Drag reduction of turbulent boundary layers by means of grooved surfaces

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. Technische

Universiteit Eindhoven. https://doi.org/10.6100/IR280307

DOI:

10.6100/IR280307

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Published: 01/01/1988

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DRAG REDUCTION

OF

TURBULENT BOUNDARY LAYERS

BY MEANS OF GROOVED SURFACES

DRAG REDUCTION

OF

TURBULENT BOUNDARY LAYERS

BY MEANS Oir GROOVED SURFACES

Proefschrift

ter verkrijging

vim

de graad van doctor aan de

Technische Universiteit Eindhoven, op gezag I

van de Rector Magnificus, prof. dr. F.N. Hooge, I

voor een commissie aangewezen door het College

van Dekanen

i

~

het openbaar te verdedigen op

vrijdag 4 maart 1988 te 16.00 uur door

CORNELIS

J~HANNES

ADRIANUS PULLES

Dit proefschrift is goedgekeurd door de promotoren: Dr. ir. G. Ooms

en

Prof. dr. ir. G. Vossers Co-promotor:

Dr. K. Krishna Prasad

This research has been supported by the Nederlands Technology Foundation (STW) as part of the program of the Foundation for Fundamental Research on Matter (FOM)

Drag reductlon of turbulent boundary layers bv means of grooved surfaces.

Contents

List of symbols.

Chapter 1 Introduetion.

§ 1.1 Historie review.

§ 1.2 Short deseription of smooth wall

turbulent boundary layer.

§ 1.3 Strueture of this thesis.

Chapter 2 Summary of existing ideas. theories and 5 7

experiments. 9

§ 2.1 Survey of different means of obtaining

drag reduetion. 9

§ 2.2 Ideas and theories eoneerning

drag reduetion. 12

§ 2.3 Experimental results from literature

eoneerning drag reduetion by means

of mierogrooves. 23

Chapter 3 Experimental setup. 29

§ 3.1 Water ehannel. 29

§ 3.2 Measurement system. 34

§ 3.3 Deseription of the roughness types. 37

Chapter 4 Point measurements. 42

§ 4.1 Introduetion. 42

§ 4.2 Profiles. 43

§ 4.3 Detailed point measurements. 51

§ 4.4 Conelusions. 62

Chapter 5 Hydrogen bubble visualisation. 63

§ 5.1 Introduetion. 63

§ 5.2 Deseription of the experimental set-up. 65

§ 5.3 Some tests of the method. 70

§ 5.4 Results of the automated visualisation

experiment.

§ 5.5 Results of the visualisation with

LDA measurements.

§ 5.6 Conelusions.

Chapter 6 Drag measurements.

75

77 89 93

§ 6.1 Survey of different methods of measuring drag.

§ 6.1.1 Indirect methods. § 6.1.2 Direct methods.

§ 6.2 Drag balance Delft.

§ 6.3 Design considerations of the drag balance.

§ 6.4 Some additional design formula of the balance.

§ 6.5 Sensor.

§ 6.6 Measurements and results.

Chapter 7 Discussion and suggestions for further research.

Appendix A rhe method of Head applied to the water channel flow.

Appendix

B

rhe accuracy of the spanwise correlation function. References. Summary. Samenva t Ung. Dankwoord. Curriculum vitae. 93 93 97 99 99 104 110 110 115 119 121 126 131 132 133 133

List of symbols. Roman symbols. A a B b Cf D H h k I! P P p U u u

*

u U

..

v

v v

w

x y

*

y z

van Driest constant

ratio between Reynolds shear stress and turbulent intensity

constant in Spaldings formuia groove width

friction coefficient pipe diameter

shape factor of boundary layer 9/ó* groove height

trigger level in burst detection procedure mixing length

pressure

pressure gradient parameter

velocity component in the direction of the free stream direction.

fluctuating part of

U. U-U

rms of U

shear stress velocity

~

w

free stream flow velocity

velocity component at right angles with the surface

fluctuating part of

V.

V-V

rms of V

spanwise velocity component

distance from start of boundary layer vertical distance from surface

viscous length v/u* spanwise distance

Greek symbols.

