The development of a microanemometer : new possibilities formeasuring very low air velocitiesCitation for published version (APA):Pluijm, M. J. F. P. (1987). The development of a microanemometer : new possibilities for measuring very low airvelocities. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR274691

DOI:10.6100/IR274691

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THE DEVELOPMENT OF A MICROANEMOMETER

New possibilities for measuring very low air veloeities

M.J.F.P. PLUIJM

THE DEVELOPMENT OF A MICROANEMOMETER

THE DEVELOPMENT OF A MICROANEMOMETER

New possibilities for measuring very low air veloeities

proefschrift

Ter verkrijging van de graad van doctor aan de

Technische Universiteit Eindhoven, op gezag van

de rector magnificus, prof. dr. F. N. Hooge,

voor een commissie aangewezen door het college

van dekanen in het openbaar te verdedigen op

vrijdag 11 december 1987 te 16.00 uur

door

MARTINUS JOHANNES FRANCISCOS PETRUS PLUIJM

geboren te Heerlen

Druk: Dissenatledrukkerij Wibro, H<!lmond.

Dit proefschrift is goedgekeurd door de promotoren

Prof. dr. J.A. Poulis

en

Prof. ir. j. Vorenkamp

Copromotor: dr. ir. C.H. Massen

Aan CherryL

en mijn ouders

TABLE OF CDN'I"I!lUS

1 . GENERAL INTRODUeTION. . . . . . . . . . . . . . . . . . ....................... 1

2. LOW-AIR-VELOCITY MEASURING PRINCIPLES .......................... 3

2.1 Introduetion

2.2 Review of low-air-velocity measuring principles

2.2.1 The Pitot static tube

2.2.2 Cup, vane and propeller anemometers

2.2.3 Hot-wire anemometers

2.2.4 Thermal marker and iontracing

2.2.5 The Sonic Anemometer

2.2.6 The Laser Doppier Anemometer

2.3 Conclusions and remarks

4

6

7

8

10

3. MEASURING PRINCIPLE OF THE MICROANEMOMETER .................... ll

3.1 Introduetion

3.2 The measuring principle

3.3 The microanemometer

3.3.1 The optica! detection system

3.3.2 The feedback system

3.3.3 The moving-coil meter

3.4 A first comparison of the usefulness of different

moving-coil meters as microanemometers

3.5 General considerations

4. CALIBRATION UNIT FOR MICROANEMOMETERS AT VERY LOW AIR

12

16

19

20

21

24

VELOeiTIES .................................................... 26

4.1 Introduetion

4.2 The calibration unit for microanemometers

4.3 Automation of the experiments

4.4 The characteristic calibration measurement

4.4.1 Supplementary calibrations

4.4.2 A characteristic calibration

4.5 Experiments and discussion

28

30

31

33

35

5. NUMERICAL ANM..YSIS OF 11fE FLOW AROUND 11fE MICROANEMOMETER ..... 36

5.1 Introduetion

5.2 The Navier Stokes equations

5.3 The Finite Element Metbod

5.3.1 Broad deseription of the metbod

5.3.2 Mathematica! formulation

37

39

5.4 Numerical results 43

5.4.1 Practical aspects and preliminary calculations

5.4.2 Velocity profiles and verification 45

5.4.3 Influence of the geometry of the cylinder 50

5.5 Conclusions and discussion 52

6 MEASUREMENTS WITH THE MICROANEMOMETER .......................... 53

6.1 Introduetion

6.2 Determining the microanemometer velocity range

6.3 Calibration measurements with different types of

microanemometers

6.3.1 Microanemometers with different pointer lengtbs

56

6.3.2 The influenee of the sphere 60

6.4 Comparison with literature: Cd vs. Reynolds curves 61

6.5 A first comparison with numerical results 64

6.6 Discussion 66

6. 7 The dynamic behaviour of the microanemometer 68

6. 7.1 Theory

6.7.2 Experiments

6.8 Discussion and coneluding remarks 71

7 MICROANEMOMETERS FOR MEASURING MULTIDIMENSIONM.. AIR VELOeifriES 72

7.1 Introduetion

7.2 Direetional sensitivity

7.2.1 Introduetion

7.2.2 Experiments todetermine G(~)

7.2.3 Experiments todetermine B(U.P)

73

75

76

7.3 The two-dimensional microanemometers: T2-90 and T3-120 79

7.3.1 Introduetion and definitions

7.3.2 Calibrations 82

7.3.3 Discussion 85

7.4 The three-dimensional microanemometers: D3-90 and 04-109 86

7.4.1 Introduetion and definitions

7.4.2 Numerical predictions of the D3-90 and the D4-109 88

7.4.3 Discussion 89

7.5 General considerations 92

8 MEASUREMENTS IN PRACTICE ........................................ 93

81. Introduetion

8.2 Measurements in our calibration unit determination

of wall effects

8.2.1 Experiments and results

8.2.2 Discussion

8.3 Measurements in laboratory fume hoods

8.3.1 Introduetion

8.3.2 Description of the experiments

8.3.3 Experimental results

8.3.4 Conclusions and discussion

8.4 Air veloeities in a surgical operating theatre

8.4.1 Introduetion

8.4.2 Description of the experiments

8.4.3 Experimental results

8.4.4 Discussion

RE FE RENCES

SUMMARY

SAMENVATTING

NAWOORD

a.JRRICULUM VITAE

96

97

98

100

102

104

106

109

110

114

115

116

118

1. GENERAL INTRODUCTION

In 1984 the project ' Development of a microanemometer was

started as a cooperation between the facul ties of Physics and

Architecture, Building and Planning at the Eindhoven University of

Technology. lts main objective was the development of a new cheap

type of microanemometer to enable measurements of air veloeities

of the order of 1 cm/s up to 10 cm/s to be made. This implied

lowering the velocity range of the commonly available

microanemometers by one decade.

Future applications of the microanemometer were focussed on our

cooperation with the department of Building Engineering. A number

of possible applications are given below.

* Measuring low air veloeities is of importance in airconditioned

spaces, such as surgical operating theatres, laborator i es and

clean rooms for microtechnics (Finck '78). In operating theatres

and their environment several zones of sterility have to be

maintained. Technically it is not possible to separate these zones

by walls. Air movements are caused by the pressure hierarchy: the

highest pressure should therefore be where the highest sterility

is required. Air movements are minimal and mainly occur in the

vicinity of the doors.

* Many physical measurements are carried out in rooms where

vent i lation is minimised (laboratories, balance cases).

Investigations of the influence of low air veloeities on weighing

in balance cases have been 1 i mi ted to theoret i cal approaches

(Massen et al. '86), because of the lack of adequate equipment to

measure such air velocities.

* Investigation of the indoor elimate in rooms with specific

requirements (Lammers et al. '84). To study the influence of

indoor elimate on human performance, research is restricted to

working situations without extreme physical conditions with their

inherent physiological consequences (such as high noise levels or

high temperatures). This research is focussed on office and

education situations where, in cooperation with scientists from

1

other disciplines, such as psychology and physiology, the

influence of illumination, acoustics, air and body temperature,

humidi ty and air veloei ties on human comfort is investigated.

Special attention is paid to undesired local cooling of the body,

draught, which is mostly determined by the frequency of variations

of the air velocity {Olesen '79, Olesen '85).

* In micrometeorological research (Desjardin et al. '86) and as a

device for detection of dangerous gases in coal and hard rock

mines (Skinner et al. '82) there is need for low-air-velocity

measuring devices.

Apart from these applications the challenge of extending the

lowest detectable air velocity was a stimulating enough reason for

starting the project.

The investigations described in this thesis can be swmnarised as

follows:

In chapter 2 the existing measuring principles are reviewed with

their possibilities, advantages and disadvantages.

As these principles are more or less unsuited to our purposes the

new measuring principle, developed to meet the special demands of

chapter 1, will be discussed in chapter 3.

In order to be able to de termine the lowest air veloei ty ~ which

could be detected with our new type of microanemometer, a

calibration unit was built and is described in chapter 4.

In order to be able to investigate the disturbance by the

microanemometer on the flowfield in the calibration unit the

veloeities in the vicinity of the microanemometer are calculated

in chapter 5, using the finite element method.

The calibration of the microanemometer wi tb the calibration unit

and the influence of the dimensions of the microanemometer on the

calibration is shown in chapter 6.

In chapter 7 a microanemometer is presented which is able to

measure simultaneously several velocity components.

This thesis is concluded with chapter 8 in which some application

measurements with the developed microanemometer are described.

2

2. IJJrf-AIR-VELOCITY MEASURING PRINCIPLES

2.1 INTRODUeTION

The literature describes several ways of detecting low air

velocities. A possible approach to dividing anemometry into

categories is given by Lilienfeld et al. '67 :

1. Instruments basedon the utilization of the kinetic energy of

the gas stream. Representative devices of this type are the

Pitot tube or the cup and propeller anemometers.

2. Instruments depending on the conductive-convective transfer of

thermal energy from a heat souree to the gas flow. The hot-wire

anemometer is a typical example of this group.

3. Instruments based on the tracer technique where the time

interval between the upstream injection of a tracer and its

downstream detection at a known distance is measured.

4. Instruments with which veloeities are determined from changes

produced in the characterics of waves propagating within the

moving medium {e.g. acoustic anemometers or Laser Doppier

Anemometers) .

It should be noted bere that in this enumeration, several types of

anemometers, such as the corona and glow-discharge anemometers

(Desai & Johnston '71) and the long-range Laser Doppier

Anemometers {Danielsson & Pike '83) are not taken into

consideration. As their minimum detectable air velocity is of the

order of approx. one m/s they are therefore not suitable for our

purposes. We should mention also that the above mentioned groups

can showsome overlap (e.g. the pulsed hot-wire anemometer).

In the next paragraph a review of some of the above mentioned

measuring principles will be given in a quasi bistorical approach.

3

2. 2 REVIEW OF LOW-AIR-VELOCI1Y MEASURING PRINCIPLFS

2.2.1 The Pitot static tube

One of the first air velocity meters ever designed was the Pitot

static tube, named after its inventor, Henri Pitot (1695 - 1771).

For reliable use, the direction of the velocity vector bas to be

known with sufficient accuracy before taking any measurements. Its

operation principle is based on Bernoulli 's law applied to a

one-dimensional incompressible frictionleas flow. The air velocity

can be determined from the density of the air p and measuring the

pressure difference between the stagnation- and the static

pressure. Because p is accurately known in most situations, the

errors can be ascribed to inaccurate measurement of the pressure

difference. Discrepancies between the real value and the measured

value of this difference are due to (Doebelin '83):

* misalignment of the tube axis and the velocity vector,

* nonzero tube diameter,

* disturbance of the velocity profile by the stem,

* the effect of viscosity. The assumption tbat the flow is

frictionleas is no langer valid at lower Reynolds numbers. At

sufficiently low Re numbers the viscosity of the flow exerts an

additional force.

Generally the Pi tot static tube is a reliable instrument for

measuring static flow veloei ties ranging from 10 cm/s - 30 m/s

{Finck '78).

2.2.2 Cup. vane and propeller anemometers

The use of the kinetic energy of a gas flow and transforming it

into a form of useful energy bas been a widely appreciated

principle for ages with a great range of applications, varying

from windmill to sailing ship. It is therefore not surprisihg tbat

on the basis of this principle, a series of maasurement devices

bas been developed, such as cup, vane and propeller anemometers.

4

* A CUP ANEMOMETER is characterised by a number of half-spheres

mounted on a vertical rotation axis. The difference in air

resistance between the convex and concave sides will cause the

axis to rota te. The rotation veloei ty is a measure of the air

velocity. However, this difference in air resistance only applies

to Reynolds numbers, Re, greater than 100, where Re is based on

the diameter of the cup. In the case of a sphere wi th diameter

3 cm, this corresponds to air veloeities > 5 cm/s (Lindley '75).

* VANE and PROPELLER ANEMOMETERS include a range of simple,

mechanica! and portable anemometers. One type employs a spring to

resist the aerodynamic force, the other type allows vanes to whirl

unobstructed as fast as is required for the net torque produced by

the aerodynamic force to become zero. The first type responds to

the square of the velocity, while the second has an output varying

linear ly wi th the veloei ty. Di sadvantages of these sys tems are

their integrating nature and a lower detection limit of approx.

20 cm/s (Leak '66), caused by friction of the journal hearing.

They are therefore used for measuring mean air veloeities averaged

over a langer period. As regards the limited sensitivity it should

be noted here that, as an exception, Desjardin et al. '86 report a

lower limit of 6 cm/s.

In the case of highly varying air velocities, these systems show a

tendency to overestimate the average value. For a fluctuating air

velocity with a frequency of 2 Hz and an amplitude of 50% of the

average value, this overestimation exceeds 10% (Finck '78).

We should at this point mention the ION DRIFT ANEMOMETERS. They

drew strong attention during the

detection limit of a few cm/s

70's because of their low

(Durbin et. al '71. Kurz &

Olin '71). However for reasans unknown to us no further attention

was paid to them afterwards.

5

2.2.3 Hot-wire anemometers

Publ ications which appeared in 1900 presented a new type of

low-air-veloci ty measuring device: the hot-wire anemometer

(H.W.A.). Its use was at first limited to measuring stea.Ciy air

veloeities (Comte-Bellot '76), but in later years eropbasis shifted

to the maasurement of fluctuating velocities.

Hot-wire anemometry is based on the fact that the electrical

reststance of a roetal conductor is a function of its temperature.

The sensors are thin metallic elements heated by an electric

current (Joule effect) which are caoled by the incident airflow.

From the temperature (Constant Current H.W.A.) or reststance

(Constant Temperature H.W.A.) attained by the sensor, it is

possible to deduce information on the flow (Bestion '83). By using

more than one sensor, measurements of multidimensional flows can

be performed (Andreopoulos '83).

The popularity of the H.W.A. is due to the following advantages of

the device (Smol'yakov '83):

* The sensor is small enough not to introduce much disturbance and

it bas good spattal resolution.

* The response time is short so that very-high-frequency eftects

(up to a few kHz) can be recorded.

* The electrical signal produced can be readily processed both by

analog and digital systems.

There are, however disadvantages:

* Calibration is necessary and requires much care. This

calibration is very sensitive to dirtcollection and needs! to be

repeated regularly (Bruun '79).

* There are deviations from the 'eosine law' which are due to the

cooling by the velocity component parallel to the wire

(Bremhorst & Gilmore '78).

* The heat exchange mechanism is dependent upon the composi tion of

the air (Andrews et al . '75).

* Interferences are caused by the stem (Vagt '79, Botteher '85).

6

2.2.4 Thermal marker and iontracing

A measurement teclmique which is specially developed for highly

turbulent flows, including regions in which reversals of the flow

direction occur, has been deduced from the H.W.A. and is called

the TIIERMAL MARKER (Bradbury '76, Castra & Cheun '82). It is based

on the pulsed heating of the flow by a thin metal wire. A second

wire, which acts as a receiving element, is placed further

downstream of the flow. The velocity is determined from the

interval of time between the emission by the thermal marker and

the detection by the receiving wire. The factors which determine

the accuracy of the velocity measurements are the probe distance,

the transit time, the duration of the pulse and the fidelity with

which the gas molecules follow the air.

