.1 o 0
§l,j9 00 0
0 ...: 60 ~ 1.0 -0
.9 s+
Figure 2.12 Drag measurements of Walsh and Lindemann [1984].
+ = 15 , h = 4) gave a maximum reduction of 3% over a larger range,
reduction occurring for 1 < s + < 30. Her data suggest that the
phenomenon is mainly determined by the distance between the grooves,
in confirmation with Walsh ea.
30
riblet tube Rl05
~ • À· AnbohNng
.E • e-AnbohlU'lg
~ 6W.~ ~20 ~
.. Q30S.R.-ClZ.
-6
4 6 8 10 15 202530405060 s+
Figure 2.13 Pressure drop measurements of Nitschke [1984], À is
dimensionless pressure drop: À = ~ . D / (~ P U2 ).
25
1.15
1.10
81.05 (,) "-;..1.00 (,)
.95
c c c
c c our data C1:J 0\ ·T·_·--ClQ... ·~' - ,-
~ Walsh '
.'~~ .900!:------=2'="0----,.&'0,...-----='60 s+
Flgure 2.1~ Drag measurement of Bechert ea [1986].
Despi te the large diff icul ties of machining the grooves and
making accurate drag measurements drag reduction on grooved surface
has been lndependently measured by several other experlments. See for
example figure 2.14, which shows measurements of Bechert ea, ldentical
to those of Walsh ea.
Gallagher and Thomas [1986] measured the drag in a water channel , 5
at Rex = 6'10 and found a reduction of about 2% . They made some hot
film probe measurements above that drag reducing surface and showed a
decreasing burst rate (figure 2 . 15) and a different spanwise
correlation function of the main velocity component. They also
performed some vlsuallsation experiments and showed that dye lnjected
in the valleys between the grooves remalned there for a remarkable
long time.
10-r----------------------------,
lÖO,5
6 Flat Plat. Q O,ooved Pla.a-P •• k a ••• IIIM
88 8 .. o g A 4
o .. o 0 ~ b-
o ~ .6. b. .6-
00 ..
00
0.. 1. 1 1.4 1.1 2.0 IC - Thr •• hold MulUpU.r
2.3
o.aor---.-:_--..... -1 ._-
0.'8 A A
Flgure 2.15 Measurements of Gallagher and Thomas [19B~]. A flat plate, 0 grooved plate. a: burst frequency, b: spanwlse cross correlations with peaks as zero helght, c: spanwise cross correlations with valleys as zero height .
26
Sawyer and Winter [1987] performed a set of careful windtunnel
measurements with a dragbalance and hot wire probe. They confirmed the
results of Walsh ea in details. The changes in thelogarithmic region
of the velocity profiles due to the different surfaces confirmed their
balance measurements.
The results of the experiments mentioned above are tabulated in
table 2.1 with some addi tional information for easy comparison. The
differences in maximum drag reduction and optimum size of grooves can
be attributed to the difficul ty in performing the measurements. Many
factors can influence the outcome of the measurements (accuracy of
calibration, slight deviations from zero pressure gradient, the
qua 1 i ty of the surfaces etc). Usually there exists no easy way to
estimate the amount of correction needed.
Tabla 2.1 Drag reduction by microgrooves reported in literature.
Hooshmand ea [1983] present some measurements of the ave rage
streamwise velocity component in and directly above the grooves (see
figure 2.16). They also noted an almost complete absence of velocity
fluctuations in the grooves, thus validating the assumption of laminar
flow used in Bechert's calculation of the flow near the grooves.
Bechert [1987] machined the three dimensional fins proposed by
him and tested a surface covered with the fins on a dragbalance. He
obtained a maximum drag reduction of 6% . Despite the larger protrusion
height of this configuration it gives no more reduction than a wall
covered with the correct simple longitudinal grooves.
The results of a testflight were presented by McLean ea [1987J.
They covered a part of an airplane wing with convnercially available
riblet film. They measured a 6% decrease in boundary layer thickness
at the end of the wing, compared with an untreated part of the wing.
This is almost equal and surprisingly near to the reduction found in
27
• • •• • • • • • y+=13
-I~
Figure 2.16 Mean veloei ty proflles above grooves [Hooshmand ea 1983]. Variation of the mean veloeity with spanwise loeation relative to the riblet surfaee at three elevations above the surfaee.
laboratory experiments.
The general eonelusion Is that drag reduetion by means of
microgrooves has been found. The maximum reduction is about 7%. This
can be obtained with carefully made triangular grooves. Many authors
comment on the experimental difficul ties encountered in the
measurements.
The eonnection with theoretical explanations is only very
tentatively made due to the complexity of both experiments and
theories concerning turbulence. In particular no clear picture emerges
of the influence of the grooves on the structures in the boundary
layer as they are observed· above a smooth plate. No estimate of the
maximum amount of possible drag reduction by means of microgrooves is
given.
28
Chapter 3 Experimental set-up.
§ 3.1 Waterchannel.
Most of the data presented in this thesis were obtained from
experiments in a water channel available in the Laboratory for Fluid
Dynamics and Heat Transfer at Eindhoven Universi ty of Techno 1 ogy .
Because of the relatively large turbulent lengthscales and low
frequencies in a low speed water channel, detailed studies of the
turbulent flow near the wall are possible by using laser doppler
anemometry and flow visualisation.
The main dimensions of the water channel are presented in figure
3.1. The measurement section is .3 m wi4e, .3 m high and 7 m long. A
simplified scheme of the water channel is presented in figure 3.2.
Considerable care was taken to have a lew turbulent mean flow and 'a
uniform velocity profile at the entrance. To obtain this the original
contraction was improved and rebuilt. The lateral cross section of the
velocity profile is shown in figure 3.3. Data on the turbulent
intensity in the free stream are presented in figure 3.4. It shows
that the turbulent intensity at the ent rance of the measurement
sectlon is .6%. The increase in turbulent intensity below .1 mis is
partly due to an instrumental error, the increase at veloeities higher
than .3 mis is caused by cavitation at same abrupt edges in the return
pipes. Presumably due to interaction between the boundary layers and
the free stream, the turbulent intensity increases downstream to a
value of 1.5% at the lower speed and to .8% at a speed of .3 mis.
The free stream speed can he adjusted from almost zero to .4
mis. The highest Reynolds numbers are obtained at the end of the 7 m
long measurement section: Rex = 2'106 and Ree ~ 3000
All measurements are performed on a flat plate mounted as a
false floor at ca 160 rmn below the water surface. The part of the
plate upstream of theroughness elements (described in §3.3) consists
of very smooth glass surfaces of 2 m long and .3 m wide. The leading
edge is . sharpened to provide a start of the· boundary layer without
separation effects. At .7 m downstream of the edge a tripping wire of
3 x 3 1IIIl2 square cross section is placed on the plate and the
29
5.6 .1
tripping wlre tree sLirtace
I~I plate 1.16 /' o==~----~~--~I~·12~---
1-------Flgure 3.1 Waterchannel dimensions and deflnition of coordinate system. a: top view. b: side view. Dimensions in m.
OEF G
- J p . K
t H
-L
o A
Flgure 3.2 Waterchannel and circuit. A: Pump with motor (5.5 kW). B: Pressure tank (300 1). C: Diffusor plate. D: Filter to equilize velocity profile. E: Rectifier .15m long. cross section of holes is 20 mmo F: Grid (3 mm). G: Grid (1.5 mm). H: Contraction 4:1. I: Measurement section 7m long .. 3 m wide •. 3 m high. waterheight about .26 m. J: Tripping wire 0 3 mm x 3°mm. K: Diffusor. L: Return piping. M:Cool1ng. heat exchanger. N: Pneumatically operated levers. used to regulate pressure gradient. 0: Rotation point of channel. P: Testplate .. 16 m below free surface.
30
1 t -2 o 10 -1
5
E
~ 0~---=::~~~-2~==~~::~~~-J
-5
Flgure 3.3 Cross section of ent rance veloçity profile. Numbers are devlation from reference velocity in percent .
. 021-o
o
.01 I- o
o
I
o .1
o
o
00 0 00000 0 ~oo 00
I I
.2 Uw mIs
.3
Flgure3.4 Turbulent intensity in free stream at entrance.
31
.4
6
u-o 5 o o
4
1 2
---__ b ---------a
3 4 5
x .m
Flgure 3.5 Calculation of boundary layer development in the waterchannel. a: Channel infinitely high and infinitely wide; b: Channel .3 m wide and .16 m high . Starting values at x = 1m: Uoo= 200 mm/s. e = 0.8 mmo H = 1.55.
sidewalls for a weIl deflned transition of laminar to turbulent
boundary flow.
No correction was made for the pressure gradient which occurs
because of the .growing displacement thickness of the boundary layers ;
With an extension of the method of Head [Bradshaw & Cebeci 1977] the
development of the boundary layer has been calculated (see appendix
A). In figure 3.5 the development of the boundary layer in a channel
with a cross section of .3 x .16 m is compared with its development in
a channel of infinite height and width. A typlcal lncrease of 8% in
friction coefficlent is the consequence of the pressure gradient. The
method also provides a value for the pressure gradient. A typical
value is 1.8 Pa/m at x = 3.6 m with local maln speed of .2 m/s
(calculation started ' from x = 1 m. with starting values H = 1.55. Um
175 mm/s. e = .8 mm). This leads to a pressure gradient parameter P
of:
p . p
v dP 1 pdx lE3
u .0021
32
p
Measurements with the LDA at this Positibn indicated a pressure
gradient of 1.8 ± .2 Palm. Although not zero Ithls is still a low value
and as we are interested in near wall pheno~na whlch are relatively
insensitive to pressure gradient. correctivEi actions were considered
not necessary.
For completeness the numerical values of some calculated
quantities at this position are tabulated in table 3.1. The calculated
friction coefficient is also compared with the value obtained from the
standard formulas. given by Schlichting:
Tabla 3.1 Calculated and measured boundar\Y layer development.
Starting at x = 1 m. %dey Cf(x) is defined i:Jy 100 * [ Cf~~) - 1]
%dey Cf (9) is similarly defined. The measured Cf value is from
drag balance measurements .
Channel calc (I) calc . 16 1x .3 m2 measured
U (1 m) 200 nrnIs 176 nun/s (I)
9( 1m) 0.75 mm 2.1 mm
H( 1m) 1.55 1.45
U(I)(3.6 m) 200 nun/s 200 nun/s 200 nun/s
9(3.6 m) 6.45 mm 6 . 19 mm 6.2 mm I
H(3.6 m) 1.44 . I
1.10 1.39
P (3.6 m) 0 0.90207 0.0021 P
Cf C3.6m) 3.84 10-3 4' 14 10-3 4.5 10-3
%dey CfCx) -3.5 3.6 12.8
%dey Cf (9) -8 . 9 -3 . 2 5.6
33
§ 3.2 Measurement system.