ó boundary layer thickness

[m]

[m]

[m]

[mis] [mis] [mis] [mis] [mis] [mis] [mis] [mis] [mis]

Cm]

Cm]

Cm]

Cm]

Cm]

6* displacement thickness Cm]

E- dissipation of turbulent energy [J/kg]

Tl dynamic viscosi ty . [kg/m s]

e

momentum loss thickness Cm]

K. von Karman's konstant 0.41

À. low speed streak spacing Cm]

kinematic 2

v viscosity [m /s]

p density [kg/m3 ]

T total shear stress [N/m2]

Tl viscous shear stress [N/m2]

Tt turbulent shear stress [N/m2 ]

T wall shear stress [N/m2 ]

w

Superscripts

(overbar) ave rage value. time or ensemble ave rage

Chapter Introduction.

§ 1.1 Historie review.

Time af ter time nature provides us withunexpected phenomena. Although very common, turbulence should be reckoned among them. It is surprising to observe how a smooth laminar flow through a pipe, sudden ly becomes chaotic. Osborne Reynolds [lB9S] was the first to investi-gate this phenomenon in some depth.

During the years most schol ars used the obvious random nature of turbulence in order to f ind a sui table model. WeIl known is the reasoning of Kolmogorov [1941] which provides an estimate of the length and timescales involved. It rests heavily on the assumption of scale invariance of turbulence.

During the last two decades it became clear that turbulence is not as random as a first glance would suggest. Patterns are detected in wall boundary layers, jetsand pipe flow [see eg Kunen 19B4]. And literature is filled with descriptions of "bursts", "horse-shoe vorti-ces", "low speed streaks" and other coherent structures, which were detected by experimenters. Some of those structures are also observed in other turbulent flows. like turbulent jets and free shear layers.

'Still more recent is the application of mathematical ideas of strange at tractors and chaotic systems to turbulence [Eckmann 19B1

J.

No unification with the former ideas is apparent yet.

i

Also noted was the easy way turbulence was modified. for instanee by suction or blowing and numerous other devices. Apparently turbulence is a very complex phenomenon and therefore i t can be influenced in many ways. T~ date no satisfactory theory describing turbulence is available but most scholars believe that all the necessary information is contained in the Navier-Stokes equations. Up till now no evidence to the contrary is available. Moreover, the direct simulation of very simple turbulent flows is just within reach of existing supercomputers [Kim ea 19B7J. and this simulation shows many of the features observed in real turbulent flows (figure 1.1). For instanee the logarithmic velocity profile with approximately the correct coefficients is reproduced. Also reproduced are the long streaky flow patterns near the wall.

3.0.---,

2.S

w~...

..

~: :::.;.

.

~.~.~:

..

--

l.--~.~.-..-:=

~,:-" ,

Figure 1.1 Some resul ts of direct numerical simulation of a turbulent channel flow [Kim ea 1987]. ---u'/u*, ---- v'/u* and •••• w'/u*. Symbols represent the data from Kreplin

&

Eckelmann

* * *

[1979]: 0 u'/u, A v'Ju and + w'/u .

One of the simplest turbulentflows is the turbulent boundary layer flow. of an incompressible Newtonian medium. This was and is still the subject of numerous studies including the present one.

A new unexpected effect in turbulence, perhaps connected wi th the coherent structures and discovered even more recently is the phenomenon of drag reduction. Although there are many ways of reducing drag (see § 2.1) this thesis is concerned with drag reduction obtained

with microgrooves. The first clue directing to the existence of this effect came from zoological studies. Reif and Dinkelacker [Reif 1976] pointed out thàt many sharks had skins covered with small longitudinal riblets. They also conclude that the grooves should provide sorne evo-lutionary advantage and conjectured they improved the swimrning capaci-ties of the sharks by lowering the surface drag. This is supported by the fact that species of sharks, known to be fast swimmers, had smal-ler grooves than the slower species. Turbulent length scales near a wall are proportional to the surface shear stress tothe power~. For a flat plate this stress is roughly proportional to the square of the free stream veloei ty, so the size of the grooves has to decrease approximately inversely proportional wi th the speed of the shark to remain effective.

A different stimulus for seeking af ter means to obtain drag reduction came from looking at graphs which describe the surface drag at different velocities (figure 1.2). The difference between the drag, extrapolated from the laminar regime and the actual drag measured in the turbulent regime suggest that i f one could stabilize the flow somewhat and keep it more laminar one could reduce the drag by a fac-tor 4 or more.