The time constant that limits the precision of measurements on

high-frequency fluctuations depends on the mimimal time interval

between two subsequent heat pulses. In practice this means that

the time constant of this method is greater by one order of

magnitude than that of a hot-wire anemometer.

The velocity range of the thermal marker starts at approx. 15 to

20 cm/s (Kielbasa & Rysz '81, Skinner et al. '82, Westphal et

al. '81).

During the last decades, in addition to heat, a variety of tracers

has been used, from smoke to radioactive gases. IONTRACING, a

typical memher of this group, is characterised by the fact that

its measurements of the velocity are not influenced by changes in

air pressure, temperature and composi ti on. Lil ienfeld et al. '67

report a veloei ty range of 0. 5 - 250 m/s wi th an accuracy of

better than 5% over the entire range.

7

2.2.5 The Sonic Anemometer

The sonic anemometer is based on measuring the changes produced in

the characteristics of waves propagating within the air. lts

features include linear dynamic response, good directional

characteristics and a frequency response limi ted only by the

sound-path length (Coppin & Taylor '83). Several ways are reported

(Kaimal & Businger '63, Mitsuta & Asai '66) of obtaining an

expression for the air veloei ty, using the difference of the

travel times, taking the difference of the inverse of the travel

times, or using a phase-locked-loop circuit (Larson et al. '79). A

resolution of a few mm/s is generally reported.

g.2.6 The Laser Dowler Anemometer

The first use of a laser Doppier anemometer (L.D.A.) to measure

gas veloei ties was reported in 1964, when a lowest veloei ty of

appox. 2 cm/s was detected. (Foreman et al. '65).

The operating principle of a L.D.A. relies on the presence of

optica! inhomogeneities or foreign particles present in the flow

or especially introduced into it. A laser beam is focussed at the

point where the velocity is to be measured and a photodetector is

used to detect the light scattered by particles transported by the

fluid. The velocity of the particles, which is assumed to be equal

to the air velocity, causes a Doppier shift of the scattered

11gbt's frequency. This can be measured with a photodetector,

whose signa! is directly related to velocity. Artificial. tracer

particles are not always necessary: the microscopie particles

normally present in liquids or gases may suffice. It should be

noted bere that experiments are mostly carried out in fluids

(Yeh '64).

S.

The advantages of the L.D.A. are:

* The measurement of velocity is direct.

* No physical object need be inserted into the flow, thus the flow

is undisturbed by the measurement.

* The sensing volume can be very smal! (0.2 mmE3).

* A very high frequency response (up to the MHz range) is

possible.

Against this must be put the following disadvantages:

* L.D.A. can only be performed in transparent tubes.

*Tracer particles in the air are required. However, in many

applications seeding with particles may not be possible and may

disturb the air velocity.

* The apparatus is complex and costly.

Sirnul taneous measurements of several veloei ty components at a

point may be achieved ei ther by polarization schemes using a

single laser (Bahnen et al. '85) or two-colour systems employing

two lasers of different wavelength {Nakatani et al. '85).

9

2.3 CX:>NO..USIONS AND REMARKS

Several measuring principles have been described in the previous

chapter. Our purpose was not to attempt completeness, but just to

give the reader an impression of some of the measuring principles

and their advantages and disadvantages. In order to be able to

compare the techniques described above, a number of standards can

be applied:

* sensitivity to other characterics of the stream, such as

pressure, temperature and humidity,

* the number of simultaneously measurable velocity components,

* spattal resolution,

* frequency response.

* complexity of the signal processing,

* cost of the apparatus,

* manufacturing complexity,

* reproducibility and accuracy,

* velocity range and more specifically the lower detection limit,

* calibration requirements.

Needless to say. that depending on the application of the

anemometer, there are several more important demands. However, we

rnay briefly say that all the rnethods described above are more or

less unsuited to our purposes. Therefore, in consultation withand

at the request of the Facul ty of Archi tecture, Building and

Planning a new measuring principle was developed and tested, which

will be discussed in th~ next chapter.

10

3 MEASURING PRINCIPLE OF TIJE MICROANEMOMETER

3.1 INTRODUeTION

In the previous chapter several measuring principles were

described which, however were not really suited for the purposes

described in chapter 1. In the present chapter a new measuring

principle, developed especially to meet the specific demands will

be introduced. It is based upon the measurement of the force (or

rather the moment of force) exerted on an object placed in an

airstream. For this force measurement a compensation balance

methad is used to prevent displacements of the object. Such

displacements could influence the measured force and the

compensating force can be determined with precision.

The measuring device includes a balance, consisting mainly of an

ordinary moving-coil meter. By sending a current through the coil,

the Lorentz couple can serve as retroactive couple. In order to

put the beam in its original position (which is detected by an

optica! detection system), the magnitude of the Lorentz couple

(the current) is adjusted with a feedback system. In that case the

feedback current is a measure of the air velocity. The measuring

principle is shown schematically in fig. 3.1.

air velocity

t Mlorentz

Vout I L J

Fig. 3.1 Schematic representation of the measuring principLe of the microanemometer

11

3.2 TIIE MEASURING PRINCIPLE

The equation of motion of the microanemometer, consisting mainly

of the moving-coil meter. is

.. . J a(t) + K a(t) + C a(t) = M(t) - G I(t) 3.1

where J is the moment of inertia of the balance with respect to

its rotation axis,

K the damping constant,

C the torsion constant,

a the angle of rotation,

M the moment of force. due to the force by the airstream

exerted on the measuring object,

I the current through the coil and

G a constant concerning the Lorentz couple,

which we shall call sensitivity constant.

When compensation is achieved by the feedback system, .. . a(t) = 0, a(t) = 0 and a(t) = 0, eqn. 3.1 becomes

G = M/I 3.2

Hence the value of M can be calculated from the value of I,

assuming the value of G is known. G bas to be determined by a

calibration experiment. which can be done in either of two ways.

* The first way is based on the use of the microanemometer with

feedback compensation. When applying eqn. 3.2 in calibration M has

to be known. Our first attempts were aimed at calibration of the

anemometer in the position in which its rotation axis was

vertical. This implied the need to apply a small horizontal force.

It proved to be unpractical to use this method.

12

Success was achieved using the apparatus in such a way that i ts

rotation axis was placed horizontally. This enabled us to provide

the couple M by suspending small weights, mass m, from the end of

the pointer {also being in a horizontal posi tion) and measuring

the equilibrium values of I. M satisfies

M=mgL 3.3

where L is the lengthof the pointer of the moving-coil meter.

By plotting I vs. M. a linear relationship is obtained so that G

can be determined from the slope of the line. Results are shown in

fig. 3.2.

24r---------------------------~--·

T 16

I (!lA)

8

0.15 0.30 0.45

M (j.!Nm) ->

Fig. 3.2: A plot of I vs M to determtne the sensitivity constant G

This metbod results in a direct measurement of G and is preferabie

when a complete microanemometer has been constructed, including

the optica! detection system and the electronic circuitry.

13

* The second, indirect way to determine G is consirlering the

Lorentz couplewhen a current is passed through the coil. This can

be written as

G I B I A N c c c c

where B is the magnet ie induction,

I the current through the coil, c A the area of a coil winding and c N the number of windings. c

For G this yields

G =BA N c c

3.4

3.5

In practice it is impossible todetermine the three constants of

eqn. 3.5 (B, Ac and Ne} without irreversible damage to the

moving-coil meter. When consirlering the moving-coil meter as it is

commonly used as ammeter or voltmeter the Lorentz couple is

compensated by the spiral springs. This leads to

G I c

-Ca 3.6

The calibration of G thus involves the measurement of a, Ie and C.

a/Ie can easily be obtained by measuring afs/Ifs , using the

full-scale deflection afs and full-scale current Ifs of the meter.

The torsion constant C can be determined in a similar way to the

sensitivity constant G, but now in absence of the feedback system.

The microanemometer is placed so that its axis and the pointer are

horizontal. Small weights, mass m, are suspended from the end of

the pointer and the angle of deflection is measured.

14

By platting a versus M, a linear relationship is obtained and C

can be determined from the slope of the line. Here M is given by

M = m g L cos a

The results are shown in fig. 3.3

0.9.-------.-------.-------.-~----,

T 0.6

a (rad.)

0.3

0.4 0.8 1.2 1.6

M (J,I.Nm) -

3.7

Ftg. 3.3 A plot of a vs M to determine the torsion constant C

It is worth while mentioning bere that this procedure is more

convenient for several purposes than the earlier mentioned direct

calibration of G. The procedure becomes specially attractive when

different moving-coil meters, chosen out of a set, have to be

compared for future use. That is because this procedure avoids the

time consuming manufacture of a complete prototype microanemometer

with optical detection sytem and feedback circuit.

In eqn. 3.1 there are two more constants, J and K, determining the

mechanica! properties of the microanemometer. However, insight

into these two constants is of minor importance bere. A further

discussion is given in chapter 6.

15

3. 3 THE MICROANEMOMETER

The three basic parts of the microanemometer are

1. the optical detection system,

2. the feedback system and

3. the moving-coil meter.

3.3.1 The optica! detection system

During all experiments the same simple, usefull optica! detection

system was used. This optical detection system consists of a small

strip of me tal attached to the pointer. a light emi tting diode

(L.E.D.) and two photodiodes, placed side by side, see fig. 3.4.

The two photodiodes used are rectangular silicon photodiodes

Siemens BPW 34. An infrared gallium arsenide L.E.D. which

reasonably matebed the photodiodes was chosen.

1. Photodiodes

2. Metal Strip

3. L.E.D.

4. Pointer

Ftg. 3.4 The opttcal detectton system

The strip is positioned so that, in the equilibrium posi tion of

the meter. the shadow of the strip covers the two photodiodes

equally. These photodiodes are circuited with an operational

amplifier in such a way that the latter's output signal is related

16

to the difference of the currents of the photodiodes. Thus, when

the pointer starts to leave the equilibrium position this causes

the output of the operational amplifier to differ from zero.

As regards the geometry and the mechanica! construction of the

optical detection system, special attention was paid to two

aspects.

* First the influence of the width of the metal strip (d} on the

relation between the output current, Iph' of the photodiodes and a

was studied. The results are shown in fig. 3.5.

It is found that the width of the strip is of minor importance. As

long as the width is not chosen greater than approx. 4 mm. the

relationship between Iph and a is linear over quite a wide

deflection range.

a-

0.01 rad.

Fig. 3.5 The output current Iph' of the photodiodes vs. a, the

angte of deflectf.on, for severa1. widths, d, of the metal strip

17

M Second the influence of the distance, h, between the strip and

the photodiodes on the relationship between Iph and a is studied.

In fig. 3.6 the results of Iph vs a are shown for h = 0.5, 1 and 2

mm and d = 3.0 mm.

0.01 rad.

0.5 1.0 2.0

a-

Fig. 3.6 Iph vs. a for three dtstances between strip and

photodiodes, h: 0.5, 1 and 2 mm (d = 3.0 mm)

In fig. 3.6 i t is shown that, for distances up to 2 mm, the

influence of the distance between the strip and the photodi~des on

the relation between Iph and a is negligible.

Summarising, we can say tbat no special care bas to be taken in

this respect during the mechanica! construction of the optica!

detection system.

18

3.3.2 The feedback system

A Proportional Integral Compensator was chosen as feedback

circuit. In fig. 3.7 the complete circuitry of the feedback system

is given.

photodiodes

R . ga1n

Fig. 3.7 Feedback circuitry

R

R c

I L coil

4---------R

s

As regards the choice of this feedback circuit, it should be noted

here that we are well aware of the fact that the feedback circuit

used may not be the optimum solution. However, the simplicity of

the circuit and the fact that it works without any complications

makes the choice acceptable.

A P-I compensator is characterised by two parameters: the time

constant t1

and the gain P:

t1

is chosen, according to the 11'/4 phase-margin cri terion (see,

for instance, d'Azzo & Houpis '66 or Banks '86).

The optimum value of P is determined experimentally. When the

value of the gain was chosen too high the pointer started to

oscillate. In each construction the optima! value of the gain is

determined by increasing P until oscillations occur and then

decreasing this value slightly. The resulting sensitivity was

always sufficient for our purposes.

19

3.3.3 The moving-coil meter

A dozen different types of such meters were tested for possible

use as microanemometers. These types differed in make, full-scale

deflection and specified accuracy. The construction of a

microanemometer with a moving-coil meter is shown in fig. 3.8

-\::->'\--- magnet coil

magnet

co it

Fig. 3.8 A schematic representation of the microanemometer

The microanemometer shown in fig. 3.8 consists mainly of a

moving-coil meter. The original pointer of the moving-coil meter

is used as force-measuring device. To complete our microanemometer

a hollow aluminium sphere is mounted round the greater part of the

moving-coil meter used. A hole in this sphere allows the pointer

to be located in the airflow to be measured.

20

3.4 A FIRST OOMPARISDN OF THE USEFULNESS OF DIFFERENT MOVING­

OOIL METERS AS MICROANEMOMETERS

First applicability aspects are discussed of a given moving-coil

meter which can readily be predicted without manufacturing a

complete microanemometer by which is meant that only G has to be

determined and that the full-scale current and the class of the

instrument are lmown. This prediction allows us to carry out a

preselection in a great number of available moving-coil meters, so

that the time-consuming manufacture and calibration experiments

can be reduced to a minimum.

For an actual preselection the values of Umi are required. the

lowest detectable air velocity which we define by the S.N.R.

(Sigrml to Noise Ratio) being equal to unity. Unfortunately this

U mi is not a readily measurable quant i ty in the sense described

above. A quantity which can however be determined is Ucl'

calculated from the class of the moving coil meter specified by

the manufacturers. It should be noted here that we are well aware

of the fact that this quantity, to be defined later on, may well

be larger by an appreciable factor than umi'

To define Ucl more precisely, the moving-coil meter is considered

again. From the specifications the full-scale current Ifs and the

class Cl (usually given in percentages) are used. The quantity Iel

is defined by

3.8

With eqn. 3.2, Mfs and Mei are defined respectively by:

3.9

3.10

21

In order to introduce Ufs and Ucl we assume the relation between M

and U to satisfy

3.11

where p is the density of air,

De the diameter of the cylindrical pointer,

L0 the length of the part of the pointer inside the sphere,

U the magnitude of the air velocity and

cd the drag coeffient.

The drag coefficient cd satisfies

c2 Cd= c 1 Ree 3.12

where c1 and c2 are constauts which can be determined from

literature by linearisation of the double logarithmic Cd vs Ree

curve and Ree is the Reynoldsnumber, based on the diameter of the

cylindrical pointer

Re = U•D /v 3.13 c c

where v is the kinematic viscosity of air.

Taking M = Mfs and U = Ufs in eqn. 3.11 leads to a relation

between Mfs and Ufs which we consider as the definition of Ufs·

By a similar procedurewedefine Ucl as a function of Mcl·

In table 3.1 we give an excerpt of the preselection results for

four moving-coil meters, three of which were considered to be good

enough for further development.