The measurements in a water channel can take a long time. due to
the large timescales involved. Iypical values of v and u* are 10-6
m2 /s and .01 rn/s respectively. Ihis leads to a timescale of .01 sec.
In a windtunnel typical values of v and u* are 15.10-6 m2 /s and .5 rn/s
respectively. which leads to a t * of 60 JlS. Roughly two orders of
magnitude smaller! Measuring a velocity profile with reasonable
accuracy. for instance. takes at least 5 hours in the water channel
(10 minutes averaging time for every of the 30 points). while in the
windtunnel i t could be done in 2 minutes. Ihis difference in time
scales makes the use of automatic datalogging equipment almost
mandat~ry. In the present operational system only an occasional
inspection during the 5 hours is necessary for this kind of
measurement.
Ihe measurement system is built around a PDP 11-23 minicomputer.
with 256 Kbyte memory. two dual density S" diskdrives (type RX02). a
VTI25 graphics terminal and a 20 Mb Winches ter diskdrive. Ihe
operating system used is RIll-VS, the standard system in use for
PDP-11 computers.
Although a Fortran and a C compiler is available. most programs
are written in PEP, an Algol-like language. Because PEP is normally
used as an interpreter, program development is very fast. For faster
execution a compiler can he used and the fastest execution is obtained
by linking handwritten assembly subroutines with the interpreter. For
most applications the interpreter is fast enough, only the sampling
programs have been written in assembly language.
In figure 3.6 aschematic description of the complete
measurement system is given. We will nowmake a few cornments on the
different subsystems.
Ihe minipropellor is an instrument to measure waterveloei ty
developed by the Delft Hydraulics Laboratory. It is used mainly to
moni tor the free stream, downstream of the LDA and visualisation·
experiment. lts measurement area is about 4 cm2 •
rhe temperature meter measures the watertemperature of the
channel. Accuracy is .1 °c, and stabi.1ity better than .01 °C. lts
reading is used to regulate the valve of the cooling spiral.
34
The LDA system is decribed in more detail in Kern [1984]. We I
point out some important details. The rotatin~ grating (purchased from
TPD, Delft) is needed to provide a preshift lfreqUency of 810 kHz in
the laserbeams of the LDA. It consists of la radial and concentric
grating. These produce nine laserbeams of whith three are used for the
measurement of two velocity components in the channel in the reference
beam mode. Two other beams are used to measure the introduced
preshift. The mixing circuit is used to subtqact the frequency of the
signal from the reference diode from the freduency of the signal from
photodiodes 1 and 2. In a second set of mixers a crystal stabilized
frequency of 217 kHz is added to the signals. The frequencies are
converted to slowly varying oe signal by Disa type 55N21 frequency
trackers. Only the range 33-330 kHz is used. !Output filt.ers limit the
response time of the . trackers equivalent to ~ 60 Hz, first order, low
pass filter . Measured spectra show that the 'amount of high frequency
information lost is negligible up to the maximum flow speed used ( . 3
mis) .
The displacement system allows a vertical translation of the LOA
over a distance of 120 DUn,
makes possible the automatic
The centrifugal pump
elecironically stabilised ac
with a resolutif' n of a few microns. It
measurement of a velocity profile.
of the waterc~annel .Is driven by an
motor . The pump I spèed can be controlled
manually or with a 20mA current loop input driven by the computer.
The picture digitizer is a plug-in unit for the PDP-II computer.
I t consists of the circuitboards QRGB-256 a~d QFG-01, purchased from
Matrox. The camera is a Philips black white CCD camera. The
videorecorder and monitor are standard HVS colour video equipment.
The electronics of the drag balance were developed together with
the balance i tself (Chapter 6). The drag baiLance output is a single
analog low frequency signal, -IOVto +10V. !
The modem is used to transfer data to 0f her computers.
Flgure 4.12 Burst frequency versus detection level at U = 95 '" + ~ mmls. y = 3.5 mm (y ~ 16). 0 : plate UU, +: plate SA, 0 : plate
SS, IJ. : plate .GG. a: Blackwelder - Kaplan criterion applied to u. b: Blackwelder - Kaplan criterion applied to v. .
a potentialof transferring a . large amount of momentum, the
Blackwelder-Kaplan burst detection criterion was also applied to the
signalof the vertical velocity component (Hgure 4.12b and 4.13b).
57
\
N l:
o
tr -1 Q) ... -en o
N l:
tr Q) ... -
-2
0
.2
.4
en .6 o
.8
.4 .6 .81
.4 .6 .8 1
1.2 1.4 1.6 1.8 2 k
1.2 1.4 1.6 1.8 2 2.2 k
Flgure 4.13 Burst frequency versus detection level at U = 140 '"
mmls. y = 2.0 mm (y+ ~ 14). D : plate UU. +: plate SA. 0 : plate SS. A : plate CG. a: Blackwelder - Kaplan criterion applied to u. b: Blackwelder - Kaplan criterion applied to v.
Apart from the remarkable fact that the smooth wall has in all
situations the lowest burst rate no clear influence of the grooves on
the burst rate is apparent.
SB
1/1 o 0-
e
1
.1
D_I!
1
0 __ 0 -°-0 0
o/' ~ 0- .=0.7 /' 0 _O-D-O_O
.-::::::..---- 0 -- c - 0
10 100
Flgure ~.1~ Burst frequency (npos) versus height of measurement
+ point (y ) according A. V. Johansson & P. H. Alfredsson [1984].
Events with positive slope only. ReD = 13800. 0: T+ = 10. 0 T+ m m
20.
Blackwelder and Kaplan considered the scaling of the ave rage
burst shape on the square root of the detection level as an indication
that some real structure caused the triggering. This argument is not
very strong; because of the exponential dependence of the burst rate
on the chosen detection level such a behaviour is to be expected. The
average burst shape will always be dominated by many lower amplitude
bursts. Nevertheless. the shape of the average burst detected could
give an indication on how the grooves affect the flow . The results for
the different walls at U~ = 96 mm/s are shown in the figures 4.15 and
4.16. The th ree different curves in each graph show the ave rage burst
shape using a detection level k of .8. 1.2 and 1.6. Generally the
scaling behaviour of the burst amplitude is as expected. The v·ery low
burst amplitude on the spanwise grooved wall is remarkable. especially
if one also notes the small vertical velocity component associated
with it. Apparently the high shear stress above such a wall is caused
by a different mechanism than exchange of momentum by turbulent
bursts. The amplitude of the vertical velocity component on the
grooved plate SS is reduced. especially the negative dip at around t+
= 10 is smaller. The other grooved wall SA however shows no such
effect in amplitude al though the total amount of vertical transport
59
0 (ot) 0
c( M
(I)
0 N
0 N
0 ... 0 ...
0+- Ot...
0 0 ... ... I I
0 N
I
0 N ,
0 N M
J
0 NM I I
0 M ~ ~ '> ~ -..... .....
~ ~ ~ >
0 (I) M
(I)
0 0 N
0 0 N ...
O"t.. O~
0 0 ... ... I I
0 0 N N I I
0 N 0 NN 0 NM N
I I I
0 NM I I
Figure 4.15 Average burst shape at Um 95 mm/s. y = 3.5 IIID (y+ ~ +
16). Tm = 11.2. Each diagram contains th ree curves obtained with
k = .8. k = 1 . 2 and k = 1.6.
60
I> ... >
o N
o ...
.... I
o N
I
~N~----~U----:N~N~--~~----~N~g I I I
~--~~ ______ r-____ -r ____ ~O
" C")
" ::::J ..... ::::J
> >
o N
o
o ... I
o N
I
~--~r-------r-----,,--__ -,O ~ > ct C")
::::J -; IJ)
o N
o ...
o .... I
o N
I
L---------l.L..-----Nc'-N,..,....----""------='N g NOl I I
o ~~----w-------~->------~----IJ)-,. C")
'; "> IJ)
o N
o ...
o .... I
o N I
+ Flgure ~.16 Average burst shape at U~ = 140 mm/s, y = 2.0 mm (y
::: 14), T+ = 12.5. Each diagram contains three curves obtained m with k = .B, k = 1.2 and k = 1.6.
61
during the time the horizontal velocity component is less than
average. is smaller. This indicates a lower sh,ear stress transport
during an average burst.
§ 4.4 Conclusions .
The differences between the boundary layers over the different
plates. as can be measured wi th point measurements. are small. but
sometimes clearly significant. Much more difficult to establish is the
exact relation of these differences wi th momentum transport. Most
troublesome is the fact that many differences (in u'. and velocity
distribution and in the shape of the burst) become more pronounced at
higher veloeities outside the range of drag reduction.
The evidence points to the following general conclusion: above '
longi tudinal riblets the flow becomes more random (increasing burst
rate, more gaussian distribution of veloeities) and transports less
momentum (lower vertical transport per burst, less tilt of the outer
elliptic shaped iso-velocity contours). ,
The fact that the diffences become larger at higher veloeities
indicates that the original drag reducing mechanism still operates at
those veloeities but lts positive effect is eclipsed by the increased
devicedrag of the riblets penetrating into the logarithmic part of
the boundary layer.
A final piece of information from point measurements is derived
from the measured spectra. It appears that the spectra show no
resonance peaks and there seems to be no distinct frequency range
which is particularly affected by the presence of the grooves. This
indicates that if the drag reduction is caused by a kind of resonance
effect between the groove spacing and the turbulent structures (for
instance the relatively regular spaced low speed streaks), this
resonance must be very weak indeed.
62
Chapter 5 Hydrogen bubble visualisation.
§ 5.1 Introduction.
In recent years the study of turbulent boundary layer flow
phenomena has paid much attention to so-called "coherent structures".
Much effort has been devoted to conditional sampling with single point
measurements in order to detect and analyse the structures. But
visualisation studies show amore comprehensive view of the flow and
its regularities. They provided the stimulus in the application of the
eonditional single point measurements. Although visualisation gives a
good insight into the dynamics of the turbulent flow it has several
drawbacks. All visualisation techniques demand that markers are
introduced in the flow and the patterns they form tend to emphasize in
a stationary reference frame. the slow moving low speed streak. Short
high speed phenomena are not easily visualized. Moreover. it is
usually difficult and very timeconsuming to get quantitative results
from the visual pictures or films. Also the absolute aceuracy of the
measurements will be lower and noise in the measurements will be
higher in comparison wi th careful single point measurements. In an
attempt to partially remedy these disavantages we have used digital.
automated picture processing. This allows us to extract quickly
quantitative flow speed measurements from the pictures. As an
application of this method we eompare the flow of a turbulent boundary
layer over a smooth surface with the flow over grooved surfaces which
have drag reducing properties.