The microgrooved wall was first studied by Walsh [Walsh 1976J. He found a maximum drag reduction of 7%. A reduction of this relativi-ly small amount can certainrelativi-ly have a technica I application. Provided the cost of installing and maintaining the grooves is low enough they could be applied to the wings and bodies of large-sized airplanes. Bertelrud [Savill

&

Rhyming 1987J argues that a decrease of 10% skin-friction of an airplane leads to a 1% decrease of operational cost which is important enough to consider its use. Test flights were plan-ned by NASA in the course of 1986, which gave encouraging results. In

1Ö3r---~

Flgure 1.2 Local skin friction factor in laminar and turbulent

-'A

boundary layers. a: laminar flow Cf

=

_{.646.Rex ' b: turbulent}

-1/5 .

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.

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 _ro

<

ij. The outer layer. Above the logarithmic region the 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 C_dx

<

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.

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

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.

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 ACOUST1C~ __

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.

, 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]. Entry Sou ree Solvent Polymer Molecular Coneentration Pipe

Weight w.p.p.m. Dnnn

A

_}

Elata ea Water , GCM 50105 400 50.7

,

[l966J BOD

0

}

Goren ea Water PEO 50106 2.5 50.8

•

[1967J 10

v Patterson ea Cyclo- PIB 50105 2000 25.4 [1969] . hexane

~

}

Seyer ea Water PAMH 30106 1000 25.4

•

[1969] 0

}

Virk ea Water PEO 6.90105 1000 32.1

Ij 1.0 iS . 2 0.8 E

:

1

0.6 ~ <> ~l; ~ Óó ~ <> " • ~

"

o i9v~ ~~: <> v

..

v ..

:a

0.4

•

] 0.2

•

0.1 0.2 0.3 0.4 O.S 0.6 0.7 Volumetrie fraclion o( air. QJ(Q. + Q ... )

Flgure 2.3 The effect of injecting micro air bubbles in wall layers [Madavan ea 1985J.

Also considered are large eddy breakup devices (LEBU·s). These are thin ribbons, mounted parallel with the wall in spanwise direction (see figure 2.4). These devlces generate a wake. Over a certain distance downstream the point at which the wake reaches the wall a

large reduction in wall shear stress occurs. Experiments indicate that this reduction more than compensates for the device drag, leading to a net drag reduction of the order of 5 per cent. Combinations of stacked or paired ribbons are also considered [Saviii 1986J.

The use of compliant walls is a different method of obtaining drag reduction [Bushnell 1978J. Due to difficul ties of matching the impedance of the wall to the flow, these wall scan only be used in liquld flows and not in gas flows.

t _ ,

O'IATPIATI

OLl"," .... O' •• l1 ... ,u. "" ••

u..0W!_

...

Figure 2.-4 The effect of large eddy breakup devlces (LEBU' s) [Savl11 1986J.

. § 2.2 ldeas and theories concerning drag reduction.

We will now briefly sununarise the classical picture of walls

with surface roughness as provided, for instance, by Schlichting

[1979]. Walls are considered hydrodynamically smooth when the

. +

roughness helght does not exceed the viscous sublayer thickness (h

<

5). These walls have the smooth wall friction coefficient. A

dimensionless roughness height larger than 70 y+ leads to a completely rough wall flow. as all of the roughness elements penetrate into the

logarithmic region.

coeff icient.

These walls have an increased friction

These considerations are derived from drag measurements as performed by various experimenters. The results are neatly compiled in figures 2.5 and 2.6 which show the local skin friction coefficient of a smooth and rough flat surface [Schlichting 1979]. Figure 2.5 shows the resul ts of drag measurements on a smooth plate compared wi th several empirical formulas. The scat ter of the experimental data exceeds 10%, which is an indication of the difficul ties one will

encounter if one wants to establish the 7% drag reduction, obtained by

means of microgrooves. The line 1 describes the friction coefficient of a laminar boundary layer. Line 3a and the measurements of Kempf show i ts behaviour during the trans i tion from laminar to turbulent

flow. The other lines and measurements describe tripped boundary

layers which are fully turbulent.

F igure 2.6 shows the local skin friction on a sand-roughened

plate. For a given roughness parameter ks' which is a length

describing the size of the roughness elements. the ratio xIk is

s constant, even if the free stream velocity is changed. So the lines

xlks

=

const in figure 2.6 describe the skin friction coefficient of a

roughened plate if one varies the free stream velocity above it. Below a certain velocity the roughness does not lead to an increase in drag

and for high velócities the skin friction coefficient becomes

constant. Also lndicated are the areas (Reynolds numbers and roughness heights) covered by the present study. The dimensionless roughness

. +

heights discussed here are about 10·y in the drag reducing regime,

...