Several conclusions can be drawn from table 3.1. First of all we

consider the conclusions which are relevant for the minimum air

velocity ucl.

22

Type Ia Ib Ie II

diam. magnet (mm) 21 21 21 55

G (10E-4 Nm/A} 44 lSO 300 40

Iel (J.IÁ.} 20 2 1 15

Ifs (mA) 1 0.1 0.05 1

L (mm} 70 70 70 50

Mcl (lOE-9 Nm) 88 36 30 60

Mfs {lOE-7 Nm) 44 18 15 40

u cl ( em/s) 7 5 4 9

ufs (em/s) 230 150 135 325

Tabte 3.1 : Characteristics of 4 mouing-coit meters

The measurement accuraey of G was approx. 3 %. The reproducibilty

within one type was found to be of the same order of magnitude.

This can fully be subscribed to the above-mentioned accuracy.

A tendency can be seen to the effect that a decrease of the full­

scale current results in a decrease of Ucl' although the value of

G increases. Hence it is important to use moving-eoil meters which

have a low value of Iel'

From the comparison of Ia and II it is found that both types have

approximately the same value of G and Iel resulting in approx. the

same value of U cl. All types of magnets used seem more or less

suitable for making a microanemometer. The type of magnet plays a

minor role. Thus in order to be able to establish the usefulness

of a moving-eoil meter as microanemometer. other characteristics

must play a more important role. such as the diameter of the

magnet (determining the diameter of the surrounding sphere) or the

maximum length of the pointer.

23

Summarising, we state tbat the values of Ucl are of the same order

or already lower as those of most commercially available

anemometers. There is good reason to believe tbat the rema.ining

step towards our aim of measuring air velocity as low as 1 cmls

can be attained with the quantity umi'

As to the values of Ufs we restriet ourselves to the remark tbat

all moving-coil meters satisfy one of the demands for measuring

air veloeities up to 10 cmls.

3. 5 GENERAL <XINSIDERATIONS

The prototypes described in the previous paragraph seem to be able

to measure air veloeities as low as a few cmls. It should be kept

in mind tbat, in obtaining these values we based the calculations

on the static value of Iel. However, in the event that the

feedback system is used, the mimimum detectable air velocity is

much lower. resulting in a lower limit of the order of a few mmls.

To find the true detection limit of the microanemometer, it bas to

be tested in practice, which means that an experimental set-up

capable of producing very low air veloeities bas to be built.

As far as the maximum detectable air veloei ty is concerned, the

value obtained of approx. 10 cmls confirms that our

microanemometer can be used to supplement the commercially

available anemometers. Experimental research bas to be done to

investigate the exact value of this upper limit by placing it in a

wind tunnel.

24

A new measuring principle bas been introduced bere, resulting in a

new type of microanemometer. It is worth while mentioning tbat in

this thesis a restrietion is made as to the type of

microanemometer in which the force was measured on the pointer of

the moving coil meter itself. However; during recent years much

experience bas been gathered with measurements in which a vane was

fixed at the far end of the pointer, for instanee see Pluijm

et al. '86.

In case of a choice between measurements with and without vane,

the following remarks should be made:

Where a measurement of a more local air velocity is required, it

seems preferabie to use a microanemometer wi th a vane. However.

the moment of force exerted on the pointer i tself cannot be

neglected. To minimise this effect, one could modify the

moving-coil meter and replace the pointer by a beam of much

shorter diameter. which is a complicated matter for practical

reasons. Another possibility is to construct a microanemometer in

which part of the pointer is shielded from the airstrearn, so tbat

no force can be exerted on this part of the pointer. Also both

rnethods can be combined. Further investigations into this new type

of microanemometer will be perforrned in the near future.

25

4. CALIBRATI«Xf UNIT FOR. Mlar.oANEIDIIITER AT VERY lDI AIR

VELOeiTIES

4. 1 INTRODUCfiON

If we are to calibrate our microanemometers and establisb tbeir

detection limit a calibration unit is needed wbicb can produce air

veloeities as low as 1 mm/s, enabling accurate and reproduetbie

calibrations wi tb a uniform stationary airflow of known veloei ty

to be obtained. This low air veloei ty eaUbration entails two

problems:

*No standard facilities are available wbicb can produce air

veloeities down to tbe mm/s range.

* Conventional calibration standards generally suffer from

insufficient sensitivity (Aydin &Leutbeusser '79}.

Several possible ways to produce low air veloeities are presented

in li terature. The basic principle is always tbe creation of a

relative air movement: tbe anemometer is moved tbrough stationary

air or set up in an airstream at a fixed place.

* Moving tbe anemometer in stationary air creates practical

problems, sucb as tbe influence of mechanica! vibrations

(Perry '82). Furtbermore, an absolutely wind-free room is a very

hard thing to acbieve as temperature differences cause free

convection currents. Bootb & Chong '78 report measurements of a

bot-wire anemometer attacbed to a pendulum enclosed in an

insulated box at air veloeities from 3 to 200 cm/s. However,

comparison witb a calibration using a low speed wind tunnel sbowed

tbe resul ts to be inaccurate owing to tbe airflow around tbe

pendulum.

Anotber metbod is to place the anemometer on a sliding cart and

pull it througb tbe air, a metbod which is similar to one wbicb is

routinely used with 'towing tanks' for ship research (Taneda '56,

Ilegbusi & Spalding '83, Tsanis '87). Tabatai et al. '85 used a

constant-velocity cart witb a lowest velocity of approx. 2 cm/s.

26

The movement was effected by connecting tbe cart wi tb ebains or

wires to tbe spindie of a manually controlled variabie-speed motor

mounted 10 m away from tbe starting position. The time of travel

was recorded by clock switcbing at tbe start and end of travel,

yielding only tbe average velocity of tbe cart.

* The second metbod by wbicb to create a relative airflow is to

place tbe anemometer in an air stream. Two basic ways can be

distinguisbed:

1. The metbod using a !ow-speed wind tunnel

The anemometer is placed in tbe working section of a low-speed

wind tunnel. A smootb flow is produced tbrougb a nozzle and tbe

airflow is tben diverted into tbe working section of tbe tunnel,

wbicb is larger in cross-sectional area in order to reduce tbe

velocity of tbe air. The pressure drop across tbe smal! nozzle can

be related to tbe veloei ty in tbe wind tunnel, knowing the two

exit areas and assuming certain veloei ty prof i les across tbe

nozzle and working section of tbe tunnel. However, at lower air

veloeities tbis conventional technique is inaccurate owing to the

instability of jet flows and to the difficulty in obtaining

reliable and accurate measurements of tbose pressures

corresponding to low velocity flows. Purteil & Klebanoff '79

report on a !ow-speed wind tunnel which can create air veloeities

as low as 5 cm/s.

2. The Piston Flow Metbod

In 1984 an experimental set up based upon tbe Piston Flow Metbod

was presented (Pluym et aL '86). Its operating principle was

based on the elementary fact that when a closed container of any

shape moves at constant velocity, the air inside will follow it at

tbe same veloei ty a short time interval af ter tbe start of the

movement. It should be noted bere that in 1985 Johannessen,

introducing the 'wind wbeel', used a metbod whicb has great

simularities witb our Piston Flow Metbod.

27

4.2 TIIE CALIBRATION UNIT FOR MICROANEMOMETERS

Based upon tbe Piston Flow Metbod and taking into account tbe

problems of tbe above-mentioned expertmental set-up, a second.

larger calibration unit was built {Pluijm et al. '86}. A

cylindrical tube (lengtb 600 cm, Dt = 125 cm} is closed at botb

ende witb two circular plates (see fig. 4.1). This tube is placed

upon a movable train. By means of a gearbox and a tootbed bar, tbe

rotations of a (servocontrolled) motor are transformed into a

horizontal displacement of the train. In the laboratory the train

can move over about 400 cm. Two safety devices are placed at

opposite ends of the stretch (maximum calibration distance}.

Fig. 4.1

28

Schematical representation of the calibration unit for tow air vetoeities

The anemometer is placed ins i de the tube as follows.

At both sides of the laboratory two heavy metal pillars are placed

vertically and fixed in the concrete of the floor and the ceiling.

A steel cable (diameter 6 mm) is tightened around these pillars.

The cable is led into the tube through two small holes (each

8 cm2) in each circular plate. On these cables is placed a wooden

standard, upon which the microanemometer is mounted. The position

of the standard with the microanemometer inside the cylinder can

be changed in the axial direction. By adjusting the pos i tion of

the standard itself, it is possible to change the position of the

microanemometer in the radial direction.

The position x 1

of the train on the rails is determined by a ten cy turn potentiometer. Thereto the voltage of the potentiometer V t po is registered which is directly related to the pos i ti on of the

train. The distance of the microanemometer to the right-hand plate

is adjusted befere the measurements, allowing easy calculation of

distances to the right and left plate during measurement.

The veloei ty U 1

of the train is determined by means of a cy tacho-generator. This tacho-generator measures the number of

revolutions per second of the motor. yielding a voltage V tacho.

Another way to calculate the average velocity is by

differentiating x 1

. cy

With this expertmental set-up, veloeities are produced in the mm/s

range up to 150 mm/s, divided into three ranges by the gearbox:

U 1 < 10 mm/s, 10 < U 1 < 70 mm/s and U 1 > 70 mm/s. The lowest cy cy cy velocity met the demands for the microanemometer (see chapter 1)

and the highest velocity was determined for practical reasons.

The expertmental set-up can be operated manually as well as

automatically by means of a computer. When operated manually the

velocity of the train can be changed by means of a potentiometer

and the actual velocity of the train, determined from the

tacho-generator, can be read off from a display.

29

4.3 AUfOMATION OF THE EXPERIMENTS

During the development of the calibration unit, the possibility of

complete automation was considered. A computer {DEC-LSI} 'and an

Eurobussystem, containing an Analog-Digital Converter (A.D.C.} and

a Digital-Analog Converter {D.A.C.) is used for the purpose. Both

the A.D.C. and the D.A.C. have a computer inaccuracy of 2.5 mV and

a dynamic range of lOV. This brought wi th i t an inaccuracy in

train position of less than 1 mm. The accuracy in producing and

determining the train velocity U 1 is less than 1 %. To minimise cy the effect of the A.D.C. inaccuracy on the determination of the

air velocity, the output voltage of the feedback system V t OU

{fig. 4.2) is multiplied in such a way that the maximum inaccuracy

due to digitising was 1 %.

The advantages of the automation of the expertmental set up are

numerous, for instance:

* the time necessary for one maasurement is shorter,

* the number of possible measurements per day (or night), is

substantially increased, resulting in more reproducible

measurements,

* the combination of D.A.C. and A.D.C. yields the possibility of

feedback of the velocity and thus control of the constancy of

the velocity during the maasurement and

* the computer enables almost any desired time-dependent train

velocity, e.g. sinusoirlal fluctuation, to be obtained.

In our calibration unit the computer fulfils three basic

functions:

* control of the experiments,

* data acquisition and data processing and

* security functions.

Control of the experiments takes place with the aid of D.A.C .. lts

output voltage Vda is used for the movement and direction

(left/right) of the calibration train. The A.D.C. gives the

30

possibility of recording. on-line, both the position of the train,

as well as the velocity of the train. Combining these two

functions, the computer can also be used for security functions:

in theevent of an unwanted value.of x 1 the motor is stopped. cy

In fig. 4.2 a schematic view of the function of the computer is

given.

Analog Digital

Converter

A.D.C.

p

u D.A.C.

Digi tal Analog

Converter

V pot

V out

V tacho

p I feedback

V da

Fig. 4.2 Schematic view of the function of the computer

4.4 THE CHARACfERISTIC CALIBRATION MEASUREMENT

4.4.1 Supplementary calibrations

Before the experimental set-up can be used to calibrate

anemometers, the calibration unit itself has to be calibrated.

This involves determination of the two relations between the

D.A.C. voltage Vda and the train velocity Ucyl and the relation

between the output voltage of the tacho-generator Vt h and the . ac o velocity of the train U

1. This is done in the following way. cy

31

First the relationship between Vpot and xcyl is determined. The

train is placed at the left and right securi ty device in the

laboratory, obtaining resp. vpot,l and vpot,r and the distance

between both devices, Llr' measured. At all times xcyl is

4.1

where xcylO is chosen as the middle of the laboratory (Vpot = 0).

Several voltages Vda are produced setting the train in motion at a

given velocity. Meanwhile the real velocity of the train U 1 is cy determined by measuring the distance the train moved in 40 (or 20

at higher velocities) seconds. During this measurement Vtacho is

also recorded. A characteric result of a supplementary calibration

performance is presented in fig. 4.3. where vda vs. ucyl (a} and

Vt h vs. U 1 {b) are presented. In each figure three lines are ac o cy drawn, corresponding with the three ranges of the gearbox.

5r------.-------.------,

T.

vda (V) 0

l

vtacho (V) 5

-5~-----L------~----~ o~----~------~----~ 0 50 100 150 0 50 100 150

ucyl (mm/s) - ucyl (mm/s)

Fig. 4.3 Results of a suppLementary culibration : Vda US. Ucyl (a) and Vtacho US. Ucyl (b)

32

From fig. 4.3 it appears that both relations are linear and can

therefore be described by:

+ cda· U 1 cy 4.2a

4.2b

where VOda' VOtacho' cda and ctacho are constants, obtained by linear regression.

The supplementary calibrations are performed for train veloeities

in both directions. The values of the eight parameters are stored

on disc. The reproducibility of these measurements over a number

of days proved to be of the order of 2 % and reproducibi l i ty

wi thin one day proved to be of the order of 0. 5 %. Th is daily

automated calibration does take approx. 20 minutes.

As bas already been mentioned, the calibrations can be automated

using the A.D.C. and the D.A.C .. The velocity, the startand the

end points of the measurement, as wel! as the number of

calibration samples to be taken, can be stipulated beforehand. An

actual calibration measurement proceeds as follows.

Before the measurement the train is sent to the chosen starting

position. Generally the starting and end position are chosen

symmetrically wi th respect to the pos i ti on of the anemometer in

the train. A characteristic course of a measurement is presented

in fig. 4.4.

33

T u cyl

I II III IV V VI VII VIII

-----+time

Ftg. 4.4 Characteristic course of a calibration measurement: U 1 US. time cy.

In this course the following phases can be distinguished:

I train velocity = 0 ; first determination of the (off-set)

output voltage of the microanemometer for 5 seconds.

II starting phase: the veloei ty of the train is increased

until the destred velocity is reached.

III time interval to cover acceleration effects of the air;

no measuring points are taken, in view of computer memory

and time.

IV

V

VI

VII

CALIBRATION INTERVAL during which 150 or 200 samples of

V t' Vt h and V t and other variables are taken. po ac o ou time interval to obtain symmetry with regard to xcylO

also no measuring points are taken (see III). '

end phase: the velocity of the train is decreased to:zero.

waiting time: 2 minutes are waited to cover

deceleration effects of the air.

VIII train veloei ty = 0; second determination of the offset

output voltage. This second offset voltage is used as a

check as to whether the air velocity again equals zero.