The total visualisation experiment eonsists of two types of
hydrogen bubble visualisation. Both experiments are done with a wire
at right angles with the free stream. parallel to the wall,
I Computer analysis of hydrogen bubble patterns. The video images
are obtained by photographing a single hydrogen bubble line a few
hunderd milliseconds af ter the voltage pulse. They are proeessed
wi th the computer and the output eontains the measured veloei ty
component in the mean flow direetion along a line. Simultaneously
LDA point measurements are made which are also recorded wi th the
hydrogen bubble information. A quantitative. statistical analysis
of the velocity profiles can be obtained. The method isespecially
63
sui ted to measure the spanwise correlation of the long i tudinal
veloci ty component and gives an estimate of the ave rage spanwise
extent of the flow structures
II Analysis of coherent structures. The process described in the
previous paragraph is repeated with a sequence of four 20ms voltage
pulses applied at the wire. The plctures thus obtained are recorded
on video tape. Simultaneous LDA measurements of two velocity
components are recorded on disk . Thls enables us to study the
relation of the flow structures and the instantaneous Reynolds
shear stress. The position of the first hydrogen bubble line is
also measured as in the experiment I. The presence of the other
three lines. however. disturbs the pattern recognition process
because the lines overlap each other occasionally. These data are
available but they are not used in the present analysis as the data
obtained in experiment I are more reliable.
The pictures which are obtained with hydrogen bubble
visualisation, can show very detailed views of the flow near the wall.
In figure 5.1 and figure 5.2 some characteristic flow patterns above
the longitudinal grooved wall SS are shown. They are taken with the
wire situated at Sov/u* above the top of the riblets and a free stream
speed of 95 rrm/s. The influence of the grooves can he seen in the
small wiggles in the hydrogen bubble lines. In the centre of figure
5.2 it is vislble how fluid Is ejected out of the valley hetween two
grooves.
§ 5.2 Description of the flow visualisatlon arrangement.
The visualisation experiments are conducted in the water channel
described in chapter 3 . The purpose of the measurements is to obtain
information about the spatial velocity field. especially near the
wall. A 40 ~ thin Pt-wire is inserted in the boundary layer.
carefully placed at right angles with the mean flow and parallel to
the plate. The length of the wire hetween theprongs 15 about 150 mmo
The outer ends of the wire are insulated wi th a thin layer of
insulating paint, leaving ca 100 mm wire free to produce the hydrogen
bubbles. The wire holder !s connected with the LDA displacement
system, which enables us to
Flgure 5.1 Example of a low speed streak above grooved surface. In the middle of the picture.
Flgure 5.2 Example of theinfluence of the grooves on the flow. Without any clear coherent structure vlsible. Left from the middle of the picture an ejection of fluid out of the groove can he seen.
65
control the vertical position of the wire with an accuracy better than
50 ~ and to retain the position relative to the laser doppler
measurement volume.
The measurement position is 4.2 m downstream the leading edge of
the measurement plate (see figure 5.3). In the case of a grooved wall
alm section of the smooth plate is removed and replaced ' by the
grooved wall. The measurements are done .7 m downstream the change in
roughness. The tops of the 2.5 rnrn grooves peak about 1 rnrn above the
leading and trailing smooth surfaces. In §.3.3 the dimensions of the
groove types used are given.
Hydrogen bubbles are generated by applying negative 50V pulse to
the wire. The cathode consists of a stainless steel grid mounted at
the side wallof the channel •. 5 m downstream of the wire. In order to
improve the quality of the bubbles 200 gram NaS04 is added to the 1500
litres of water in the channel.
The video pictures of the two types of measurements are taken
with a Philips CCD camera which provides stable and distortion free
black and whi te pictures. The smal I size of the camera makes i t
possible to mount it also on the LDA displacement system so traversing
the boundary layer vertically can be done conveniently. virtually
without recalibrating the field of view. The video output is connected
with a videoframe digitizer (256 x 256 pixels of 16 intensities).
consisting of two printed circuit boards inserted in the PDP-11
By measuring the distance between a single hydrogen bubble line
and the bubble producing wire one obtains an instantaneous velocity
profile along the spanwise direction. Figure 5.8 shows a typical set
of velocity profiles together with the registered LDA data.
Several statistical properties of those velocity .profiles were
investigated. As a check on the performance of a method the ave rage
velocity and the rms value averaged over the 500 profiles were
calculated. Figure 5.9 shows a typical example of the measurements on
the grooved surface. The non uniform mean velocity can be explained by
a misalignment in the height of the wire of .2 mmo This is about the
accuracy with which one can position the wire with the naked eye. The
uniformi ty in rms values indicates that the hydrogen generation and
pattern recognition is equally uniform over the wire.
An obvious quantity which can glve a clue to the influence . of
the grooves on the boundary layer is the spanwise velocity
correlation. Gallagher and Thomas [1984] present a measurement which
indicates a decrease in correlation length. Dur measurements show for
plate SA indeed the same trend (figure 5.10). The correlation length
is derivedfrom the correlatlon functions by a least squares fit of an
exponentially decaying funetion wi th the appropriate estimation for
the variance in the measured correlation. The resul ts are shown in
figure 5.11. The results for the plates SS and CG are remarkably
similar while the results at the higher velocity, outside the
dragreducing area, indicate even larger differences.
In order to compensate for a possible displacement of the
reference height above the different types of grooves, the
lengthscales are also plotted against the mean velocity, measured with
the hydrogen bubble lines (Figure 5.12). In that case the graphs
suggest a decrease in lengthscale near the grooves and an increase
above the bufferlayer. The first is to be expected because the
lengthscale near the wall should coincide with the distance between
the grooves which is smaller than the distance between the low speed
streaks which determlne the lengthscale somewhat higher up in the
boundary layer.
Figure 5.13 shows a measurement indicating both the velocity
75
Flgure 5.8 Example of 10 of the registered instantaneous velocity profiles and the LDA signals from 180 ms before to 40 ms af ter registering the profile. Shown are 10 profiles out of 500 with
largest velocity sweep in U(t). A: IT~ 50 mmls, B: V = 0 mmls, C: position of LDA measurement volume. Measurement done above smooth plate. Uw = 140 mmls. YWire = 2.7 mm, YLDA = 2.0 mmo Veloeities
are scaled arbitrarily, spanwise distance reckoned from left side of measured bubble line. Strong local velocity minima are indicated by crosses.
components U and V in a low speed streak. These canbe extracted from
the present measurements as follows: firstly the position of the most
prominent low speed streak in the velocity profile is determined. As
almost all the velocity profiles contain at least one low speed streak
the position of thè absolute minimum coincides in all probabillty with
a low speed streak. Then the velocity components as measured with the
LDA are taken and filed against the distance from the low speed
76
8 -7r::'" a U/u·
6
5
4
3
2
1 b U"/u·
00 100 200 300
Flgure 5.9 Typical example of the measured maan flow velocity (a) and turbulent intensity (b) along the wire.
streak. The results are averaged for the 500 profiles. In figure 5.13
the ave rage velocity proflles in the low speed streak above four
different walls are shown . The measurements above the smooth and
spanwise grooved wall show a positive vertical velocity component at
the position of a streak as can ba expected. This feature however is
almost absent in the maasurement over the longitudinal grooved wall
SA.
§ 5.5 Visualisation combined with LDA measurements.
The procedure described above, but now with a sequence of four
hydrogen bubble lines, was applied to three surfaces, at two va lues of
free stream speed and four different heights above the plates. This
17
0 ... _----------------- -0
0 100 z+ 200 300 0 100 z+ 200 300
y+:18 t=13 c c
.5 .5
\
\
0 -------- - - - - :......:-- - - - - - 0
0 100 z+ 200 300 0 100 z+ 200 300 1
\ y+=25 y+=17
c \ C •
.5 ~ i
\ ..
0 \~-~---
0
0 100 z+ 200 300 0 100 z+ 200 300
1
\ /=32 y+=36
\
c c '\ .5 \ .5
\ , \ , \
\
\ \
\
0 ~-----,--.::::..: .~~ . 0 ---- ... -
0 100 z+ 200 300 0 100 z+ 200 300
Flgure 5.10 Spanwise correlation functions. Left column: measurements at U = 140 nun/s. Right column: measurements at U 00 (IJ
-10~--~--~----~--~----~--~--~----~--~--~ o 100 200 300 400 500
N
Flgure 5.1~ Distribution of measured Reynolds stress over the 500 sequences. Vertical axis arbitrarlly scaled. a: Plate UU. b: Plate SS. c: Plate CG.
II The low speed streak .
III The wide high speed region.
IV The narrow high speed reglon.
V The accelerating region.
We made the following twelve visual categories which cover all of the
sequences (the numbers refer tothe numbers used in figures 5.21 and
5 . 22):
1 (Ia) Longitudinal vortex. The vortex cause the hydrogen bubble
!ines to twist and it is recognlzabl'=! as .loops in the hydrogen
bubble lines. A typical example is shown in figure 5.15.
2 (Ib) Longitudinal vortex with low speed streak. Of ten a
longitudinal vortex is clearly associated with a low speed streak .
83
This is recogn1zed as a separate category although this comb1nation
could be a logical development of an intense low speed streak.
3 (1Ia) End of a low speed streak. If the four bubble lines showed
all a minimum at the same spanwise distance and the minimum was
clearly disappearing. this was catalogued as an end of a low speed
streak. A different ülterpretat!on could be that the top of the
streak temporarily went below tbe w1re height. Because no video
pictures directly after digitizing were avallable. an eventual
reappearance of the streak at the same placecould not be observed.
A typicalexample of this pattern is figure 5.16.
4 (IIb) Low speed streak. (figure 5.17). If all four hydrogen
bubble lines show a progressive V-shaped minimum this is taken as a
low speed streak. The difference hetween Ila and Ilb is clearer in
the moving video because one then also observes the folding of the
lines to a increasingly V-shaped minimum. This last aspect is
absent from category IIa.
5 (1Ic) Side of a low speed streak.
6 (lila) Side of a high speed region. The distinction between this
category and category IIc is a bit diffieult as low speed streaks
are of ten adjacent to high speed regions. The decision is made on
the basis of whether the local veloeity is higher than the average
between the maximum veloe1 ty in the high speed region and the
minimum velocity in the low speed streak. No distinction has been
made between the sides of the different high speed regions (111 and
IV) .
7 (IIlb) Narrow high speed region. This could also be ealled a high
speed streak although the maximum is not extremely peaked.
8 (IVa) Wide high speed region. This term is used for an area in
which the veloeity is higher than average and where the velocity is
more or less constant along the z-direction. No very distinguished
maximum can he located. Figure 5.18 shows a typièal example.