....: U

,

,

7 . i SI-~" 1

o

Ol.!

o

1

,..

15 ~. 4

K3

_~. 1 f"'" [\.

'"

1:-- f1eiJSUred 1Jy: • Wieselsberger • Gebers 2 • froude • Kempf

....

• Schoenherr I 14. "'II~

!1

tl

_~

_~. 1 V.15 115J • Si 'f)'1S 115J ~ 56 if)1 IS 27SJ • S6

'ti'

IS 1151. S6 '11 !5 1153 , S Rel

Flgure 2.5 Resistance formula for smooth flat plate at zero incidence: comparison between theory and measurement. Formula's:

-112

1 Cf 1.328 Re (Blasius)

2 Cf .074 Re-1/5 (Prandtl)

3 Cf 455 (log Re)-2.58 (Prandtl-Schlichting)

-2 58

3a Cf

=

.455 (log Re) . - AlRe

-264 4 Cf

=

.427 (log Re - .407) . (Schultz-Grunow) 15 10 _ 5

U

o

O l

o

z.s

,..

lS ~/Xp.. ~"z~, ~ ;><. ~

A

f

-"

_""

_'"

Î"-.

"-""

"-""

"

-.= . -

--..

"'-., ~

---.

---.

r---

r--:<~ ~ :::-f-

---.

--

---.

r

-

-B

s.;;;;;~~ 10' 1 5 10' 1 t;-CQMt ... -,

-

----,

-

-

--'::: ~ 5 'KI' .1 Rex 1 1

r

vJ

fw.

f'OS

1 2)'/0'

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).

· 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.

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.

· 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

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) ; U

_{o ;}

constant

The solution of this equation is described using the errorfunction:

U( y, t ) ; U

_o

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.

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 v (U + _{Uzz )} 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 :

u

_yy +

u

_zz

P

_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

=

U

_o

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

'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 U

_o

cannot be choosen freely, but must satisfy:

- 1 -2

Ua

=

Uuu(O)

=

h'+

2 P

p h

o

must be

We are now able to derive the expressions for the mass and momentum flux: M uu

h

o

_uu =

z

f

U

_uu (y)dy

o

h

Z

h

2 (

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

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 i f 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

L

h

r-I

r

h

L

...;:.

r

- S j

-:). '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 _{. p} versus element height h. with

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).

. + +

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.

2.0~----~--~---T---r---ïl---~---;

1.0

s/h

0.4L-______ ~ ______ ~~ ______ ~ ______ _ J _ _ _ _ _ _ _ _ ~ _ _ _ _ _ _ _ J

o

2 4 6 6

10

12

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.

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 0 0

1.1

0 0 o 0 §l,j9 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 ).

1.15 1.10

81.05

(,) "-;..1.00 (,) .95 c c c c c our data C1:J

0\

·T·_·--ClQ...·~'

-

,

-~

Walsh'

.'~~

.90 0!:---=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.

1 0 - 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. .6-0 .6-0 .. 0 0 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.

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. Author s + h+ Re reduction method Gallagher 1984 15 15

-

-

1200 (9) :::: 2% momentum loss Walsh 1982 15 13 :::: 1300 (9) 7% drag balance Bechert 1986 15 7 :::: 1000 (9) 7% drag balance Nitschke 1984 16 5 20000 (0) 3% pressure drop Nitschke 1984 12 11 16000 (0) 4% pressure drop Sawyer 1987 12 10 :::: 1000 (9) 7% drag balance

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

•

_•

_••

_•

•

_•

_•

_•

_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.

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

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.

O E F 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 equili-ze 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. water-height 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.

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

0 0 0 0 0 0 0 0 0

~oo

00 I I

.2

Uw

mIs

.

3

Flgure3.4 Turbulent intensity in free stream at entrance.

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. U_m

175 mm/s.

e =

.8 mm). This leads to a pressure gradient parameter P of: p. p v dP 1

pdx

lE3

u .0021 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 . 161x .3 m2 measured U (1 m) _(I) 200 nrnIs 176 nun/s

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. 1.10 I 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

§ 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

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 preshiftlfreqUency 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.

!