During maasurement the data are stored on disc, enabling

subsequent data processing. During calibration a complete

digitised record of the whole calibration run is available for

graphical and analytica! preview, so that any anomalous behaviour

can immediately be observed and reacted upon.

34

4. 5 EXPERIMENTS AND DisaiSSION

Several experiments were carried out to establish the usefulness

and the limitations of our calibration unit.

* First the influence of the two holes made in each plate was

studied by varying the size between 8 cm2 and 4 cm2. For this

purpose Vout was recorded with our microanemometer at air

veloeities between 5 and 130 mm/s. From the results we concluded

that the size of the holes did not affect the measured Vout· lt

should be noted bere that small holes are not always possible, as

the size of the holes is directly related to the distance the

train can move, in view of the fact that the mass of the

anemometer and the standard bend the steel cables.

* During calibration the anemometer is attached to a hollow

cylindrical stem resting on a massive waoden standard (see

fig. 4.1). The influence of the lengthof the stem on calibration

performance was studied. The characteristic height of the stem is

of the order of 60 cm, so that the anemometer is located at the

centre of the cylinder. Measurements were carried out at heights

between 60 and 30 cm and V out was measured wi th the anemometer

placed on the standard. The veloeities ranged from 5 to 130 mm/s.

The measurements indicated no differences, so that the inf1uence

of the standard on the veloei ty profile in the vicini ty of the

anemometer can be neglected.

* For many practical purposes it would he of great value if our

microanemometer could be calibrated at sinusoidally fluctuating

air velocities. Unfortunately our present eaUbration unit does

not allow these train velocities. It proved to be possible,

however, to produce train veloeities which were a superposition of

a constant and a sinusoidally fluctuating velocity {frequencies up

to approx. 1 Hz). Calibrations performed at such train veloeities

will not be dealt with.

35

5 NUJIERICAL AJW.YSIS OF THE FLOI AROOliD THE III<llOANEIDIETER

5.1 I.NTRODUCfiON

The calibrations required for the development of the

microanemometer are performed by means of the eaUbration unit

described in chapter 4. Due to the presence of the microanemometer

in the calibration unit, the velocity profile is disturbed and the

assumption that the air veloei ty at the pos i tion of the pointer

equals the veloei ty of the surrounding cylinder might well be

inaccurate and deserves special attention.

In li terature, the flow past a sphere bas been studied

extensively. The macroscopie hydrodynamica! characteristics,

exemplified by the drag coefficient, are well established over a

large range of Reynolds numbers by numerous experimental studies.

Our interest however is the velocity profile in the vicini ty of

the sphere. At very low air velocities, the Stokes approximation

is correct and yields an analytica! expression for the flow field.

For intermediate Reynolds numbers the complete Navier Stokes

equations have to be solved and an analytica! solution is not

available owing to the nonlinearity of these equations.

A number of approximate descriptions of the entire flow field

through the use of trial stream function polynomials {Chow '79,

Kawaguti '55), the boundary-layer assumptions (Schlichting '79) or

the finite difference metbod {Jenson '59) are known from

literature. These methods, however, are unable to predict

accurately the flow behaviour in the region we are interested in

(Hamiliec et al. '67).

We started to calculate the flow in the surroundings of our

microanemometer in the eaUbration unit using the Fini te Element

Metbod {F.E.M.) .with the Penalty Function Approach (P.F.A.). By

calculating the macroscopie hydrodynamica! characteristics, such

as the drag coefficient, from the velocity profiles obtainèd with

the F.E.M. comparison of these values with those from literature

is possible.

36

Once having calculated the velocity profiles, the influence of the

finite dimensions of our calibration unit can be established. In

practice this would mean that several cylinders of different

diameter have to be used, which would cause a great deal of

practical problems. However, by varying the diameter of the

calibration unit in our numerical calculations, a measure for the

influence of the cylinder wall on the veloei ty profiles can be

obtained in a simple way.

5.2 THE NAVIER STOKES EQUATIONS

In order to be able to approach the problem of the flow effects in

the vicinity of our microanemometer in the experimental set-up,

several assumptions and restrictions have to be made.

* Only the sphere surrounding the moving-coil meter will be taken

into consideration.

* The problem to be solved is restricted to the situation in which

the location of the microanemometer in the experimental set-up

is on the axis of rotation of the cylinder, so that the problem

becomes axisymmetrical.

* The flow is assumed to be stationary.

To calculate the velocity profiles in the vicini ty of the

we u se cylindrical coordinates (r, '{), z). The

Stokes equations governing the

incompressible flow, can be written as:

1 2 (~.v)~ = -Vp + __ vu

Re -s

with the Reynolds number Res =U •D /v cyl s

flow,

dimensionless

assuming

sphere

Na vier

steady

5.la

5.lb

5.2

37

Here u(u ,u ,u ) is the dimensionless velocity, being the actual - r <p z

air velocity divided by ucyl'

p the dimensionless pressure, obtained by dividing the actual

pressure by 0.5pU 21• cy

ucyl the velocity of the cylinder,

D5

the diameter of the sphere and

v the kinematic viscosity.

The centre of the sphere is chosen as the origin of the coordinate

system and coincides with the axis of symmetry (z-axis}. At the

boundaries of the surrounding cylinder the air is assumed to be

flowing at velocity ~ = (0,0,1) parallel to the z-axis.

Axial symmetry yields that 8/B<f! is zero and, in addi tion, we

assume u = 0. Hence only half of the ( r, z) plane need be 'P

considered. Boundary conditions for ur and uz are dictated by our

expertmental set-up, see fig. 5.1 :

* Çylindrical train (1,2,3} u = 0 r * Sphere surface (5) u = 0 r * Axis of symmetry {4.6) u = 0 r

The boundary condition for p reads as

* (3) p=O

' UZ = 1

,u = 0 z 8u /8r = 0 z

5.3a

5.3b

5.3c

5.3d

Eqns. 5.1, 5.2 and boundary conditions 5.3 together govern the

solution of the velocity and pressure profiles.

6 4

1 ê·--·-·--·-·--6-:·--·--·--·--·--·~ ê 2

Fig. 5.1 Geometry and boundary condttions used in the numerical analysts

38

5.3 THE FINITE ELEMENT METBOD

5.3.1 Broad description of the metbod

As al ready mentioned, the Navier Stokes equations wi th boundary

conditions have not yet been solved analytically. Therefore the

problem is solved numerically, using tbe Fini te Element Metbod

(F.E.M.) with tbe Penalty Function Approach (P.F.A.).

The F.E.M. is a numerical metbod for solving partial differential

equations for a given region (0} and prescribed boundary (r)

conditions. In this particular case tbe equations to he solved are

the Navier Stokes equations. The veloei ty and the pressure are

wri tten as a linear combination of, in principle. an infini te

number of base functions. By restricting tbe number of these

functions to a finite number an approximation of the exact

salution can be constructed (Chung '78}.

5.3.2 Mathematica! formulation

First tbe region is divided into a finite number of smaller

regions called elements (fig. 5.2a) whicb. when joined together,

cover the complete region and show no overlap. The result wbich is

called tbe 'mesb' is shown in fig. 5.2b,c. In our case the element

used is the 7-noded (P2+,Pl) modified triangular Crouzeix-Raviart

element (Cuvelier et al.'86).

The next step is to express the unknown veloei ty components and

pressure in terms of interpolation functions, called p.(r,z) and J

op.(r,z) respectively. Polynomials q>. and op. are used such that J J J

tbey are piecewise continuous on 0 and have a prescribed behaviour

for every element (e.g. linear or quadra tic).

and t.(x.) = óij are satisfied, where x. is J -1 -1

nodal point (see fig. 5.2a).

Also q>.(x.) ó1.J. J -1

the location of a

39

Ftg. 5.2

Velocity: ~ quadratic

7 nodal points ~i

Pressure: + linear

1 nodal po~nt 0

2 derivatives

The 7-noded (P2+,Pl) modtfted triangular Crouzetx-Rnvtart eLement (a); enLarged detaiL (b} and complete mesh (c) used for the numertcal anatysts.

The procedure for solving the Navier Stokes equations is discussed

briefly. For a detailed description we refer to Cuvelier et

al. '86.

In order to linearise the convection term at the left hand side of

eqn. 5.la, the Newton Raphson iteration processis used, giving

i i i-1 i i i-1 (~ •v)~ = (~ •v)~ + (~ ·v)~

i-1 i-1 (~ ·v)~ 5.4

Substitution of eqn. 5.4 in eqns. 5.1 yields for the i-th

iteration:

1 2 i i 1-1 i-1 i i ---- v u + (~ •v)~ + (~ •v)~ + vp Re -

s

0 5.5b

The principle of the P.F.A. is that the equation of continuity

(eqn. 5.lb) is perturbed and replaced by

5.6

where T is a large penalty-function parameter.

Substitution of the interpolation functions ~j(r.z) and ~j(r.z) in

the Navier Stokes equations yields a set of 1 inear equations.

called the Galerkin equations. In matrix notation these equations

can be written as:

41

where D is the pressure matrix,

L the divergence matrix,

N the convection matrix,

s the diffusion matrix,

u the vector containing the velocity parameters and

p the vector containing the pressure parameters.

This set of equations can be solved numerically in an efficient

way. The salution of the Stokes flow is taken as a starting

solution. Once a salution has been obtained for one Reynolds

number, it is used as a starting approximation in the next

calculation. In each case the computations were terminated when

5.8

The main advantage of the P.F.A. over the direct salution of the

Navier Stokes equations is that the pressure is eliminated from

the momenturn equations, resulting in a set of equations that can

be solved without partlal pivoting procedures. This results in a

substantial decrease in computer time and memory. With eqn. 5.7a

the approximated salution of the veloei ty components are

calculated, after which the pressure can be obtained with

eqn. 5.7b. A disadvantage of the P.F.A. is tbat the

penalty-function parameter T must be chosen carefully, since

otherwise loss of accuracy may arise because of the singularity of

the resulting matrix (Cuvelier et al. '86). This subject will be

further discussed in §5.4.1.

5.4 NUMERICAL RESUL TS

5.4.1 Practical aspects and preliminary calculations

First some preliminary calculations were carried out to study the

influence of the chosen mesh and boundary conditions on the

solution. For this purpose the dimensionless veloeities u and u n p

and the relative distance, Ç, from the origin are introduced

(fig. 5.3), where

Fig. 5.3

5.9 D /2

s

A

.. u

Coordinate system, introducing the dimensionless vetoeities u ' u ' e, the angle of flow separation e n p s and the tength of the standing eddy W

The velocity profiles at e = ~/4, ~/2 and 3~/4 are compared. Since

the pointer is located in this range, special attention is given

to the range of Ç < 5. Several types of mesh were used. For low

Reynolds numbers one can expect a 'symmetrical' flow pattern with

respect to the origin, whereas for higher Res numbers the flow

pattern will become more asymmetrical. Most mesh elements are

concentrated in the region where the gradients in the flow field

are expected to be big. The mesh presented in fig. 5.2 proved to

he satisfactory for lower Re6

numbers as well. Doubling the number

of elements of the mesh showed variations in the solutions for

Ç < 5 of less than 1 %.

43

The effect of the boundary conditions ( i.e. two plates at ~he far

ends of the eylinder) was then calculated. For this the distance

between the plate in front of the sphere and the centre of the

sphere was varied from 300 cm to 75 cm. The velocity profiles at

C < 5 showed no significant changes. Therefore in all further

calculations this left boundary was placed at 75 cm, i.e. 15Ds.

The other boundarjf was kept at 300 cm, which is the minimum

distance used during the measurements in our calibration unit.

As mentioned before, a disadvantage of the P.F.A. is that the

value of T bas to be chosen with great care. If T is chosen too

large, the matrix in eqn. 5.7a may become singular and if T is too

small the calculations can become too inaccurate, because eqn 5.6

is no longera good approximation of eqn. 5.1b. Oalculations were

performed wi tb 4 values of T: 10E4, 10E5, 10E6 and 10E7. No

significant changes in the solutions of the velocity profiles at

C < 5 were found, except that for T = 10E6 at a higher Reynolds

number (Re > 300) the matrix became singular. s

To examine possible numerical oscillations, due to the fact that

at boundary (3) the Dirichlet boundary condition (eqn. 5.3a) was

chosen, calculations were also performed with the Neumann bbundary

condititon. This condition reads as

5.10

The use of the Neumann boundary condition is more advantageous

from a numerically point of view (Cuvelier et al. '86) and is also

acceptable from a physical point of view. However, no sign'ificant

differences in the velocity profiles at r < 5 were discovered, so

that the Dirichlet condition was chosen in our numerical

calculations.

44

5.4.2 Velocity profiles and verification

The flow fields are calculated at a number of Re values between s

3.4 and 313. This range is basedon two criteria:

* The lowest Re8

number corresponds to an air velocity of 1 mm/s,

which is the lowest air velocity we use for calibration.

* The upper limit is determined by the assumption of axial

symmetry (boundary condi tion, eqn. 5.3c). At Res numbers higher

than approx. 340 a vortex street will form bebind the sphere, for

instanee see Magarvey & McLatchy '65. The flow has become

non-stationary and has to be described by the time dependent three

dimensional Navier Stokes equations, which will not be considered

in this thesis. It should be noted bere that the Reynolds number

of 340 above which non-stationary phenomena occur, is still matter

of discussion, which is illustrated by the fact that for this

Reynolds number several values between 300 and 450 are reported:

Taneda ('56) finds 300, Goldburg & Florsheim ('66) 340 and

Pruppacher ( '70) 400. If the veloei ty profiles are calculated

numerically from the stationary Navier Stokes equations for higher

Reynolds numbers, an unstable solution will he obtained. This

would only occur in the experimental set-up in the case of a

slightest disturbance.

The resul ts of the veloei ty profiles for r < 5 and 9 =~J/2 are

presented in fig. 5.4a and b. With increasing Reynolds number both

figures show an increasing maximum value of the veloei ty at a

decreasing value of r. see table 5.1. where some results of the

numerical calculations are presented. In fig. 5.4a it is shown

that at 9 = v/2 for C > 3, the influence of the sphere on un is

less than 0.05. In fig. 5.4b oscillations occur at Res = 313,

especially obvious at C ~ 3.5. These oscillations can be ascribed

to the fact that the elements of the mesh in this particular

region are chosen too large. The parabolic behaviour between

r = 3.3 and 3.7 is due to the choice of a quadratic polynomial as

interpolation function.