9 (IVb) End of high speed region. If a new minimum appeärs in a
wide high speed reg ion or a high speed area evolves into a less
pronounced feature this is ealled the end of the high speed region.
The ends of the different type of high speed regions are not
separated out beeause of the difficulty of recognizing the specifie
type at the end of its existence on video.
84
10 (V) Accelerating flow. Ir the last released bubble line moves
faster than the previous ones or even overtakes them. this was
categorized under this heading. Figure 5.19 shows a typical example
although with an additional non standard vortex associated with it.
11 Miscellaneous. This category is used for those sequences which
show clear. but rare patterns like verticalvortices . very peaked
high speed streaks and violent ejections of fluid from the wall.
12 Outside classification. Occaslonally a pattern is encountered
which defie's any classification. Sometimes no distinctive features
are present. sometimes a rare mixture of several patterns is seen
(figure 5.20).
In figures 5 . 21 and 5.22 the results of the classification are
shown. Categories which can be easily confused are placed adjacent to
each other. All the 500 sequences at 1 mm above the smooth plate have
been evaluated. Their distribution can be compared wi th the
distribution of twenty random selected sequences. As expected twenty
samples are not enough to oblain an accurate distribution over 12
categories but as those twelve categories can be divided infour
essentially different patterns the broad outline of the distribution
can be taken as what can he expected from a comprehensive analysis.
lt appears that most of the turbulent stress at the lower + investigated height (y = 8. figure 5 .21) is produced in the narrow
high speed regions (category 7). This is particulary apparent above
the transverse grooved wall (figure 5.21a). a flow which is visually
dominated by the presence of strong low speed streaks. On the smooth
and longitudinal grooved plate (figure 5.21d and 5.21g) the high speed
regions still contribute most to the turbulent stress al though less
strikingly . It also appears that at the side of a low speed streak
there is a region which produces turbulent stress rather than the
center of the low speed streak itself. (As the horizontal velocity
near a low speed streak is less than average. for a positive
contribution to the turbulent stress the vertlcal velocity component
here must be 'directed upwards.)
The analysis also shows an increased number of not classifiable
sequences in the set of random samples (category 12 in figure 5.21b. e
and h. compared with the other .six tableaus). A similar increase is
seen comparing the results of plate CG with UU (figure 5.21a. b. c
85
Flgure 5.15 Example of longltudinal vortex.
Flgure 5.16 Example of the end of a low speed streak .
86
Flgure 5.17 Example of a low speed streak.
Flgure 5.18 Example of a wide high speed region.
87
~ .
Flgure 5.19 Example of an accelerating region.
Flgure 5.20 Example of a pattern outside classification.
88
with 5.21d, e, f) or comparing UU with SS (figure 5.21d, e, f with
5.21g, h, i). This can be explained by the more chaotic behaviour of
the flow above the longitudinal grooves compared with the smooth and
spanwise grooved wall. + Higher up in the boundary layer (y = 17, figure 5.22) the
contribution of the high speed regions to the turbulent stress
distribution decreases compared to their contribution at y+= 8. If we
compare the number of their occurrences at a single height between the
different plates in the set of sequences of maximum stress we see a + relative decrease at y = 8 (comparing 5.21a with 5.21d and 5.2Ig) but
a relative increase at y+= 17 (comparing 5.22a with 5.22d and 5.22e).
This implies that the role of these structures in producing Reynolds
stress is different at different heights.
§ 5.6 Conclusions.
From the analysis of the combination of the visualisation
measurements with LDA measurements we can draw the folloWing
conclusion. Automatic visualisation and simultaneous LDA measurement
is quite possible. Correlation between bath methods is good;
Correlation coefficient is between .9 and .95 for the instantaneous
U-velocity component. No correlation between the velocity measured by
hydrogen bubble visuallsation and local shear stress, or turbulent
intensity is observed. This sustains the belief that the method gives
an accurate view of the relative veloeities (rather than . other
physical quantities as for instance shear stress) occuring in the
turbulent flow, despite the velocity defect induced by the wire.
The experimental resul ts show the following trends. Generally
the flow above longitudinal grooved surfaces is more chaotic than the
flow above a smooth wall. In the case of a spanwise grooved wall the
flow appears even more regular due to the presence of intense low
speed streaks. The measurement of spanwise correlatlon leads to
ambiguous results , caused by the difficulty of defining a suitable
reference height. Moreover both a more chaotic flow and a more intense
89
o ..., ...., ....
§~ y 1.7mm y+: 8 maximum random minimum
g"(11 Uo 95 mm/s 1 234 56 7 8 9101112 2 3 4 5 6 7 8 9 101112 23456 7 8 9 101112 ., . fII N a b c .... '1 I 0 I
""'0 I I ..... 15 C') fII I» t+ plate GG t+'1 (I) .... oqr::r o l:! 10 I I ., t+ ......... (I) 0 fII :::I 5 fII 0 (I) ...., (I)
fII t+ t+ d e I I (I)
~ >< I I t+ n
t+ 15 I l:! .,
plate UU I I (I) fII I I
I» 10 I
t+ I I
'<+ 5 11
ex>
'Tl 9 h 0 '1
(I) 15
~ plate SS ~
10 I» :::I ... ... I» t+ I I .... 0 5 :::I
low speed streak patttern can apparrently lead to a decrease in
measured spanwise correlation length.
Although the visualisation plctures clearly show the presence of
the riblets. very little qualitative dlfference in structures
occurring on smooth plates and grooved plates could be detected .. only
some quantitative differences can be' observed. From comparison between
Reynolds stress measurements and flow visualisation. it appears that
no single structure can be identified which produces the bulk of the
Reynolds stress. The changes in wall shear stress of several per cent
are apparently not accompanied by major changes in flow
characteristics.
The conclusions of this chapter are in Hne wi th the main
conclusion of chapter 4 . Both single point measurements and
visualisation studies indicate that the flow above a longi tudinal
grooved wall is more chaotic than the flow above a smooth surface .
The visualisatlon does not show a clue why the turbulent
intens i ty above a longi tudinal grooved wall is 10% lower. compared
wi th a smooth wall. As no strikingly different structures are seen.
the dlfference must be due to some decrease in intens i ty of the
structures already present.
92
Chapter 6 Drag balance.
§6.1 Survey of different methods of measuring drag.
There exist several possibilities to measure the drag which is
exerted by a flow on the wall. Every method has its own advantages and
problems. Here we present a review of the available methods. We will
concentrate this discussion on the absolute accuracy of each method.
Prev ious measurements showed a maximum dràg reduction of about 5%
[Walsh 1979, Nitschke 1984]. So we will demand an accuracy of 2% or
better for our measurements.
§ 6.1.1 Indirect methods.
It is possible to measure the drag with indirect methods. We can
measure the Reynolds stresses or we can measure the velocity profile
and use lts shape to obtaln the wall shear stress.
The total shear stress in an equilibrium boundary layer can be
written as:
The theoretical relation
layer and the wal! shear
layer is [Townsend 1976]:
diT T ~ -p uv + v dy
between the shear stress
stress in the inner part
.T ~ + Y dP T
dx w
in the boundary
of the boundary
dP - -The ·measurement of dx' U(y) and uv(y) is needed to calculate the
drag. The first two quantlties are relatively easy to measure. The
Reynolds stress uv is much more difficult but it is the most important
quantity in the equation.
Except for the obvious difficul ty of measuring the U and V
components at the same position, two other problems beset the
measurement of uv. First one needs to calibrate the coordinate system
93
' very carefully. If one tiIts the x-axis by lö t and the y-axis by 1ö2 a
systematic error in the measured stress is introduced .. Instead of U
and V. one rneasures the quantities:
U U COS(löl) + V sin(löl)
V = V COS(1ö2) - U sin(1ö2)
So the formula for the shear stress gives:
uv (U -U )-(V -V
Iö a rotation . we get:
uv = uv-cos(21ö) + (y2 - U2)-sin(21ö)/2
In the buffer layer we have ~2 ~ 9uv and y2 ~ uv [Hinze 1972]. so:
uv ~ (1-81ö) uv
In order to obtain 2% accuracy. we need to determine the orientation
with an accuracy of .0025 rad or .15 degrees!
A second problem is the long time over which we have to
integrate t.o obtain an accurate estimate of the shear stress. A
formula for the standard deviation u of the estimator for uv (which uv 1 T
- f U(t)-V(t)dt- U-V) ) . T 0
is discussed by Bessem is in this case
[Spalding & Afgan 1977. p 343]. He derives the forrnula:
uuv 2 (T)
Here nu and nv are the frequencles at which the u- and v-spectra reach
their maxima. n is a normalized frequency of the uv-cospectrum C, o
which is approximated by:
C(n) n (1+1.5 (nln ))2.1
o
With a free stream velocity of .2 mis and a displacement thickness ó*
of 10 mm those frequencies are nu 2 Hz , n = 2 Hz and n = 2 Hz, so v 0
the demand of 2% accuracy leads to:
3 0uv(T) < -.02 uv
T > 20000 ( 3 I (nu +nv )+ .06 I nol
T > 15000 sec = ~ h !
It will be very difficult to maintain constant conditions during this
long time and the time is anyhow inconveniently long.
When one or several veloei ty profiles are known some
semi-empirical formulas are available for determination of the drag.
Most formulas use the free stream velocity Ua>' momentum loss thickness
a, the shape factor Hand the pressure gradient dP/dx. The first
formula is Von Karman's equation:
Cf 2 [: + a· (2+H) : I p U! ]
In a two dimensional flow it is exactly valid, because it is derived
from the principle of conservation of mass and momentum. The formula
is very sensitive to small errors in dP/dx. For example, if Cf ~ .004,
U Q)
3 = 200 mm/s, p = 1000 kg/m , a 7 mm and H = 1.35 and we want to
calculate Cf with an accuracy of 2%, then the error in dP/dx should be
less than .07 Palm, (7 ~20) which is nearly impossible to achieve.
Other formulas with their empirical constants are:
[Schlichting 1979]
95
Cf .246 10-. 678 H Re~·268
[Ludwieg & Tillmann 1949]
[Rotta 1972]
2 2
5.75 loge H Rea) + 3.7)
The results of the formuias for typical values of Rea and Hare shown
in table 6.1.
With help of the so called "log-law" it is also possible to + + calculate the drag. Between y = 20 and y = 250 the logarithmic form
of the velocity profile can be used to calculate the friction
coefficient:
In (J.....) • U Z (11)
o
]2 k • U(y)
k and Zo are eonstants. which are weakly dependent on Rea and dP/dx.
Zo is strongly dependent on the roughness of the wall . Because of the
uncertainties in the value of the eonstants this formula cannot be
used to determine the absolute drag accurately.
A different problem is the choice of the correct reference
height in case of a rough (grooved) wall. This choiee has a large
influence on the calculated friction coefficient. especially in low
Reynolds number flows. Tbe applicability of these empirical formulas
in the case of a wall which shows drag reduction is at least
questionable. Their accuracy is anyhow limited to a maximum of 3%.
Tabla 6.1 Calculation of friction coeffieient aeeording the different formuias in the text. Rea = 1400. H = 1.35.
Formula of Cf Deviation
Schlichting .00414
Ludwieg & Tillmann .00429 +3.6 %
Rotta .00394 -4.8 %
96
because they contain constants derived from best fit procedures over a
wide range of experimental conditions. So it seems that drag
measurements based on point measurements or based on semi-empirical
formulas are not appropriate if we demand 2% accuracy.
A differerit indirect method is the use of hot film wall probes.
Here we use the theoretically founded idea that the amount of power
needed to maintain a piece of the wall at a certain temperature is
directly related to the local and instantaneous wall shear stress. But
even lf the problems of cal1brating such a device on a smooth wall
could be solved we would still face the problem of the different heat
transfer of a grooved wall. This would demand a separate calibration
for each of our grooved walls which makes this method useless in our
situation.
There are several other methods which depend on the existence of
a universa I velocity profile near the wall. for example Preston-tube
measurements. We wHI not discuss these methods as they are not
applicable to the flow above grooved walis.
§ 6.1.2 Direct methods.
A second group of methods can be called "Direct drag
measurements".We discern balance measurements and pressure drop
measurements. In the first method a part of the wall is disconnected
and suspended from a balance which measures the forces exerted on that
part of the wall. The forces are rather small in our si tuation:
because of the dlmenslons of our water channel the maximum area of
such a plate wHI be about .12 x .25 m2 and the drag force will be
about 2.5 mN. The resolution and accuracy we demand is 50 ~ (this is
equivalent to 5 mg). This force can be measured in several ways.
A second way of determining drag directly is the measurementof
pressure drop in a long straight pipe. The connection between the
pressure gradient and the wall shear stress in a pipe of diameter D
is:
The main conceptual difficulty is the definition of the pipe diameter
97
. wi th a rough wal 1. I f the roughness height is less than IX of the
diameter. the error associated with this problem is not significant so
we can calculate a minimum pipe-diameter for our measurements. Ihe
* optimal groove height is about 10 viscous units (y ) so:
* 10 y < .01 D
* An empirical formuia for y is [Schlichting 1979] :
* y -7/8
5 .03 D ReD
So ReD should be larger than 17000. A minimum height for accurately
machined grooves is .5 mm so the minimum D is 50 mmo Ihis implies a
pipe length of 10 m (100-D) which is needed to obtain a fully
developed turbulent flow. Ihe Reynolds number demands a flow velocity
of at least .34 mis in water (or 5 mis in air) which implies a minimum
volume of .7 lIs in water (or 10 lIs in air). The pressure gradient in
such a pipe will be:
dP dx=
2 16 -E2....- _ R 7/4
. 3 eD D
Over a length of 4 m we will measure a pressure difference:
AP 16 Pa in water (or 4.4 Pa in air)
For 2% accuracy we need a resolution of .32 Pa (32 J.UIlH20) in water
which is possible. We refralned from using a pipe circuit because data
were already available [Nitschke 1984]. Moreover. the difficulties of
performing visualisation studies in a pipe are much larger compared
with those of a flat plate. Also obtaining suitable pieces of piping
is more difficult than making grooved plates.
9B
§ 6.2 Drag balance Delft.
At the Technical University Delft a dragbalance was developed
and used in a windtunnel. lts measurement section has the dimensions
of 5 m x .7 m x .9 m (length x height x width). The balance is
described by Van der Steeg [1985]. Several configurations of grooves
were tested. See figure 6.1 for a picture of the grooves. More details
are presented in Van Dam [1986].
The results are shown in figure 6.2. The symbols denote
different measurements and indicate the reproducability of the
measurements. The solid line is a best fit curve through the
measurement points obtained above the smooth plate.
The grooved plate measurements indicate a drag reduction of
about 6%. These results confirm the measurements of Walsh and other
experimenters. With additional hot wire measurements differences were
seen between flow above smooth and dragreducing surfaces; these were
discussed in chapter 4.
0 . 64
Flgure 6.1 Geometry of. groove types used in windtunnel experiment. Dimensions in mmo
§ 6.3 Design considerations of the drag balance.
For the application we had in mind. several considerations in
the design of the balance have to he taken into account. The balance
99
4r----------------,----------~----~
-u (')
'0 ,.. Cf = 0.0610 Re-0 . 208
3r-------~z~~----~~~--------~~------~ &~ ~'!>
.-z + ~ •
21~----------------2L---------~3------~4
10-6 Rex
Flgure 6.2a Friction factor versus Re for plate A (described in x
figure 6 . 1).
4r-----------------.----------.------~
-U (')
'0 ,.. C • 0.0610 Re -0.208
f
2~----------------~--------~------~ 1 2 3 -6 4
10 Rex
Flgure 6.2b Friction factor versus Rex for plate B (described in
figure 6.1).
100
has to opera te in water and if possible it must ba able to measure the
drag force in the range of speeds where the visualisation studies were
performed. Of course the balance has to fit in the channel wherethe
other experiments were performed. The following specifications.
therefore, must apply:
I Drag plate surface area ~ 120 x 250 nrn2 •
I I Sui table for measurements between .1 and .4 mis free stream
velocity.
111 Nominal dragforce (at .15 mis) 1.7 mN. IV Resolution and reproducibility ca 20 ~.
V Dragplate and its surroundings must be exchangeable.
VI The total apparatus should he as flat as possible. to minimize
its influence on the flow in the channel.
VII The apparatus must ba able to withstand water, if possible
slightly saline water.
Several possibil i ties exist for the construct ion of a sensor.
One can design a stiff balance with a sensor which measures the force
directly or one can measure the displacement of an elastically
suspended drag plate caused by the drag forces. But we must take into
account the dynamic range of 1:500 which we would like to have. The
detector must also operate without friction and without exerting force
on the plate.
Measuring with strain gauges falls in the first category, but
their sensitivity is just barely enough. Also there are problems of
slow aging and measuring small resistance changes under water. Also
considered were force transducers of piezoresisUve material which
would make for a very sUff suspension of the dragplate but their
mechanical stabili ty was insufficient. There is also the problem of
obtaining a low drift chárge amplifier, needed to re ad out the
devices.
To use the second method one must suspend the plate on small
springs and measure the displacement caused by drag. 8y choosing a
suitable stiffness. we can obtain the displacement desired.
Considering the relevant lengthscales a maximum displacement of .1 mm
seems acceptable, and the displacement sensor needs to have a
101
'resolution of at least .2 1JlII. Displacement sensors can he based on
optica!, inductïve or capaci tive principles . Optical means would be
excellent but were excluded hecause of relative complexity and cost.
Capacitive means were excluded because of the high and variabie
dielectric constant of water.
The most promising candidate seemed to be a sensor operating on
inductive principles. We decided to measure the inductance of two
coils which were mounted beside a ferri te plate connected wi th the
drag plate. A movement of the plate causes a variation of the
inductance of the coils which can be measured with suitable
electronics. Krischker [1982] describes a simple system, which is used
to measure displacements of less than .1 nm; it can easily he adapted
to our range by changing the distance hetween the plate and the coils.
Af ter further consul tation wi th various experts we came to the
design discussed here (see figure 6.3). The drag plate is suspended on
six thin steel wires (.3 mm diameter). In this way the plate is
suspended at th ree points while the spanwise stability is assured. The
drag force will displace the plate slightly and this displacement is
measured with the inductive sensor. The maximum allowabledisplacement
is determined by the width of the slits around the dragplate. Their
maximum width should he limited to several viscous units in order to
prevent irregularities in the flow over the plate near the gaps. We
chose a nominal slit width of .2 II'1II, as a compromise hetween the
demand of not , disturbing the flow and ease of manufacturing. The
nominal displacement of the plate at maximum speed should he .1 mm, in
order to have sorne space left to account for fluctuations in dragforce
and vibrations before the plate collides with the surrounding surface.
Additional devices in the balance are the plates, whlch give the
neccesary damping force. They are constructed from clear perspex, to
see eventually trapped airbubbles in between them. The rest of the
spac'e inside the balance is f!lled with stainless steel plates. which
should distribute the temperature evenly in the balance. Also inserted
are a temperature sensor, a magnet connected with the dragplate and an
adjustable chromium nickel steel pin for nulling the balance and an
electromagnetically driven relay, whlch can kick the dragplate if
102
Flgure 6.3 The drag balance.
partic1es in the slits disturb the operation of the balance. Also
present is a device for fixing the drag plate whlch is used when the
balance is transported in order to prevent damage to the fragile
suspension .
A prototype of the balance was made of aluminium for ease of
construction. Despite the surface coating applied the surface corroded
and particles of aluminium hydroxide interfered with the measurements.
The plating of the steel wires also corroded slightly. Despite these
problems some measurements were conducted with the balance. It turned
out that the mechanical stability of the mechanism for positioning the
plate was not stabie enough. A second version of the balance was
therefore constructed from stainless steel and the positioning
mechanism was deleted. The relative position of the dragplate to its
surrounding surface can now be regulated by adjusting this surrounding
plate. The maximum corrective displacement in all directions is ca .5
mmo
103
In testing this second version several additional problems
surfaced. It appeared that leakage of the balance case could influence
the measurement drastically. Although this was known to be possible
from the very beginning, diagnosing it by excluding all other possible
defects and remedy it turned out to be very time consuming. Also some
small drift remained which was caused by water absorption in the
ferrite co re of the coils. Coating the coils in plastic and,
necessarily, mounting them differently solved the problem. The
influence of water absorption of the ferrite plate between the coils
can be minimized by keeping this plate constantly under water.
By now we can conclude that a lot of the problems which caused
the long development time of the balance originated from the use of
water as fluid in which the measurements were performed. Also
troublesome were the long timescales involved: it takes several
minutes to bring the channel to a new stable velocity and the
temperature time constant of the balance is about 15 minutes.
Refilling the channel causes a delay of at least one day because air
bubbles originate from the water preferentially in the sli ts of the
balance (at least there they are most apparent because of the problems
they cause).
§ 6.4 Some additional design formula of the balance.
The response of the position set) of the dragplate of the
balance to a force, can be thought as that of an ideal second order
system: 2
K ds - A s F(t) = M d s _
dt2 dt
Here F is the driving force, consisting of about five different
components.