1.2 0.18

t 1.0 t

u 0.8 u n

t

p s

p 0.6 a

0.4 0.06

0.2 0.03

o~---L----L---~----~--~ 0 0 1

Fig. 5.4

3.2

2.0

2 3

c-4 5 0 1 2 3 4

c -Velocity profiles: u (a) and u {b) as a function of C

n p at a = 11'/2. 1: Res= 3.4, 2: Res = 6.8, 3: Res = 13.6, 4: Res~ 27.2,

5: Res = 54.4, 6: Res = 109, 7: Res = 313

11'/2

- e

0

t

f s

14

11

8

5

7

v/2

-a

Fig. 5.5 The pressure, ps' and the uorticity, f5

, at the surface

of the sphere US a. 1: Res= 3.4, 2: Res = 6.8, 3: Res = 13.6, 4: Res= 27.2,

5: Res = 54.4, 6: Re5

= 109, 7: Res = 313

46

5

0

u cyl mm/s 1 2 4 8 16 32 77 92

Re 3.4 6.8 13.6 27.2 54.4 109 262 313 s max. u 1.01 1.02 1.03 1.05 1.08 1.11 1.12 1.12 n

rmax )5 4.7 2.6 2.1 1.7 1.5 1.4 1.3

Table 5.1 Values of max. un and Çmax

In fig. 5.5a,b the dimensionless pressure ps and the dimensionless

vortici ty t s at the surface of the sphere are presented as a

function of e. where

f V x u 5.11

In our calculations the sphere surface was segmented into 14

points, connected by straight lines. This might be the reason why

in fig. 5.5b for e ~ and e = 0, the vorticity is not equal to

zero: the vorticity is calculated with eqn. 5.11 so that the

accuracy of the vorticity is one order of magnitude less than the

accuracy of the velocity profiles and around both mentioned points

the velocity shows relatively great variations, which might cause

the extra errors in ts·

From fig. 5.5a it can be seen that Res ~ m leads to p5 ~ 1 at

e = ~ which agrees with Bernoulli's stagnation pressure.

At Res = 313 both profiles show a pattern which differs from the

patterns found at lower Re5

values. In fig. 5.5a and b the curves

intercept at one point, except for curve 7. This fact and the

os ei lla ti ons shown in fig. 5. 5, gi ve us reason to conc l u de tha t

the solution at Res = 313 is not very reliable.

47

From the results presented in figs 5.4 and 5.5, the drag

coefficient Cd' the length of the standing eddy Wand the angle of

flow separation Ss are calculated.

* The drag coefficient cd is defined by

where F is the force exerted on the object (sphere) and

A (= T•u2/4} the area of the sphere. s

5.12

Using the calculated velocity and pressure profiles, Cd can be

determined from

T

sin 20 d9- 4/Res· J fs sin29 dO

0

5.13

* To obtain W the velocity profile of u is calculated for 9 = 0 p

and 1 < C < 4. The dUferenee in C from C = 1 to the point at

which u = 0 (point A in fig. 5.3) yields W. p

* To determine as the point on the sphere surface (C = 1} at which

éJun/éJÇ = 0 (point B in fig. 5.3) bas to be fourui. Hence the

velocity profile of un is calculated every 2.5 degrees.

The results of Cd' W/Ds' and 05

vs. Res are presented in

fig. 5.6a, c and d respectively. In fig 5.6b Cd/Cs-1 vs. Res is

shown, where Cs is the drag coefficient in the case of Stokes flow

(C = 24/Re ) . Our numerical resul ts (*) are compared wi tb the s s numerical results of Jenson '59 (e). Pruppacher et al. '70 (o),

Rimon & Cheng '69 (A) and the experimental results of Taneda '56

(!), Maxworthy '65 (*) and Perry '50 (1) and with results obtained

from Stokes {2) and Oseen's theory (3).

48

1 10

1

0.1 1

i

W/D

1.2

1.0

s

0.4

0.2

0 0

r 8

s

0.01 10 100 1000 1 10 100

Re ~ Re ~ s s

20 40 60 80 100 120

Re ~ s

100

50

o~~-----L--~~~----~--~--~----~-~

1 2 5 10

Re ~ s

100 1000

Fig. 5.6 : Variation of Cd (a), Cd/C5

-1 (b), W/Ds (c) and Ss (d)

vs. Res. For explanation of the symbols see text

49

1000

In fig. 5.6 the agreement of our calculations with values from

Uterature is clearly shown. The critica! Reynolds number is found

to be just under 20, which corresponds well with the values

presented in literature, where Taneda finds 24, Dennis & Walker ( '71) find 21 and Pruppacher 20. Taneda's value fqr the

critica! Re5

seems to be rather high. However the extreme

difficulties in visualising the flow at small Res numbers may well

have caused an inaccurate determination of the critica! Reynolds

number in Taneda's work. The values of Cd obtained by Jenson are

too high, which could be caused by the dimensions of his numerical

geometry, where the radius of the surrounding cylinder is chosen

3.5 times the sphere radius.

5.4.3 Influence of the geometry of the cylinder

In order to determine the influence of the finite geometry of the

eaUbration cylinder on the velocity profïles, calculations are

performed where the diameter of the eaUbration unit, Dt' is

varied between 24Ds and 5Ds. In fig. 5. 7 the veloei ty profile

un(C,Dt/Ds)' Aun and Aun'un(C.24) at 1 < C < 4 arepresentedas a

function of C at 9 = v/2 for different Dt at Res = 3.1 (a),

13.6 {b} and 109 (c),where

5.14

In fig. 5.7c it is shown that for calibration units with diameters

larger than approx. 10 times the diameter of the anemometer the

veloei ty profile alters less than 5 %, compared to the veloei ty

profile obtained wi th our eaUbration unit {Dt/Ds = 24), for all

Res values between 3.4 and 109. For smaller values of Dt/Ds the

difference in velocity profiles decreases from 30 % max. at

Re = 3.4 to 6 % max. at Re = 109. So the influence of the s s dimensions of the calibration unit on the velocity profile u (C)

n at e = v/2 is larger at lower Re numbers, which agrees with the

. s commonly accepted wall-effects theories (Happel & Brenner '73).

50

1.2 .20 30%

i i i u Au Au

n n ___Jl

u n

Re = 3.4 s

0 1 2 3 4 2 3 4 2 3 4

r- ,_ r-

1.2 12 % ----·

6

i i i ~ u Au .Au

n n ___Jl

u

--------n Re = 13.

s 0 0

1 2 3 4 2 3 4 1 2 3 4

r- r- r-

1.2 6%\ r I

6

i i t \

~ 1-

u .Au Au n n ___Jl 2. u n '---- 3 Re 109 --.._

s I 0 I o--

1 2 3 4 2 3 4 1 2 3 4

r- r- r-

Fig. 5.7 u (( ,Dt/D }, the absolute and rel.attue deviation from n s un((,24) at Re

6 = 3.4 (a). 13.6 (b) and 109 (c)

Dt/D6

5 (1), 6 (2), 8 (3), 10 (4), 16 (5) and 24 (6)

51

5. 5 OONCLUSIONS AND DISCUSSION

The comparison of the quantities found in our numerical research

with those presented in literature show for Reynolds numbers lower

than approx. 313 good agreement in the case of the; drag

coefficient, the eddy length and the angle of separation.

Therefore we conclude that the results for the veloeities u (C) in n

the vicini ty of the sphere are reliable. It is shown that for

( ) 3 and 9 = T/2 the influence of the sphere on the flOW is less

than 5 %.

Once having calculated the velocity profiles in the vicinity of

the sphere, we can try to calculate the influence of the fact that

the velocity at the position of the pointer is not equal to U 1

. cy To that end the relationship between the velocity and the moment

of force on the pointer has to be known. This relationship and a

first at tempt to discount the numerically calculated ve'loci ty

profiles will be discussed in chapter 6.

52

6 MEASUREMENTS WITII TIIE MICROANEMOMITER

6.1 INTRODUeTION

In this chapter experiments for the calibration curve of a

microanemometer are presented at air veloeities ranging from

1 mm/s to several m/s, using the previously described calibration

unit at low air veloeities (chapter 4) and a wind tunnel at higher

air velocities. We shall use the word calibration curve for the

re lat i on between the output voltage of the feedback sys tem V out

and the air velocity U. Vout is related to the current I through

the coil of the moving-coil meter by

V = I R out s 6.1

where Rs the resistance in series with the coil of the moving-coil

meter.

We also determined the influence on the calibration curve of

several dimensions of the microanemometer, such as the length of

the pointer and the diameter of the surrounding sphere.

The dynamic behaviour of the microanemometer is described in the

second part of this chapter.

6. 2 DETERMINING TIIE MICROANEMOMETER VELOCITY RANGE

The calibration unit is used at lower air veloeities to determine

the veloei ty range of a microanemometer (wi th moving-coi l meter

type Ia, see table 4.1). Experiments are carried out measuring

Vout at air veloeities up to 130 mm/s. Four calibration

measurements were performed at each air veloei ty, twice wi th a

'positive' and twice with a 'negative' train velocity U 1. In the cy cal i bration resul ts wi th negative train veloei ties, the negative

values of Vout were multiplied by a factor of -1.

53

The averaged value of the four measurements is presented at a

pos i tive value of U 1. A wind tunnel is used to calibrate the / cy

higher part of the velocity range. In this rectangular wind tunnel

(51 x 70 cm2) the air veloei ty. which is determined wi th a: Pitot

static tube, can be varied from approx. 10 cm/s up to several mis.

Several preliminary experiments before the actual calibration

measurements determined the optimum pos i tion of this Pi tot tube

inside the wind tunnel with respect to the position of the

microanemometer.

The results of the calibration are shown in fig. 6.1. In fig 6.1a

vout is shown vs. u. which is either taken equal to ucyl or

calculated from the measurements with the Pitot tube. In fig. 6.1b

the velocity range under 40 cmis is shown on an enlarged scale.

45.---~.---------~-----, 900

• T * T

30 • 600

V out *

V out (V)

15

..... ..... ..... • •

*

~··I I o--~~----~----~--~ I

0 100 200 300 400

U (cm/s) -

(mV) ....

300 • 11

11 _"..' 0 I I I

0 10 20 30

U (cm/s) -Fig. 6.1 Galtbration curve of a microanemometer: Vout vs. U.

Measurements in the calibration unit (•}. Measurements in the wind tunnel. befare (i} and after (*) changing R

5•

The calibration resul ts, shown in fig. 6.1. can be used to

determine Umi. defined as the air velocity at which the S.N.R.

equals unity. It appeared that the S.N.R. equalled 1.2 at ian air

54

40

velocity

In fig.

13 cm/s)

of 1 mm/s, hence Umi is somewhat less than 1 mm/s.

6.1 there is a good overlap (air veloei ties of 9 to

between the two regions of calibration. At an air

velocity of 225 cm/s the value of V t amounted to 15 V. so that OU

the air velocity Ufs = 225 cm/s. This value shows good agreement

wi th the estimated veloei ty given in table 3. 1. In order to he

able to measure even higher air velocities, the value of R was s

deereased, after which it was found to be possible to measure air

veloeities of up to 4 mis. Above those air veloeities the pointer

started to oseillate and no measurements were performed.

Experiments for studying the co i l at values of I varying from

50•Ifs up to 300•Ifs were performed to investigate the effect of

increasing the current above the full scale current Ifs" Even at

sueh large eurrents there were no irreversible effects.

The experimental results obtained with our calibration unit (air

veloeities up to 130 mm/s) are fitted with a quadratic relation

between vout and ucyl' using a numerical least squares fitting

procedure which was available as a subroutine on a microcomputer.

For the microanemometer used in the experiments this resulted in

V t = VO(U) OU

6.2

In fig. 6.2 the relative discrepancies (RD) between the

experimental values of U and the values, obtained with eqn. 6.2 at

air veloeities up to 40 cm/s is shown.

From fig. 6.2 it can be seen that at air veloeities lower than

13 cm/s, the air velocity can be predicted with an accuracy better

than 6 %, whereas for air veloeities lower than 40 cm/s the

accuracy is better than 8 %.

55

10%

T '• "' "'

RD 0 •• ... "' • -· .

(%) • ......

-10% I I I

0 10 20 30 40

U {cm/s) -Ftg. 6.2 Retattve dtscrepanctes between the expertmental vatues

of U and the vatues calculated with eqn. 6.2. • :measurements tn the caltbration untt, .l :measurements tn the wind tunneL

6.3 CALIBRATION MEASUREMENTS WITH DIFFERENT TYPES OF

MICROANEMOMETERS

6.3.1 Microanemometers with different pointer lengtbs

Several calibration series were performed in our calibration unit

to determine the influence of the length L of the pointer' of the

microanemometer. Each of these series consistedof measurements at

air veloeities of between 1 and 130 mmls. At each velocity, six

measurements were performed and averaged, three times wi th a

'positive' train velocity and three times with a 'negative' train

veloei ty. The length of the pointer was decreased by approximately

5 mm after each series and a new calibration series started. In

this way we got 9 values of L between 67 and 26.5 mm. The tenth

calibration series was performed with L equal to L0 .

In fig. 6.3 Vout is shown vs. Ucyl at several pointer lengths. For

each L the values of c3

and c4

were determined and the curves

corresponding to eqn. 6.2 are also shown in fig. 6.3.

56

400

T 300

V out

{mV)

200

100

50

0 0

Fig. 6.3

1.1

r 1.0

V 0.9 out

u 0.8 " cyl z'kx:z:

0.7 (Vs/m)

0.6

67.0 mm

.. 64.0 mm

58.5 mm

53.5 mm

48.5 mm

43.5 mm

25 50 75 100 125

u cyl (mm/s)

Cal.ibration curves (V t us. U I.) of the OU C!J

microanemometer at severat tengths L of the pointer. The curvesdrawnare the parabotte curves (eqn. 6.2).

2.5

.....;. 2.3

2.1

1.9

150

L 43.5 mm 1.7 L 64.0 mm

1.5 0 25 50 75 100 125 0 25 50 75 100

u cyl (mm/s) ~ u cyl (mm/s)

Fig. 6.4 V /U vs. UC"' at two different tengths out cyt "c

57

125

~

As far as the measurements with L=Lo are concerned, it is noted

bere that V t amounted to 0 ± 1 mV and was independent of U 1. OU cy

V /U 1 vs. U 1 is plotted for two values of L in fig 6.4 in out cy cy order to make discrepancies between the values of Vout calculated

with.eqn. 6.2 and the experimental results more readily visible.

Deviations between the measured data and eqn. 6.2 should result in

deviations from the straight lines drawn.

From fig. 6.4 we learn that at air veloeities higher than approx.

15 mm/s the relation between vout/Ucyl and ucyl is linear in

accordance with eqn. 6.2. We see discrepancies between the results

calculated with eqn. 6.2 and the expertmental results at air

veloeities lower than 15 mm/s. At these air veloeities V t/U 1 OU cy tends to independenee of ucyl·

We shall use M, the moment of force exerted on the pointer. for

the discussion of the results of the measurements depending on L.

Substituting eqn. 6.1 in eqn. 3.2 yields

M = G•V /R out s 6.3

The value of G was determined as previously descri!bed in

chapter 3. This was done before and after the calibration series:

both va lues of G so obtained agreed wi th one another wi thin

measurement accuracy. Using this value of G, the values of M were

calculated from the values of vout"

Assuming that the force per unit of length normal to the pointer

F!(Ucyl) is not dependent on L, the following model is introduced

6.4

58

2.0

* 1 mm/s

• 5 mm/s

* 10 mm/s

l 1.5

M (nNm)

1.0

0 0 1000 2000 3000 4000 5000

L2 (mm2) -24

• 50 mm/s • 60 mm/s

* 75 mm/s

l 16

M (nNm)

8

o~~-L----~--~~---L--~

0 1000 2000 3000 4000 5000

L2 (mm2

}

l M

r M

10

5

48

32

16

•: 20 mm/s • 30 mm/s *: 40 mm/s

1000 2000 3000 4000 5000

L2 (mm2) -

•: 90 mm/s . : 110 mm/s *: 130 mm/s

o~L--L----~--~-----L--~

0 1000 2000 3000 4000 5000

(mm2

)

Fig. 6.5 M vs. L2 at different air vetoeities

59

In fig. 6.5 the values of M ealculated with eqn. 6.3 from the

measured values of V t are plotted vs. L2 at different air OU

velocities. The measurements were the same as those of fig. 6.3.