I A fluctuating dragforce of ave rage value Tw-L-W (L-W is the
11
surface area), which we want to measure as accurately as
possible. dP
Unwanted pressure forces { dx L WH),
104
III A force F due to the vary1ng t1lt A~ of the channel:
F = (M g - Fh)Af.
IV Forces due to temperature changes.
V Unwanted inert1al forces due to vibrations.
The sensitiv1ty A [Nm-1] cons1sts of two parts because two types
of forces try to pull back the drag plate aga1nst the drag force. One
is the force of gravity (the drag plate is suspended as a pendulum)
and the second one is the elastici ty of the wires suspending the
plate:
Where M
g
mass of the dragplate
gravitat10nal constant
1.0 kg -2
9.S ms
Fh : lifting force on dragplate in water 4.2 N
e .p
d
E
length of suspension wires 45 mm
angle of the wires with the horizontal 30 0
diameter of the wires .3 mm
elasticity modules of the stainless steel wires 2 1011 Pa
We want the gravity part of the stiffness as small as possible
because this part causes the changes in sensitivity as the drag plates
of different grooves are exchanged . Moreover. it is also a lower limit
for the sensitivity of the balance.
For critical damping the factor K needs to be 2 ~ • the time
constant is then t = c J ~ . Damping can be achieved by using
vertical slits in which plates connected with the dragplate can move.
The pressures induced by this movement counteract the movement and
genera te a force proportional to the veloei ty. We can derive an
expression for this force if we assume a time-dependent Poiseuille
flow in the slits and the pressure gradient caused by it. We finally
obtain:
~L K = 12 p v --3-
D
With H
L
height of the slits
length of the 51its
D width of the slits
105
p, v density and viscosity of medium in the slits.
Practical values for H andD are 30 mm and 1 mm respectively. As
K needs to he about 20 Ns/m, it follows L must he 60 mmo
From our previous considerations it follows that the stiffness
of the suspension must be at least 120 N/m. And preferably not much
larger. Ihe stiffness Ab of a round beam of material with a modulus of
elasticity of E N/m2 , a diameter d and a length e, both ends fixed,
is :
3'1r E II 16 e
The minimum diameter of the wires is given by the maximum
vertical force the suspension should be able to wi thstand , and the
tensile force under which they still opera te elastically. For
stainless steel the maximum allowable stresses are Tb = 700 MPa
(tensile strength), T = 140 MPa ( proportionality limit). m
I f we assume a maximum force F of 20 N perpendicular to the
surface, and the wires are mounted under an angle ~ of 300 , each wire
bas to withstand a force 6.7 N. Ihis leads to a minimum diameter of:
J -4 F/6 'Ir T sin(~) m
.25 nin
Also considered must be the influence of torques on the drag
plate, al though under normal operation only the pressure gradient
generates a small variabie torque M on the plate, with its axis p
parallel to the z-direction:
M -L dP L3 B < 2 10-3 Nm p 12 dx
Ihe stiffness A in the vertical direction of a two wire v
combination is, if the wires are taut:
106
A v TE d2 sin2(+) = 1.6 105 N/m
2 I!
Tbe resistance Aw against a torque in the z-axis can now b~
calculated:
A 2 L2 A w v
2 The turning point is located at 3 the distance between the suspension
points because the stiffness of the suspension upstream is twice the
stiffness of the suspension downstream. This also causes the factor 2
in the formula above. Tbe plate rotates therefore around a point
inside tbe ferrite plate. approximately at a beigbt h of 20 mm above
tbe axis of tbe coils. We can now estimate tbe additional displacement
da of tbe ferrite plate due to a moment M:
d = ----=h.:.....::;M __ a 2 L2 A
v
This is less than 20 nm if we use tbe value of tbe maximum moment
mentioned above. and is negligible compared to tbe displacement of 100
~ caused by drag.
In figure 6.4 tbe impulse response of tbe balance is shown. Witb
the known mass M of the dragplate (1.0 kg) we can now check the
stiffness. damping and Q of tbe balance. Tbe results are A = 130 N/m.
K = 2.9 Ns/m and Q = 3.9 .. Tbis is in reasonable agreement witb our
demands and calculations. The damping however could he improved.
Another problem is the heat conduction inside the balance. If we
consider the balance as a can filled with stagnant water. we can
calculate a penetration time associated with the dimensions of tbe -1 -}
balance. Tbe specific heat of water ( Cp H2 0 ) is 4.2 kj kg K . and
its heat conductance k is .6 W m-1 K-1. Together with a distance of
the water to the wallof the balance ( 30 mm). and the density p = 103
kg m -3 can form a typical time we
T d2 p C / k c p
107
dl lil c: o Q. lil
~I-----~
o 1 2 Figure 6.4 Impulse response of the balance.
3 time sec 4
This time Tc is in our case about 60 minutes. By inserting cooling
-1 -1 fins in the balance, made of a material which has a higher kC p
p -1 -1 -3 2-1
product, (stainless steel kC p = .13 10 m s compared to water p
-6 2-1 .14 10 m s ) we can theoretically shorten this time considerably.
Fins wi th a separation of 20 mm and made of perfectly conducting
material, should reduce the time with a factor 9. Inserting stainless
steel plates, thickness 1 mm and separatiori 20 mm, however only
reduced the time constant to 15 minutes.
In the design of the balance one must consider the pressure
forces on the dragplate. Ihis force, is proportional to a volume
derived from the dimensions of the plate and proportional to the
pressure gradient. Due to the difference in pressure at the points A
and 0 (figure 6.5) a flow around the plate will he induced. If the
slits are narrow compared with the width of the flow above and under
the plate, the total pressure drop along the line ABCD will be in the
slits AB and CO. Ihe slits should be so narrow and so long that the
flow does not al ter the pressure"s at A and O. Some inspection shows
that the pressure force on the plate is proportional to the grayareas
108
in figure 6.5b and 6.5d. 50 the slits MUst he as short as possible.
We can now estimate whether the pressure gradient parameter P p
influences our results significantly. We demand:
Fpressure < .01 Fdrag
dP L W h dx 2 < .01 T L W
w
* h+ = ~ < .02 v --P-p
Ihis condition can be met. We remark that P ~ 2.1 10-3 in the channel p
as U = .2 mis. Ihis leads to a demand that h < 2 mmo Wecan also Ol
deduce from figure 6.5 that as long as the pressure drop is linear in
the slits. a difference in width does not affect the pressure force on
the plate. So the slits should be long compared with their width in
order to minimize the unknown end effects .
A .. D :Cl J
1
z ~ ~
1 ,- - B
,
F ,~ A B C D
I Î~ EP'OUU_'O ---
- , ABC 0
Figure 6.5 Influence of pressure forces on the drag plate.
109
,§ 6.5 Sensor.
The sensor consists of two coils (diameter 22 mm) which are
separated by about 5 mmo In between is a ferrite plate, 4 mm thick,
extending at all sides at least 5 mm beyond the coils. This plate is
connected rigidly with the dragplate. The sensor is only sensitive to
the longitudinal component of the displacement of the dragplate. A
vertical or spanwise displacement due to the not absolute stiffness of
the suspension in those directions, will only have a marginal
influence on the sensor.
The electronic part of the sensor consists of a resonance bridge
in which the coils are included. The bridge is operated at its
resonance frequency of 45 kHz and the difference signal from the
brigde is measured with a lockin amplifier. The shielded leads from
the coils to the electronics were kept as short as possible (.5 m) to
avoid influence from parasitic capacities.
A main problem is the absorption of water in the coils, the
ferrite plate and the cabie, which causes a change of the electrical
resistance and stray capaci ty of the electronics . The problem was
solved by encapsulating the coils in araldite filled w!th quartz
powder and using tedious care in making and insulating the electrical
connections. By keeping the ferrite platelet always wet, its change of
magnetic permeability is brought to an acceptable low level. A plate
should be keptat least a week under water before it is stabie enough
to be used.
§ 6.6 Measurements and results.
Drag measurements were performed on six different surfaces with
at least two measurements on each surface. A measurement consisted
typically on measuring the ave rage drag as indicated by the balance
and the average free stream speed as indicated with the LDA during a
two minute period at a certain channel speed. A complete measurement
sequence consisted of about 25 measurement points, half of them during
the increase of free stream speed, the other half during the return to
zero speed. This enabled us to estimate the effects of drift due to
110
temperature changes and other causes. Typically a drift of about 1 mPa
(on 250 mPa full scale) was registered and accounted for by
interpolation between the zero point of the balance just before and
af ter the measured sequence. The reproducibility was within 2% at Rex
2.105 , and better at higher Reynolds numhers.
Before and af ter the measurement of a single plate the balance
was calibrated. The calibration of the balance is done in situ, with a
specially designed calibrating balance (figure 6.6). The calibration
procedure consisted on placing weights from 100 to 1500 mg on the
balance, and record the readings averaged over 15 seconds. Afterwards
a third degree polynominal was fitted with a least squares fit through
the points. A typical calibration curve is shown in figure 6.7. The
deviation from the points to the curve is less than 7 mV on a full
scale of 3.5 V. Consecutive calibrations showed differences less than
.5% in measured sensitivity.
Figure 6.8 shows the smooth plate measurements before and af ter
the total experiment. It appears that the measurements are rel1able
only for Reynolds numbers above 2.105 The measured friction
coefficient is about 10% above the value predicted by Schlichting's
formuia. This is presumably caused by the the fact that the boundary
layer develops in a favourable pressure gradient as discussed in §3.1.
In figure 6.9 the results of the drag measurements above the
different plates are summarized. The largest reduction (7%) is found
with plate RR. Also indicated are the speeds and plates at which the
visualisation experiments took place. Unfortunately the results of the
drag balance measurements came too late to help in choosing the
optima I speed for the visual1sation experiments. Also remarkable is
the difference in behaviour of the plates at higher Reynolds numbers,
although the grooves (with the exception of plate RF) are all of the
same height. Apparently the concept of protrusion height is also
applicable in this region but now for indicatlng the effectlve
roughness height. The protrusion height appears to he approximately
proportional to an equivalent sand roughness height.
The results of the direct drag measurements indicate that all
surfaces show some drag reduction. The precise velocity at which the
111
Flgure 6.6 The calibration balance.
3500
3000
2500
2000
~ 1500
1000
500
o o 200 400 600 800 1000 1200 1400
weight mg
Flgure 6.7 Typical calibration curve of the balance. + calibration points. -------best fit third degree polynominal.
112
+
7
+ ~
6 +
103C, + +
+ 1 5 + + t + + * +
-#" *. t 1: t * tt
t+) •• 4 1.2 1.5 2 3 4 5 6 8 10 l;-+t
·5 10 Rex
Flgure 6.8 Smooth plate drag measurements before and af ter all the grooved plate measurements.
maximum drag reductlon occurs is at a groove spacing s+ of Less than
15. somewhat contrary to the optimal spacing found by other authors.
There are several alternative explanations. Further research is needed
to decide which one applies:
I The sensitivity of the balance to pressure forces is
underestimated. rhe s11 ts along the grooved plates are somewhat
higher than those along the smooth plate so the grooved plates are
more and differently affected by the pressure forces.
11 Reynolds number effects. rhe measurements of the balance are
done at low Reynolds numbers near the transition to turbulence.
Ihis could affect the position of the optimum.
111 The drag reduced boundary layer is not completely adjusted to
the grooves. The beg inning of the drag plate is about 12 a downstream the change from smooth to grooved. the end is 37 a downstream the change. (These numbers are only approximate. the
exact values depend of course on the mean flow velocity) . It is
Flgure 6.9 Grooved plate drag measurements. Vertical bars indicate the Reynolds numbers at which the visualisation studies were performed, the points indicate which plates were studied. The thick, straight !i ne is the Cf(Rex ) accordlng to
Schlichting's formula.
possible that the boundary layer needs a longer distance before it
is completely adjusted to the new grooved surface.
IV Ihe balance i tself alters the pressure distribution and
distorts the boundary layer development in the channel. So locally
around the drag plate the pressure gradient in the channel could be
higher than measurements'over a longer distance seem to indicate.
From a technica 1 point of view the balance operates now
satisfactorily: Calibration curves are repeatable within 1 promille of
ful! scale (15 mN) and can perfectly be fi tted with a third degree
polynominal. Reproduèibility of stress measurement is 1% between U = 70 - 380 mmls (maximum ± .3 mPa error).
114
Chapter 7 Discussion and suggestions for further research.
In the previous three chapters we presented the experimental
data collected so faro Now is the time to connect these data with the
theoretical ideas stated in chapter 2 and also with more speculative
ideas. Evaluating this we will try to point out .some areas of further
research.
Both the windtunnel measurements and the water channel point
'measurementsshow only marginal changes in the mean velocity profile.
A decrease in Reynolds shear stress (-uv) is observed at both
measurement sites and the amount is comparable with the reduction in
wall shear stress. The combination of both facts means that the
relation between velocity gradient and shear stress is affected (the
mixing length 2). which questions the very validity of the present
statistical turbulent models in this type of flow. Itis. however.
possible that the difference in veloei ty profiles imp lied by the
difference in shear stress profiles falls within the experimental
errors.
A decrease in u' is observed at all veloeities. the maximum of
u' is ca 10% lower. Significant changes in third order correlation ~
are observed. but the changes in the other quantities Vü2. uv2 and ~
are less pronounced and probably not statistically significant. The
first observation indicates a change in the ratio between shear stress
and turbulent kinetic energy a = -üV / (u' 2 + v· 2 ). This indicates
again a breakdown of the turbulent modelling. which of ten assumes that
a is constant. The measurements show also that on a spanwise grooved
wall the ratio a is largely unaffected. The fact that those changes
also occur at higher speed. outside the range of maximum drag
reduction. leads to the speculation that the observed effect on the
drag is the outcome of two opposing processes:
I The increased surface ·area of ribs penetrating the boundary
layer whichs tends to increase the drag.
11 The influence on the turbulent structures near the wall which
tends to inhibit the turbulent momentum exchange and thus lowers
the drag.
It also sustains
visualisation experiments
the assumption
which study
115
that the
particularly
outcome of the
the turbulent
structure near the wall (the second process), is not very sensitive to
the precise velocity of the flow.
The results of burst detection in the buffer layer are somewhat
ambiguous. Although some differences in burst frequency can be
detected it is questionable whether they are significant. Particularly
if one considers the potential influence of choosing a different
reference height or trigger level. The dependence on trigger level
which Is similar In all cases, leaves only two possible conclusions.
Either no changes occur in the boundary layer, or the method itself Is
not sensitlve to changes in turbulent structure. The last possibility
is reinforced by the observation that the shape of ave rage .vertical
velocity component during a burst over a spanwise grooved wall is
drastically changed without a very clear effect on the burst frequency
measured.
The study of the visual flow patterns did not indicate that
different turbulent structures exist above a longitudinal grooved
wall. In particular the low speed streaks are still visible. To the
naked eye some differences in the details of the turbulent structures
between smooth wall and longitudlnal grooved wall flow are also
visible but they are difficult to quantify. The following observations
apply :
I
11
The flow appears to be more chaotic.
Near the wall the bubble lines show small wiggles of the
spacing as the riblets, which are clearly caused by the
riblets.
III The apparent length of the low speed streaks is shorter.
same
IV It is observed that the low speed streaks are not attached to
the riblets, the minima clearly meander over the topsand
valleys.
When we try to summarize the visual differences between the
smooth wall flow and the transverse grooved wall flow, we note the
following points:
I The flow appears to be more regular.
11 The low speed streaks are more intense, the minima are lower.
The most obvious conclusions are:
I The longitudinal riblets hinder the formation of low speed
streaks, without completely inhibi ting U~em.
116
11 If there Is more wall shear stress low speed streaks bacome
more pronounced.
With LDA measurements, performed slmultaneously with
vlsuallsatlon we are able to investigate the relation between low
speed streaks and shear stress. rhe moments of large instantaneous
Reynolds shear stress cannot ba indentified wUh a single structure
visible in plan view, instead both in high speed regions and in low
speed streaks there can be a large amount of momentum transfer. No
simple clear connection appears between large toont and instantaneous
Reynolds shear stress as measured wi th LDA and the v isual ised low
speed streaks. This indicates that the momentum transport is
presumably a property of the complete set of structures and their
interactions in the lower part of the boundary layer and not of only a
single structure.
This is, however, not the complete story. Statistical analysis
shows some shift in distribution of structures seen at posi tions at
which Reynolds shear stress is extreme compared to the distribution at
random points. So in a statistical sense there is a connection but
this does not translate in a direct cause and effect relation. A more
direct clue is the observation that the vertical velocl ty in a low
speed streak on a grooved wall is nearly zero although this needs to
be confirmed by more elaborate measurements. This implies a lower
momentum transfer in such a streak.
As is noted in chapter 2 the current ideas are not adequate to
obtain a quantitative estimate of the amount of possible drag
reduction . The experiments indicate that only the flow in the buffer
layer and below is affected by the grooves. A model should concentrate
on phenomena which occur there: the change from momentum transfer by
viscous forces to turbulent ' exchange. The first stage of this process
is apparently the format ion of low speed streaks (and of course the
high speed regions in between) . An extension of the laminar flow
calculations (§2.2) with secondary flow could" give insight into the
flow but it will not predict drag reduction .
For practical purposes and perhaps also to provide more ideas
for the theor ies, an extension of the measurements to f lows wi th
different pressure gradients could ba helpful. Much could be learned
also by performing the experiments on a set of geometrically scaled
grooves over a range of Reynolds numbars as large as possible.
117
A different ideais the application of the theory of Perry ea
[1986]. They considered the turbulent boundary layer flow as composed
of wall attached structures. The size and frequency of these
structures follow certain sealing laws. Assuming the destruction of
those structures by the grooves the influence on the spectra and
velocity profiles can be estimated.
From the present thesis it is hopefully clear that the problem
of turbulent drag reduction is far from solved. This is not surprising
because turbulence itself is a subject which is barely understood. An
implication of this statement is that whichever experiment is
performed over a grooved wall. it should also be done on a smooth wall
as a reference. A second lesson. now that the simple ideas do not seem
to work properly. is that seriously more effort should be put in
developing a theory which has at least the potential to explain the
drag reduction.
118
Appendix A Tbe method of Head applied to the waterchannel flow.
Head's method to calculate the development of a turbulent
boundary layer is an integral method which uses three ordinary
differential equations to solve for the unknowns e (the momentum loss
thickness), H (the shape factor ö*/9) and Cf (the friction
coeff icient) .
The equations used are:
with empirically determined algebraic functions:
{ 0.8234
1.5501
(H - 1.1)-1.287 + 3.3 H ~ 1.6
(H - 0 . 6778)-3.064 + 3.3 H ~ 1.6
F = 0.0306 (H 1 - 3.0)-0.6169
which describe the entrainment of the boundary layer.
Von Karman's equation:
de 9 dU 1 dx + (2 + H) ij a;c<" = 2" Cf
co
and the Cf law given by Ludwieg and Tillmann [1949]:
Cf = 0 . 246 10-0 . 678 H R -0.268 • ee
In order to predict the pressure gradient too, we extend the
system by an equation which describes the conservation of mass flowing
through a channel with constant width wand height h :
~ [ Uco (w - 2 H 9) (h - H 9) ] = 0
119
The interaction between the side wall boundary layers and the
bottom boundary layer is not taken into account in this equation.
Nevertheless 1f a « wand e « h the accuracy of this equation is
acceptable.
Ihis set of equations can be used with any standard method to
solve a set of ordinary differential equations to obtain aprediction
of the boundary layer development.
120
Appendix B Accuracy of the spanwise velocity correlation.
In §5.4 is explained how 500 instanteneous spanwise velocity
profiles are used to estimate the correlatlon function. A previous
experiment using 2000 profiles and also physical intuition indicated
that 500 profiles is areasonabie amount to obtain an accurate
estimate of the correlation function and the other quantities of
interest.
Such an experlmental result, however, is always obscured by
unknown influences like a possible drift in velocity • a change in
lighting and various other circumstances. A mathematical and
statistical analysis to determine the minimum number of profiles
needed for our purpose yields very unwieldy formuias . Therefore an
additional numerical simulàtion was made.
We proceed in two steps. First a large number (2000) artificial
velocity profiles must be generated. These profiles must mimic the
statistical properties of the natural velocity profiles. Secondly we
derive the statistical quantities we are interested in, from different
sets of velocity profiles.
The creation of the artificial velocity profiles is done in
several steps: We generate a sequence xi (i = 1. .100000) of random
numbers between -0.5 and 0.5 and pass it through a digital filter,
giving a new sequence Yi . Inspecting the experimental results it was
determined that a satisfactorily approximation of the real correlation
function can be obtained using a damped, oscillating impulse response
h(z) for the filter. A general formuia for this Is:
h(z) -az e sin(boz)
The advantage of this formula is that it . has a simple z-transform
whlch can he used to calculate the digital filter constants needed.
The actual transformation is .done uslng the formula:
121
Yi = al x1- 1 - bI Yl-1 - b2 Yi - 2 -a
sin(b) al = e
bI = 2 e -a
cos(b)
b2 = e -2a
It is only fair to note that experiments lndicate that
correlations functions measured in turbulent flows have a slower than
exponential decay [see eg Hinze 1972]. This means that the numerical
experiment can give a somewhat more optimistic view than really
warranted. But a non-exponentially decaying function has no simple
z-transform and compllcates the mathematlcs.