The lines drawnare the results of linear regression betweenMand

L2 . The intersection with the L2 axis yields La 18 + 2 mm. This

value closely corresponds to the actual value of La that is 19 mm.

From fig. 6.5 we see that the measurements correspond closely to

relation 6.4 at air veloeities higher than approx. 10 mm/s.

Discrepancies occur at lower air veloeities and at shorter pointer

lenghts.

6.3.2 The influence of the sphere

A moving-coil meter with a pointer length of 74 mm was

successively mounted in four spheres differing in diameter D5

{44,

52, 80 and 98 mm) to determine the influence of the sphere mounted

round part of the microanemometer, on the results. In all cases L0 was 14 mm. Measurements were performed at air veloeities ranging

from 1 to 13a mm/s. At each velocity, six measurements were

performed and averaged. In fig. 6.6a the eaUbration curves are

shown at the four values of D . It is shown that at all air s

veloeities an increase of Ds results in an increase of Vout' These

differences of Vout between the calibration curves at different

values of Ds can be interpreted as corresponding differences in

air velocities. Fig. 6.6b gives these differences in air

veloei ties, AU, of the eaUbration curves values at Ds = · 52, 8a

and 98 mm resp. and the eaUbration curve at D5= 44 mrit. From

fig. 6.6b we see that this increase in V t results in differences OU .

in air veloeities of 1a mm/s max.

60

390 ~

T ~

V ~ out

~ (mV) • 44 mm

130 I)

0 52 mm è • D 80 mm

'- A 98 mm

~·· I 0 0 50 100 150

u cyl (mm/s) -12

/;),.

/;),. /;),.

D

T D

D 4 8

AU 0 0 0

(mm/s)

-4 0 52 mm

D 80 mm

A 98 mm

-12 0 50 100 150

u cyl (mm/s) -Fig. 6.6 V out vs. U l at severat values of D (a) cy s

AU U(D ) - U(D = 42 mm) us. U t (b) s s cy

6.4 COMPARISON WITII LITERATURE Cd VS. REYNOLDS CURVES

In order to compare the results of our experiments with those of

cd given in literature, we u se cd ' to characterise our resul ts.

Assuming that the force on the pointer is exerted at (L+L0 }/2,

which we shall call the effective pointer length. we get

61

6.5

In fig. 6.7 Cd' is plotted vs. Ree on a double logarithmic scale,

where Re is based on the diameter of the cylindrical pointer. The c

values of Cd' are obtained from the experiments shown in fig. 6.1.

These values are compared with Cd values for an infinitely long

cylinder (Schlichting '79}. lt is clearly seen that, at Re0

values

above approx. 1, which corresponds to an air velocity of 4 cm/s,

the expertmental values agree well with literature values. So at

these Ree values the cylindrical pointer can be interpreted as a

infini tely long cylinder. Also the assumption that the force is

effectively exerted at (L+L0)/2 seems correct. At lower Ree values

the experimental values are systematically higher than the values

from literature for an infinitely long cylinder, which will be

further discussed in § 6.6.

1 C'

d

lOOr-------r-------r-------r------, •

10

1

0.1~------~------~------~----~

0.1 1 10

Re -c

100 1000

Fig. 6.7 A plot of Cd' vs. Ree ---- : Cd for an inftnitety long cylinder (Schtichttng}

62

1000

* i ~· t 1::.

100 "'"' · ... !, c· d

10

1 I I

0.01 0.1 1

Re ~ c

Fig. 6.8 The influence of L on Cd' vs. Ree

L = 64.0 mm (*) ; L = 38.5 mm (*)

At:.~::.

10

Tritton (o), ]ayaweera 8 Mason {D), Huner 8 Hussey (A)

The effect of the finite pointer length on the drag coefficient is

presented in fig. 6.8 where Cd' vs. Ree is presented at two

different pointer lengtbs on a double logarithmic scale. The

values of Cd' are calculated from the experiments shown earlier in

fig. 6.3 and are compared with experiments of Tritton '59,

Jayaweera & Mason '65 and Huner & Hussey '77 referred to in

literature.

It appears that, at higher Reynolds numbers. there is a good

agreement between our results and those of literature. At smaller

Reynolds numbers, Cd' values are higher than the values of Cd

which can also beseen in fig. 6.7. We see that. generally the Cd'

values corresponding to a shorter pointer are higher than those

with a longer pointer.

63

T 45

c· d

30

15~~~~c=~c=~ 40

Fig. 6.9 The inftuence of D8

on Cd' at seuerat uatues of Ucyt

The influence of Ds on the drag coefficient is presented in

fig. 6.9, where Cd'' based upon the results shown in fig. 6.6, vs.

D is shown at several veloeities of U 1. We see that an increase s cy of 0

8 results inaslight increase of Cd'. This increase amounts to

approx. 15% at air veloeities of 8 mm/s and to approx. 6% at air

veloeities higher than 50 mmls. Hence at lower air velocities, this

increase is larger than at higher air velocities.

6.5 A FIRST CûMPARISON WITII NUMERICAL RESULTS

A first at tempt is made to campare the resul ts obtained in our

experiments wi th the numerical resul ts given in chapter 5. These

numerical results, however, only concern velocity profiles in the

vicinity of the sphere, calculated in the case where there is no

pointer. Batchelor '70 and Cox '70 showed that a linear relation

between Ft(U) and U (1) could be used where U {1) is the normal n n component of the velocity at position 1. This, however, was shown

using the slender-body theory in the case of Stokes flow and of a

cylinder (pointer) of infinite length. We shall apply their results

to higher Re numbers and to finite cylinders.

64

The velocity profiles un(l) presented in fig. 5.4a are used in the

numerical determination of the moment of force Mn. For Mn we get

6.6

In a first approximation the constants c5

and c6 are chosen in

accordance with c3 and c4 (§ 6.2). Ds and L0 are chosen equal to

the corresponding values used during the experiments. In fig. 6.10

the results are shown of the comparison with the measured moment

M. In this figure {Mn/M - 1}*100% is plotted as a function of Ucyl

at three values of L.

We learn from fig. 6.10 that at air veloeities higher than 10 mm/s

and pointer lengtbs longer than 53.5 mm, the discrepancy between

the numerical and measured values is less than 5 %. This means

that, in the case of longer pointers, the influence of the fact

that the veloei ty profile in the vicini ty of the sphere is not

equal to the undisturbed veloei ty, plays a less important role

when calculating the moment of force on the pointer.

T

M/M- 1 n {%)

Fig. 6.10

5

0

-5

-10

* L 38.5 mm

* L 53.5 mm

-35 67.0 mm

-40 0 25 50 75 100

u (mm/s) ----+

Comparison between numerical and experimentat values (M /M -1)*100% US. u 1

n cyc

65

6. 6 DisaJSSION

In this cbapter

microanemometer

estimated to be

U . measurable with a m1

the mimimum air veloei ty

(with moving-coil meter

less than 1 mm/s. This

type Ia) bas been

meets the demands '

formulated in cbapter 1. It bas to be mentioned tbat the i

calibration curves of the other two types (Ib and Ie) resulted in

the same estimate of U .: the S.N.R. at U 1 equal to 1 mm/s did m1 cy

not differ significantly for all three cases. Thus, in further

research, all three types of moving-coil meters can be used in

constructing a microanemometer.

The results of the calibration obtained with our calibration unit

can be extended to air veloei ties as high as 40 cm/s wi th an

accuracy better than 8%. At air veloeities higher than 4 cm/s,

however, the pointer can be assumed to be infinitely long and the

theoretica! relation between Cd and Ree for an infinitely long

cylinder can be applied (see fig. 6.7). The relation between vout

and U can be determined from this theoretica! relation. Hence,

from a combination of this theoretica! relation and the

calibration curve of the anemometer the calibration can be

extended to air veloeities as high as 4 mis.

In fig. 6.7 and fig. 6.8 it is shown tbat, at lower Ree values,

qur values of Cd', calculated on the basis of eqn. 6.5, are

systematically too high. Possible reasans for this are:

* The lengtb/diameter ratio of the cylinder used during our

experiments (max. 125) is lower than those mostly occurring in

literature (varying from 100 up to 1000). This lower ratio would

re sult in an increase of F 1 (U cy 1) and thus of Cd' (Huner &.

Hussey '77). This assumption is confirmed by our data.

66

* The assumption that the force is exerted at the effective

pointer length is questionable at lower air velocities. This doubt

is sustained by the comparison with the numerical results, which

show that the influence of the fact that the velocity profile is

not uniform can be neglected only at bigher air veloeities and

long pointer length. In our measurements the surrounding sphere

disturbs the velocity profile, whereas in literature only

plug-flows are considered. In par. 6.5 it is shown that the

influence of the sphere on the velocity profiles, and therefore on

the moment of force, is negligible only at higher air velocities.

At lower air veloei ties the experimental values of M are higher

than M . The fact that the air velocity is higher than U 1 would n cy

result in a decrease of Cd' calculated from eqn. 6.5, so

compensating the overestimation of Cd' as

* As far as the influence of D5

is concerned, an increase of Ds

involves an increase of Cd' and Res at the same air velocity. The

influence of this increase of Res is negligible, which can be seen

in fig. 6.10 where the difference between Mn and M is constant at

higher Res numbers. An increase of D5

, however, brings with it a

decrease in the value of C ( see eqn. 5. 9) . A decrease of C generally yields an increase of U(Ç), resul ting in an

overestimation of Cd' as mentioned before.

* Other reasons could be the inaccuracy of the measurement of G

and the length of the cylindrical pointer. However, this only

could result in a vertical translation of the curves in figs. 6.7

and 6.8. Hence, in view of the fact that the curves compare well

at higher air velocities, this explication is questionable.

67

6. 7 THE DYNAMIC BEHAVIOUR OF THE MICROANEMOMETER

6. 7.1 Theory

To determine the dynamic behaviour of the microanemometer the

transfer function S(w) is found by means of

S(w) == I(w} M(w)

For this purpose eqn. 3.1 is written as

2 [-Jw + jwK + C] a(w} = M(w} - G•I(w)

The feedback system (see § 3.3.2) yields

6.7

6.8

6.9

The transfer function S(w) is obtained by substituting eqns. 6.8

and 6.9 in eqn. 6.7 and reads as

1 + jwti S(w) = P ·-----------­

PG- w~t1 + jwt1(PG + C- w2J}

6.7.2 Experiments

6.10

Several preliminary experiments were carried out to determine the

constants G, J. K and C. The values of G and Care determined as

described in chapter 3. The moment of inertia J and the damping

constant K are obtained from a step response without feedback

system. For this purpose the induction voltage over the coil is

measured as a function of time. With these values of G, J, K and C

the frequency response of the meter can be calculated.

68

The frequency response can also be measured directly in the

following way.

An extra alternating current I5(t) is superimposed on the current

through the coil. This extra CUTTent will cause a deflection of

the pointer. The feedback system will react by adjusting the total

current I(t) through the coil. This procedure was foliowed for

several frequencies of Is(t) between 0.25 Hz to 45 Hz. In

fig. 6.11 the quotientof the amplitudes I/Is is shown vs. the

frequency f. The data are connected with a curved line. The second

curved line in fig. 6.11 corresponds to IIS(f)ll with eqn. 6.10.

From fig. 6.11 we see that IIS(f)ll is independent of f at

frequencies lower than approx. 10 Hz. Discrepancies between the

experimental values and IIS(f)ll, calculated from eqn. 6.10 can he

traeed to errors in the determination of Pand j.

48

40

l 32

I/Is 24

16

8

0 0

Fig. 6.11

10 20 30 40

freq. f (Hz)

I/I6

vs. frequency. Data are connected by a curve.

The curued tine represents IIS(f)ll (eqn. 6.10).

50

69

l (mA)

l (mA)

I( t)

0 0.5

.Is(t) j ft __jy

____,j

I(t)

I

0 0.5

p = 1200

1.0 1.5 2.0

time (s) ~

p = 1750

I I

1.0 1.5 2.0

time (s) ~

Ftg. 6.!2 :I(t) as a functton of time, 18(t) ts a step funcHon

The applicability of the microanemometer in the case of

fluctuating air veloei ties can also be concluded from fig. 6.12.

Here the response of our microanemometer to a step function in

I5(t} is shown at two different values of P, resp. 1200 and 1750.

It is shown that the feedback system of our microanemometer

follows the step reponse within approx. 0.1 seconds. The delay

time between I5(t) and I(t) is due to a !ow-pass filter which is

included in the circuit at 20Hz.

70

6.8 DISCUSSION AND a>NCLUDING REMARKS

Our microanemometer is able to measure air veloei ties as low as

1 mm/s up to several mis. Both veloei ty 1 imi ts are dependent on

the length L of the pointer. An inerease of L resul ts in a

decrease of both limits. The microanemometer feedback system also

allows measurements up to frequeneies higher than aimed at. Our

microanemometer can be considered as a welcome supplement to the

commercially available anemometers and will in many cases be a

less expensive but more reliable alternative.

In this chapter we discussed the calibration of the

microanemometer in an uniform plug flow and investigated the

influence of the length of the pointer and the surrounding sphere.

It has to be mentioned that in the case of fluctuating air

veloeities a number of phenomena, whieh will undoubtedly influence

the eaUbration curve, will have to be taken into account. In

future research, consideration will have to be given to the

influence of non uniform and of non stationary flow on the

calibration curves.

71

7 JIIClOANEIDIIITERS FOR MF.ASURING IIULTIDIJIEifSIC:JfAL AIR VEI..OCITIFS

7. 1 INTRODUGriON

It bas been sbown bow tbe magnitude of tbe air velocity was

obtained by measurement in tbe case of an air velocity with known

direction. In many practical purposes, bowever, tbe magni.tude as

well as tbe direction of tbe air veloei ty will be unknown. We

developed a new type of microanemometer, wbicb we shall call a

multidimensional microanemometer for measuring botb quantities.

Sucb a microanemometer can be obtained in two ways.

The first is to use a one-dimensional microanemometer (witb a

single moving-coil meter) and carry out more measurements witb tbe

pointer in different directions.. This metbod is very sui table in

tbe case that a constant air velocity is to be measured, but it

may cause considerable errors when tbe air veloei ties are not

constant in time.

The second metbod wbicb will now be discussed, is based on tbe

sirnul taneous measurement of several veloei ty components using a

number of moving-coil meters wi tb tbeir pointers in different

directions.