The procedure described here leads to a sequence Yl with a zero
mean and a rms value cr of y
and a correlatlon function ~ (z) of yy
~ (z) yy
cr; e -az [ cos(bz) + !b sin(bz) ]
The actual values used for a and b are: a = 0.18 and b = 0 . 25. These
va lues are such that we obtain a correlation function of the correct
width (first zero point at 10) and with a first minimum of a depth of
.1. The generated sequence Yi (i= 1 .. 100000) has a rms value of 0.275.
the theoretical correct value is 0 .2760. The agreement is
satisfactorily. The numbers of the sequence Yi are multiplied by 25.
and incremented with 50. to put them in the range of the numbers from
the actual experiments. Next. the resul ting numbers are rounded and
stored on disk in 2000 groups of 50. just as the sequences from the
experiments are stored. The sequences generated in this way mimic the
behaviour of the proflles stored in the water channel experiments.
With the computer programsused in the actual experiment we can
now extract the statistical quantities. We present the results of this
exercise in Table B.la-d. Table B.la displays the numbers as they
122
theoretically should beo The columns show from left to right the
position along the wire (the z-coordinate). the ave rage velocity. the
rms value of the velocity. the correlation function and an estimate of
the variance of the correlation function. Table B.lc gives the numbers
derived from the 500 artificial profiles together with an estimate of
the variance of the correlation (5th column). The variance in the rms
value of the velocity is about 5%. The width and the depth of the
Brst minimum of the correlation function are reproduced wi th an
accuracy of 1% and 10% respectively. The deviations from the
theoretical curve are in line with the estimate of the variance which
is provided.
The numerical experiment also indicates that the averaging over
125 profiles (tabIe B.lb) can lead to an error of 30% in the dep th of
the first minimum. This would be unacceptably high for our purposes.
The averaging over 2000 profiles (tabie B.ld) leads of course to more
accurate results. The increase in accuracy is. however. only marginal.
The conclusion is that under ideal circumstances 500 velocity
profiles are enough to reconstruct the correlation function with an
accuracy suited to our demands.
123
Tabla B.1 Results from artificially generated bubble line data. a: exact results. b: results from averaging over 2000 sequences. c: averaging over 500 sequences, d: averaging over 125 sequences.
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130
Sunmary.
The subject of this thesis is the recently discovered phenomenon
that the friction factor (the so called Cf coeffic1ent) of a flat
plate can be decreased by coating the surface with small longitudinaI
grooves. This phenomenon occurs in a turbulent boundary layer flow and
apparently the grooves are able to influence the eddies in the flow in
such a way that the stress transport shows a 7% decrease.
Some. ideas and theories to explain this phenomenon are proposed
in the literature. Chapter 2 reviews these theories. The phenomenon is
very complex, like all turbulent flow problems, and the ideas stated
are not a complete explanation of thls unexpected and contra intuitive
phenomenon.
In order to enable the development of further theories
experiments are performed. These are discussed in the chapters 3 to 6.
The experiments are mainly performed in a low speed water channel but
some addi tional measurements have been done in a windtunnel. The
measurements can be distinguished into th ree parts: the single point
measurements (chapter 4), the visua11sation experiments (chapter 5)
and the direct drag measurements (chapter 6). The measurements show
the occurrence of drag reduction even at the low Reynolds numbers used
in the method of hydrogen bubble visua11sation. The effect of the
grooves on the turbulent burst frequency differed from the description
in 11terature. The visua11sation experiments show further that the
grooves influence the flow only ,rather marginally.
In chapter 7 is discussed how the ideas proposed in the
11 terature are tenable in relation to the experimental findings in
this thesis It appears that the most obvious ideas are not completely
justified in their uncorrected version.
131
"Samenvatting.
Het onderwerp van dit proefschrift is het recent ontdekte
verschijnsel dat de wrijvingscoefficient (de zogenaamde Cf-waarde) van
een vlakke plaat verminderd kan worden door het aanbrengen van kleine
longitudinale groeven op het oppervlak. Dit effect treedt op bij een
turbulente grens laag stroming en klaarblijkelijk zijn de groeven in
staat een zodanige invloed op de wervels in zo'n stroming uit te
oefenen dat het schuifspanningstransport met maximaal ongeveer 7%
verminderd wordt.
In de literatuur worden enige idee~n en theori~n geopperd om dit
verschijnsel te verklaren. Hoofdstuk 2 geeft een overzicht hiervan.
Het verschijnsel is echter zeer complex, zoals alle turbulente
stromingsproblemen, en de geopperde idee en vormen een verre van
volledige verklaring van dit intuïtief niet verwachte verschijnsel.
Om een betere theoretische beschrijving mogelijk te maken, zijn
experimenten uitgevoerd. Deze worden in de hoofdstukken 3 tot en met 6
beschreven. De experimenten zijn grotendeels verricht in een lage
snelheden waterkanaal, terwijl enkele aanvullende metingen in een
eveneens lage snelheden windtunnel verricht zijn. Ze kunnen worden
onderscheiden in drie gedeelten : de eenpunts snelheidsmetingen
(hoofdstuk 4) , de visualisatiestudies (hoofdstuk 5) en de directe
schuifspanningsmetingen (hoofdstuk 6). Uit de metingen blijkt dat het
effect van de wandwrijvingsvermindering ook optreedt bij de lage
Reynoldsgetallen die bij de methode van waterstofbellenvisualisatie
gebruikelijk zijn. Het in de literatuur beschreven effect op de
turbulente burstfrequentie kon niet bevestigd worden. Uit de
visualisatie blijkt dat "de groeven de stroming slechts op tamelijk
marginale wijze beinvloeden.
In hoofdstuk 7 wordt tenslotte een overzicht gegeven in hoeverre
de geopperde ideeen houdbaar blijven in het licht van de experimentele
resultaten. Het blij~t dat de meest voor de hand liggende idee~n in
ongewijzigde vorm niet volledig juist zijn.
132
Dankwoord.
Dit proefschrift was nooit tot stand gekomen zonder de hulp van
velen.
Zonder de inzet van drs. A. Koppius. dr. K. Prasad en ing. C.
Nieuwveldt was het project Dragreductie van het STW nooit ontstaan.
Ook de inzet en het enthousiasme van prof. dr. ir. G.Ooms. en zijn
bereidheid dit werk tot het einde toe te blijven begeleiden stemmen
mij tot dankbaarheid.
Ook alle leden van de werkeenheid Turbulentie hebben veel bijge
dragen. Met name de inzet van ]. Stouthart bij het ontwerp en gebruik
van de balans is onmisbaar geweest. Uiteraard zou deze zonder de hulp
en het meedenken van mensen op de diverse werkplaatsen van de TU niet
tot stand zijn gekomen.
De samenwerking met de TU Delft in de personen van prof. dr. F.
Nieuwstadt. ir. H. Leijdens. W. van Dam. F Verhey is altijd plezierig
verlopen en heeft zeker bijgedragen aan de opzet van dit proefschrift
te verbreden.
Verder ben ik erkentelijk voor de bijdragen en inspanningen van
de studenten van de TU Eindhoven (in chronologische volgorde) H. Smol
ders. ]. Kern. T. Gielen. C. Lamers en C. Delhez.
Curriculum Vitae.
3 januari 1959 Geboren in Eindhoven.
17 juni 1977 Diploma Gymnasium ~.
23 maart 1983 TH Eindhoven; diploma Technische Natuurkunde.
20 april 1983 - Wetenschappelijk assistent bij Technische 14 juli 1983 Hogeschool Eindhoven.
15 juli 1983 -15 juli 1987
1 sept 1987
In dienst bij STW/FOM. voor project Drag reduction. Werkzaam aan TU Eindhoven bij de vakgroep Transportfysica
Werkzaam als wetenschappelijk medewerker bij het VEG-Gasinstituut te Apeldoorn.
1~
Stellingen.
Behorende bij het proefschrift van
C.J.A. Pulles
Eindhoven , 4 maart 1988.
1 Het aantonen van verschillen in turbulente grenslagen boven een
gladde en boven wrijvingsverminderende oppervlakken is slechts zinvol
als er een relatie met het schuifspanningstransport gelegd wordt .
Dit proefschri ft .
2 Het optreden van wrijvingsvermindering in turbulente grens lagen
maakt de beperkingen van de huidige, .op statist i sche sluitingsrelaties
gebaseerde turbulente modellen duidelijk .
Di t proefschrift .
3 Het meten van burstfrequenties als indicatie voor kleine verschillen
in schuifspanningstransport is alleen dan zinvol wanneer meer bekend
is over de. relatie tussen burstfrequenti e , schuifspanning, detekt i eni
veau's en effectieve meethoogte boven een ruwe wand .
J .M.G. Kunen (1984) , On the detection of coherent structures i n turbu
l.ent. fl.OlDS . Thesis . Del.ft University Press .
Dit proefschrift.
4 Het ontbreken van een fundamentele theorie over turbulentie vermin
dert de waarde van indirecte methoden ter bepaling van de wandwrij
ving, met gebruik van empirisch bepaalde grootheden ten zeerste.
Dit proefschrift.
5 Voor het meten van instantaan schuifspanningstransport in een turbu
lente grenslaag beperkt men zich meestal tot de Reynoldse schuifspan
ningscomponent. Maar met name dicht boven wrijvingsreducerende opper
vlakken zijn de resterende visceuze krachten een belangrijke parameter
J.M.. Wallace, J. BaUnt B P. VuJwslauceuic 1987 On the mechanisllt of
uiscous drag Reduction using streamwise aligned riblets: a reuiew with
some new results. Proc. Int. Conf. on Turb. Drag Reduction by Passiue
Means ., Roy. Aer. Soc., London.
6 Om te kunnen beslissen welke metingen goed zijn en welke niet
gebruikt een onderzoeker vooroordelen over het verschijnsel dat hij
onderzoekt. Met andere woorden metingen worden gebruikt ter
bevestiging van eigen en andermans vooroordelen.
N. Cartwright 1983 How the lQlOS of physics Ue. CLarendon Press,
Oxford.
7 Het gebruik van een waterkanaal in plaats van een windtunnel bij
experimenten met turbulente grenslagen is alleen dan te overwegen als
er voldoende tijd is. De factor honderd verschil in noodzakelijke
meettijd maakt een stage met waterkanaal experimenten voor de huidige
twee fasen studenten niet aantrekkelijk.
8 Als de groeven op haaienhuiden inderdaad de functie hebben de wrij
vingsweerstand te verminderen, dan verdient het overweging schilvers
van geschikte afmetingen te mengen in de verf waarmee schepen geschil
derd worden. Door slijtage van de verflaag kunnen dan de