In tbis chapter two types of mul tidimensional microanemometers

will be introduced:

* tbe two-dimensional microanemometers, referred to as tbe

T-series. having at least two moving-coil meters witb tbeir

pointers in one plane, wbicb can be used for measuring air

veloeities of known direction in a given plane,

* tbe tbree-dimensional microanemometers, referred to as tbe

D-series, witbat least tbree moving-coil meters, wbicb are

useful in all otber cases.

72

7. 2 DIRECfiONAL SENSITIVITY

7.2.1 Introduetion

As it is our aim to measure the air velocity ~ with respect to the

position of the microanemometer. a coordinate system XYZ is

introduced which is assumed to be 'fixed' on the microanemometer.

A multidimensional microanemometer usually consistsof a number of

moving-coil meters, but we shall first restriet ourselves to a

microanemometer with only one moving-coil meter. The position of

this moving-coil meter is characterised in the coordinate system

by the unit veetors ~r· ~Pand ~n· where

e represents the rotation axis of -r e the direction of the pointer and -p e the direction of the movement of -n

about its rotation axis, with

the moving-coil meter,

the pointer

e x e . -r -p

rotating

In the coordinate system the air velocity U can be written as

U = U•e -u 7.1

where U is the magnitude of the air velocity and ~u is the unit

vector characterising the direction of U.

A series of experiments was carried out to determine the output

voltage V out of the microanemometer wi th the single moving-coi l

meter at air velocity ~· To facilitate a discussion of the results

we use a model incorporating the results of the preceding chapter.

In this model we assume that Vout(~) can be written as

7.2

where VO{U) is a relation analogous to eqn. 6.2.

73

--~~----- u - -

Fig. 7.1 : Introduetion of the angLes ~ and 7

For practical reasons we will use the angles ~ and 7 defined in

fig. 7.1. In the plane through U and e we define ~ as the angle - -p hetween a line normal to U and e . Pos i tive ~ corresponds to a

- -p situation in which the pointer is located in front of the sphere

(upstream). We take 7 as the angle between e x U and e . -p - -r Using ~ and 7 eqn. 7.2 can be written as

7.3

! 7.4a

7.4b

The results of the experiments B and G are presented by exp exp

B == Vout(U.~) 7.5a

exp vout(U.O)

G == V t(7) OU 7.5b

exp Vout(O)

74

7.2.2 Experiments to determine G{7)

Measurements were carried out in our calibration unit todetermine

G In these experiments we restricted ourselves to the exp situation in which ~ = 0. First the microanemometer was mounted in

the calibration unit so that ' ~ 0. Six calibration measurements

were carried out at a single value of Ucyl' Positive train

veloeities correspond to measurements at < = 0 and negative train

veloeities at < = -180 degrees. This procedure was repeated at

several values of U 1 ranging between 12 and 120 mm/s. Then < was cy increased by 15 degrees, the microanemometer being rotated by

means of a stepping motor. This resulted in a range of ' between

0 ~ < ~ 90 and -180 ~ ' ~ -90.

In fig. 7.2 the results are shown for G (-r) vs. < at two exp

different air veloei ties. The curved line represents cos <. For

clearness' sake the values of G (<) arepresentedat values of ' exp as well as values of -<. In this figure we see that the values of

G (<} correspond to cos 7 within the measurement inaccuracy and exp

that it is correct to assume that G {<) is independent of U. exp

120%.-----.----,,----,-----,

T 40%

G (7) exp

-40%

u cyl

-120% '----------''---------'-------'-------'

-180 -90 0 90 180 -180

< {degr.)

u cyl

-90 0 90

< { degr. ) -----7

Fig. 7.2 G (<) vs. < (~ 0). The tines drawn represent cos<. exp

U 1 = 37 mm/s (a) and 120 mm/s (b) C!J<

75

180

7.2.3 Experiments todetermine B(U.B)

For the B measurements we concentrated on two types of exp two-dimensional microanemometers which we developed and tested,

that the T2-90 and the 13-120 (for a detailed description of both

meters see § 7.3.1}. The pointers of both microanemometers

protrude 60 mm from the sphere but they differ in Ds of ~esp. 52

and 64 mm. These meters include two and three moving-coil meters,

respectively. For the measurements reported in this par~aph we

refer to the results of only one of these moving-coil meters.

The experiments to determine B were similar to those described exp in § 7.2.2. Here the procedure involved measurements at different

values of ~ and U 1 and the value of 7 was taken as zero. The air cy veloei ties used are given in table 7.1 along wi th the

corresponding Reynolds numbers of the T2-90 and T3-120.

series A B c D E F G H

U 1 (mmls} 12 25 37 cy 50 60 75 90 105

Re T2-90 43 87 130 s 177 208 260 312 364

Re T3-120 53 106 160 213 256 320 384 448 s

Table 7.1 The veloeities of the catibration unit for severat calibration series and the correspondtng Reynolds values of the T2-90 and T3-120

I

120

416

512

In fig. 7.3 B (U.~) at U = 90 mm/s obtained with the T3-120 is exp .

represented vs. ~- The curve drawn corresponds to cos ~-

In fig. 7.3 we see a discrepancy between Bexp and Brood·

76

120%

i • • 40% •

Bexpan ..

-40% til lil

• I

-120%

-180 -90 0 90

(3 ( degr . } ----7

Fig. 7.3 B (U,{J) vs. (3 at U= 90 mm/s (~ exp

The tine druwn represents cos (3

180

0)

In fig. 7.4 this discrepancy [B (U,p) Bmod(13)]*100% is exp presented as a function of f3 and with U l as parameter for the cy measurements with the T2-90 and the T3-120. The capita! letters

correspond to those used in table 7 .1. One interval on the

vertical axis corresponds to 15 %.

Camparing the experimental results in fig. 7.4 with those of the

model, we may conclude that at air veloeities above 25 mm/s the

deviations seldom exceed 20%. When we restriet ourselves to the

values of (3 > -30 degrees we even find that deviations of more

than 10% are exceptional for air veloeities above 25 mm/s.

The comparison of the experimental results of the T2-90 with those

of the T3-120 can be performed in two different ways. One can

campare the results in the 7.4a and b plots at equal air

veloeities or at equal Reynolds (Re5

) numbers. Contrary to the

first one, the second comparison shows that there is no apparent

difference between the results of the two microanemometers.

77

30

15

0

0

0

0

l 0

Dev. (%)

0

0

0

0

. -15

-30

I T2-90 I

i I ., a I - :11 I • I

• ,. ... • .. J: . ... • • • !I !!l

111 I

"' m .. 11 w .. • IB

w

11 111

• • • I • " . .

4> • • .. IJl • I l m .. • • ~

1!1 .. . I I •

ll: I lil i ..

f I i 1 I " • i • I ll: I I " 2 I

" .. t .. .. .. .. • .. .. "' "' . - "' t • .. • . .. .. 2 • !

• 1!1 m

• .. ' .. m .. "' - .. :: .. ..

m .. .. " l!l I .. I .. .,

• .. .. .. . l

! . .

• . . • • . • . .. . .. • • *

I I I I I I . ,

-90 -60 -30 0 30 60 90

f3 (degr.) -

• T3-120

I I I . .

I I • . ... I .. I I .. I • .. .. • •

lil • • .. I ,. • .. H

• I .. t .. 111 111

I • • • • '" I • • • I • • • • 11 I •

G

• • • • ! • ! • ' .. I • • a .. .. • I •

F

• 111 .. • • I • I

• I 11 I ll: I I • I

E

I I I - I I D

a • I I .. I I .. .. .. • • • .. - ' I c • I • I • • .. I • • I I I 111 . .. . ;

ii !fi .. I • . • i I .

B

. 3 * . .. . • .. • • :

i • : I

* : I • ;

A

• I I I I I I I

-90 -60 -30 0 30 60 90

f3 (degr.) -

Fig. 7.1J Dev := [B (U,/3} - B 00(f3)J * 100% vs. f3 exp m 12-90 (a) ; T3-120 (b)

78

7.3 TilE TWO-DIMENSIONAL MICROANEMOMETERS: T2-90 AND T3-120

In the previous paragraph we considered the results of one of the

moving-coil meters of the microanemometer. In this paragraph,

however, we will use the complete information of the two

microanemometers, that is the T2-90 and TI-120. Both

microanemometers are always used in such a way that 7 = 0.

The T2-90 is shown schematically in fig. 7 .5. It is designed on

the principle of simultaneous measurement of two perpendicular

components of the air velocity using two moving-coil meters. These

meters are positioned in such a way that the directions of their

pointers are perpendicular to each other (Ds = 52 mm). The

distance between the far ends of the pointers is approx. 12 cm.

The direction of the air veloei ty is restricted to the XY plane

and is characterised by the angle ó, that is the angle between the

bisector of e 1 and e 2 and U_. The moving-coil meters are mounted -p -p in the microanemometer in such a way that the Y and X-axis

correspond toe 1 and e 2

, respectively. This results in: -p -p

Fig. 7.5

= (0,0.1) ~p1

~p2

(0,1,0)

(1 ,0,0) ~nl

!':n2

(-1,0,0)

(0,1,0)

Schematic representation of the T2-90

7.6a

7.6b

79

\ 1 1u lrr--/1f31=Ó

Ftg. 7.6 Schematic representation of the 13-120

The T3-120 is schematically shown in fig. 7 .6. It consists of

three moving-coil meters placed inside the sphere in sucl;l. a way

that the pointers, all in the XY plane form angles of 120 degrees

to one another. This is done because in chapter 5 we have found

that, at higher Reynolds numbers, a wake appears bebind the

sphere. Using the T3-120. two pointers generally remain :outside

this wake. However, using three moving-coil meters implies a

bigger sphere (Ds = 64 mm} and the distance between the far ends

of the pointers becomes approx. 15 cm. The coordinate system XYZ

and the angle 6 are defined as shown in fig. 7.6. This results in:

~r1 = (0,0,1) ~p1 = (0,-1,0) !n1 = (1,0,0} 7.7a

~r2 = (0.0,1) e 2 = (0.5v3,0.5,0} ~n2 = (-û.5, 0.5v3,0) 7.7b -p

~r3 = (0,0,1) !p3 = (-0.5v3,0.5,0} ~n3 (-0.5,-o.5v3,0} 7.7c

80

Two quant i ties are introduced for the data processing wi th the

T-series microanemometers: MA1 and DI1 concerning the magnitude

and direction of the velocity, where i is the number of pointers,

so that i = 2 corresponds to the T2-90 and i = 3 to the T3-120.

* Definition of MA2 and DI2

The output voltages of the two individual moving-coil meters Voutl

and Vout2 can be written according to eqn. 7.2. so that:

With eqn. 7.6 in mind. wedefine MA2 and DI2 as:

MA2 := vfv~utl + V~ut2

DI2 := arctan(Voutl/Vout2 ) + 45 if Vout2 ~ 0

arctan(Voutl/Vout2) - 135 if Vout2 < 0

* Definition of ~ and DI3

7.8

7.9

7.10

7.11a

7.1lb

As in the case of the T2-90 but now keeping eqn. 7.7 in mind, we

define ~ and DI3 as

MA3 :: vf(2/3)•(V2outl + y2 + y2 ) out2 out3 7.12

DI3 == arccos(Voutl!MA3 )

:= arccos(Voutl!MA3 ) - 180

if (Vout2-Vout3) l 0 7.13a

if (Vout2-vout3 ) < 0 7.13b

81

7.3.2 Calibrations

In §7 .2.3 we reported deviations between B and B d for a exp mo single moving-coil meter. To investigate the influence of this on

the performance of the T-series we carried out calibratio~ series

with the T2-90 and the T3-120, each series having its own value of

Ucyl and measurements at diff~rent values of 6. In the case of

measurements with the T2-90 this resulted in values of 6 ranging

from 0 ~ fj ~ 90 (pos i tive train veloeities} and - lSO ~ 6 ~ -90

(negative train velocities}. In the case of measurements with the

T3-120, ö ranged from 0 ~ fj ~ 120 and - lSO ~ 6 ~ -60.

* The MA1

calibration results

We use the symbol MA1m for the average measured value of MA1

averagedover one 6 series. In fig. 7.7 the relative discrepancies

RD between the measured and the averaged values are presented with

RD = [ MA.(ö) - MAi ]IMAi * 100% 1 m m 7.14

The capita! letters between figs. 7.7a and b correspond to those

in table 7 .1. One interval of the vertical axis corresponds to

15 %.

Both figures 7.7 show a tendency that, at lower air velocities, RD

values deviate more from zero than at higher air velocities. From

the comparison of fig. 7.7a with fig. 7.7b one can also see that

the RD values of T3-120 are lower than those of the T2-90. In

fig. 7.7a we see that the deviations of the T2-90 are lar~est at

ó = 0 or lSO. These angles correspond to the situation that both

pointers are located in front of or bebind the sphere. We can

conclude that, for all values of U considered, the RD is less than

12 % at 30 < ó < 150 and less than 18% beyond this range.

82

30

15

0

0

0

0

r 0

RD (%}

0

0

0

0

-15

-30

• i

l •

~ 11

~~ i . ..

• !ll

j I

• •

• Sl "'

l . •

I

0

I I

T2-90

I • I • I "' • t. !I i

I

• • • t • - ll - • .. . t

!!! .. .. 1!1 !i!

"' "' w m

lil 1!1 ., 11

2 ~ .. • " •

l : .. .. " • • 111

~ 11 ... .. i

11 I

" f I a A i I !I i I

x I I

• t .. • • .. t .. ..

~ t * "' "' "' 111 "' "' "' "' w lll "'

,. "' 111

"' "' 11 1!1 "' ; " "' .. "' ..

" • .. . .. . .. il : . .. . .

• . I I I I I I

30 60 90 120 150 180

ó (degr.) ~

l' I •

H

G 1!1

F .. •

E l!l

D • I

c .. a

B 11

. . iJ A .

I

0

T3-120

" . "' . " I I s • -

'" • • • .. .. - •

; .. . • lil il 111 "' ~ - '" I

; . . . . .. •

a ll • • • lll i • • @I

.. ., ... 11 •

" I • I I

I - I I

"' •

• • • • ~ . .. t .. • l

• I .. 11 • 1!1

.. I • 11 .. "' 1!1

I . . 3 l

* ' . i • .. • ' • I I I I I I

30 60 90 120 150 180

ó (degr.} ~

Ftg. 7.7: The reLative dtscrepancy RD of MA2 (a) and MA3 (b) vs. 6

83

20

10

0

0

0

0

l 0

DI-a

0

0

0

0

-10

-20

I

• T2-90 • I I I . " "111 • I I I .. ..

* a .. ; .. . ..

t .. 11 • 111 111 •

1111 !11 -IT 111 1!1 î!r 11 • ..

• • • • • • ,. ~

• .. • • t . • 6l • 11 .. • • I.

"" ~ -. I I • 11 I s • I I I • 1 .. w "' ,... .-..-~ ll

I I I

..

'., 111 ·m

'. .. •

I

0

" ,. l . * .. i i . .. .. . . . • m .. .. m ~ .. m

"' i .. I!! !B i "' m .. ., m m .. "' --.r • • .. 1!1 . .. "' . .

: . .. • :1: .. .. .. .. .. • .. .. . • .. I I I I I I

30 60 90 12 15 lSO

a (degr.} -

I

I •

• H ..

1!1 G "'

"' m

F •

• E -

• D I

11

c . . .. B

"' 11 "' ..

A

• •

I

0

• I • T3-120 s •

I .. s • " • • .. • • .. ..

111

t .... . .. • • • • I

1!1 I -

I • • • • • '

.. • 111

• • I

• • • • • .. • I • .. • •

111 11 lll .. 11

I • I 11 !I i 11

I • i I • .. • 111 .. 111 * .. !I

I .. • .. 111

111 • I • 111 t 11 111

I .. 11 ..

I

I . . • • .

a . .. . : ' . • * .. .. ..

I I I I I i 30 60 90 120 150 lSO

a {degr.} -

Fig. 7.8 DI2 - 6 (a) and DI3 - 6 (b) vs. 6

84

In fig. 7. 7b we see that the T3-120 deviations are largest at

6 = 30, 90 or 150. These values correspond to the situation that

one of the pointers is located just in front of (P ; 90) or just

bebind the sphere (P -90). It is also concluded that RD is less

than 8 % for all values of ö and U.

We conclude that, when using the procedure considered above, one

can measure the magnitude of the air velocity significantly better

with the T3-120 than the T2-90.

* The DI. calibration results 1

In fig. 7.8, DI2-6 and DI3-6 are presented as a function of 6 at

all air velocities. One interval of the vertical axis corresponds

to 10 degrees. From this figure we conclude that. with our

measurement procedure, both microanemometers are able to determine

6 to an accuracy better than approx. 10 degrees.

The fact that the RD values of the T3-120 are less than those of

the T2-90 can be explained by consirlering the construction of the

microanemometers. In the case of the T2-90 i t is possible that

bath pointers are located bebind the sphere. Fig. 7.4 shows that

both moving-coil meters then overestimate the air velocity so that

MA1 overestimates U. A similar reasoning applies to the situation

in which both pointers are in front of the sphere and yields an

underestimate. When, two pointers of the T3-120 are located in

front of the sphere, then one pointer is located bebind the

sphere, thus reducing the overestimate. In genera!, a more regular

distribution of the pointers in the plane is favourable.

It should be noted that corrections can be made if the accuracy of

both microanemometers mentioned in §7.3.2 is insufficient for

practical purposes. One could start from what is known about B exp and calculate the influence on MA. and DI. or one could use the

1 1

MA1 and DI1 data to make corrections.

85

7.4 THE TIIREE-DIMENSIONAL MICROANEMOMETERS: D3-90 AND D4-109

7.4.1 Introduetion and definitions

In the development of the three-dimensional microanemometers the

same two construction principles will be used as in the

two-dimensional microanemometers.

* The D3-90 is based on the measurement of three perpendicular

components of the air velocity. This results in a construction of

the microanemometer in which ~nl' ~n2 and ~n3 form an orthogonal system. We chose a design in which the three pointers, marked by

~1 , ~p2 and ~p3' also form an orthogonal gystem. The diameter of

the surrounding sphere is 80 mm and the length of the pointer

outside the sphere is 60 mm.

When we ehoose the ~nl' ~n2 and ~n3 veetors to coineide with the X, Y and Z-axes, we get:

~rl = (0,1,0} ~pl = (0,0,1} !!nl = (1,0,0) 7.15a

~r2 = (0,0,1} ~p2 = (1,0,0} ~n2 = (0,1,0) 7.15b

~r3 = (1,0,0} ~p3 = (0.1.0) ~n3 = (0,0,1) 7.15c

* The D4-109 is ba.sed, as far as possible, on the . regular

distributton of the ~n veetors in space. In the construçtion of

the D4-109 the ~n veetors point to the angular points of a

tetrahedron with (e .• e j) = -113. It is geometrieally impossible -n~ -n

to direet the pointers also in a tetrahedron, so that, for

constructional reasans a set-up is made in which:

~rl = (0,0,1) ~pl = ( v2/3,v'l/3,0) ~nl = (-v'l/3,v2/3,0} 7.16a

~r2 = (0,0,1) e 2 = (-v2/3,v'l/3,0) ~n2 = (--v't13,--v2/3,0) 7.16b -p ~r3 = (0.1,0} ~p3 = ( v2/3,0,v'l/3} ~n3 = ( v'l/3, 0. -v2/3} 7.16c

~r4 = (0,1,0} ~p4 = ( --v2/3. 0. v'l/3) ~n4 = ( v'l/3. 0. v2/3) 7.16d

Both microanemometers are shown schematieally in fig. 7.9.

86

x

z

x

Fig. 7.9 Schematic representation of the D3-90 and the D4-109

The magnitude of the air velocity is again characterised by MAi.

Using eqn. 7.2 it is easy to see that MA3 can bedefinedas

MA3:=jy2 l+y2 2+y2 3 out out out 7.17

and, in the case of the D4-109, MA4 can be defined as

MA4 := j(3/ 4)·(y2 1 + y2 2 + y2 3+ V2 4) out out out out 7.18

The direction of the veloei ty can be represented by the three

components of ~u·

87

7 A. 2 Numerical predictions of the 03-90 and the D4-109

With the expertmental results of §7.3 we are able to predict the

response of a single moving-coil meter at any chosen airflow: we

use eqn. 7.4b for the dependenee on ~ and. for the dependenee of

{3, we use the resul ts obtained in !i 7 .2.3. By combining the

responses of three or four moving-coil meters, the response of the

complete microanemometer can be obtained.

A new coordinate system at rest is introduced to present the

calculated resul ts of the three-dirnensional microanemometers in

addi ti on to the coordinate system XYZ which is fixed to the

microanemometer (and therefore rotates during calibration

measurements). This is chosen such that the X'-axis coincides with

the direction of posi tive Ucyl" Two angles 6 1 and 6 2 are also

introduced, which relate the coordinate system X'Y'Z' to the XYZ

system by means of two rotations.

In fig. 7.10a the relative discrepancy RD between the calculated

~ and MA3m is presented as a function of e1 and e2 . ~ is now

averaged over all values of 6 1. This is done at Res = 208 and

-180 ~ e1 ~ lSO and -45 ~ 6 2 ~ 45. The results are presented as

described below. Each drawn curve {connecting the dots)

corresponds to a single value of e2 . These values are given at the

left vertical axis. For each of these e2 values a horizontal line

is drawn indicating RD = 0. The RD scale is indicated at the right

vertical axis. The horizontal axis gives 6 1.

The ability of the D3-90 to represent the air velocity cornponents

is shown in fig. 7.10b. For this purpose the X. Y and Z cornponents

are calculated. Once these cornponents are known we can make the

transformation to the velocity cornponents in the X'Y'Z' system by

a purely mathematica! procedure. If the microanemometer were

ideal, this calculated direction would in fig. 7 .lOb coincide with

the actual air velocity (pointing in the x· direction). The

deviations from ideality of the microanemometer are shown:in this

figure by the deviations between the plotted points and the x·

ss

axis. In each figure the predictions at all ~1 values are shown at

a constant ~2 value. We have presented the results in fig. 7.10b

af ter projection on a sphere wi th radius 1 for clearness · sake.

This is done at Res = 208 also and ~2 = -45, 0 and 45 degrees.

Similar figures are presented in fig. 7.11 for the predictions of

the D4-109.

Calculations were performed for all Reynolds values up to 416 (see

table 7.1). From the results we conclude, as far as the magnitude

of the air velocity is concerned, that at Reynolds numbers greater

than approx. 100, both microanemometers can be expected to have

standard deviations of less tban 10%. The results with the D4-109

are (significantly) better tban those wi th the 03-90. We also

conclude that an increase in air velocity generally results in a

decrease in the relative deviations.

As far as the results for the direction are concerned, we can

conetude that both microanemometers are able to predict the

direction of the air velocity with an accuracy of 0.01 steradian.

7.4.3 Discussion

Predietiens as to the behaviour of two three-dimensional

microanemometers were given in the previous paragraph. We have to

bear in mind, however, that these predictions are based on the

experiments with the two-dimensional microanemometers. Future

research will be dedicated to the expertmental verification.

89

é2 l

45~~--~~~~~~~~--~~------~~~

Re = 208

-180 -90 0 90 180

e 1 {degr.) -

Fig. 7.10 Numerical predictions of the D3-90 at Re8

= 208

90

The relative discrepancy RD of MA3 with MA3m. vs e1 and e2 (a)

Direction of the D3-90 (b) at e2 = -45, 0, 45 degr.

l 15

Re = 208

-180 -90 0 90 180

E-1

( degr.)

Fig. 7.11 Numerical predictions of the D4-109 at Re8

= 208

The relative discrepancy RD of MA4 with MA4m vs E-1

and E-2 (a) Direction of the D4-109 (b) at E-

2 = -45, 0, 45 degr.

91

7.5 GENERAL CX>NSIDERATIONS

In the present chapter calibration results for two two-dimensional

microaneoometer are presented. However i t must be realised that

the calibration experiments were performed at uniform and constant

air velocities. When we deal with time-dependent air velocities,

the applicability of the results obtained so far is not

self-evident. In that case the distance between the pointers

becomes an important factor.

It should be mentioned bere also that the measuring principle

suggested in § 3.5 seems more suitable for measuring air

veloeities dependent onspace and time.

In future research we intend to pay extra attention to this

development, so that we will not restriet ourselves to testing

microanemometers of the T-series, but new multidimensional

microanemometers based on the new measuring principle will he

built and tested, as well.

92

8 MEASf.IREMEI'IT IN PRACTICE

8. 1 INTRODUeTION

A first attempt to test and establish the usefulness of the

microanemometers in practice is reported in this clJapter. For this

purpose measurements were carried out wi th all three types of

microanemometers: a one-dimensional microanemometer was used to

study the behaviour of the microanemometer in the vicini ty of a

wal!, a two-dimensional microanemometer (T2-90) in a project in

cooperation with the Faculty of Chemica! Engineering to study the

performance of a laboratory fume bood and a three-dimensional

microanemometer (D4-109) to study air veloeities in a surgical

operating theatre.

8. 2 .MEASUREMENTS IN OUR CALIBRATION UNIT DETERMINATION OF

WALL EFFECTS

8.2.1 Experiments and results

To establish the effect of the vicinity of a wall on the

performance of a microanemometer, measurements were performed near

the walls of the cylindrical train of the calibration unit. Two

kinds of measurements were carried out: measurements near the

front and near the side walls.

* Todetermine the 'front-wall effect' measurements were performed

in which the front wall was moved towards the microanemometer. A

one-dimensional microanemometer (D8

= 52 mm, L-L0

= 52 mm) was

placed inside the calibration unit wi th i ts pointer parallel to

the front wall and its rotation axis placed vertically. The

starting distance between the front wal! and the microanemometer

was 330 cm. The cylinder was set in motion wi th a veloei ty of

10 mm/s, for instanee and after the starting phase (phase II in

fig. 4.4) the output voltage V t as wel! as the value of V ~ ~t

93

450

V ==--...,_. .. cc <> out - :0. 40rc::=t

(mV} 300

l 150

U 1 = 40 mm/s cy

0 110 220 330 sf (cm) -

Fig. 8.1 The front-wutt effect Vout vs. SF

were registered on line. The distance between the front wall and

the microanemometer sf was calculated from vpot and decreased from

330 cm to approx. 10 cm. The measurements were performed at four

values of U 1

, that is 10, 25. 40 and 60 mm/s. cy In fig. 8.1 V out was presented as a function of Sf for two

measurements at U 1 = 40 mm/s. From fig. 8.1 we see that, for cy Sf > 10 cm, there was no significant front-wall effect at this air

velocity. This figure appeared to be representative for all values

of ucyl'

* In the case of the measurements of the 'moving' side wall, two

one-dimensional microanemometers we re used sirnul taneously, wi th

their pointers perpendicular to the cylindrical wall and their

rota ti on axis placed vertically. The right-hand microanemometer

was placed in such a way that the pointer was directed towards the

wall and the left microanemometer was placed in the opposite way.

The distance between the side wall and the middle of the pointer

of the microanemometer was called S . After both microanemometers s were placed on a rail at Ss measurements simtlar to the

calibration measurements described in chapter 6 were carried out,

four measurements in all, two in each direction.

94

~~--~.--r-,--r-,--~--r-,--r-,--r-,~

V out * * •• • • • {mV} 300

T

Fig. 8.2

150

I I

U = 40 mm/s 1 Cil I I I

0 10 20 30 40 Ss (cm)-

The effect of 'mouing' side walls Vout US. SS.

* and • indicate the results of the right and left microanemometer, respectiuely

Then both microanemometers were placed in another position on the

rail, thus varying Ss, and another experiment was done.

Measurements were performed at four values of Ucyl: 10, 25, 40 and

60 mm/s.

A characteristic result of a measurement with 'moving' side walls

was shown in fig. 8.2, where the averaged Vout was shown vs. Ss at

U 1

40 mm/s (it appeared to be representative for all values of cy Ucyl). From this figure we see that, within the measurement

inaccuracy, there is no significant side-wall effect, even if the

end of the pointer was located only approx. 1 cm from the side

wall. We also see that there is no significant diEferenee between

the results of the leftand right microanemometer.

To investigate a possible mutual interf erenee of both

microanemometers at S s

32 cm, two measurements were performed:

one wi th and the other without the second microanemometer, both

indicated in fig. 8.2. In this situation the distance between the

eentres of the spheres was approx. 4D5

• We can see that there was

no apparent difference, so that the two microanemometers do not

affect each other's behaviour significantly.

95

8.2.2 Discussion

The measurements with the front wall and the 'moving' side walls

showed that the size of the cylinder is large enough to prevent

any interterenee from the surrounding walls. It is also shown that

both microanemometers do not influence one another at a distance

of 4Ds. This agrees well with the numerical results reported in

chapter 5.

Both effects have been compared with literature values of Huner & Hussey '77 and values of Stalnaker & Hussey '79, who fourid that,

at these air veloeities and these distances towards the wall, the

effect of the bottorn of a container on the end veloei ty of a

falling cylinder was a few percent maximum. Al though comparison is

possible to ~ limited extent only, the results of both their and

our experiments showed that no significant effect occurs.

As these effects generally decrease with increasing air veloeities

(Happel & Brenner '73) we conclude that, at air veloeities higher

than 10 mm/s, the influence of the front and side walls: on the

calibration can be neglected.

From the resul ts of our experiment we conclude that one can

calibrate · several microanemometers simultaneously. During the

calibration experiments, one microanemometer could even be placed

axially bebind the other. However, in the case of higher air

velocities, a wake bebind the first microanemometer will influence

the signa! of the second microanemometer. It is therefore

preferabie to place both microanemometers in a plane perpendicular

to the cylinder wall at mutual distances greater than 4Ds.

96

8. 3 MEASUREMENTS IN LABORATORY FUME HOODS

To test the experimental behaviour of our two-dirnensional

rnicroanernorneter, several prelirninary experirnents were carried out

in cooperation wi th the Facul ty of Chemica! Engineering: air

veloeities were measured in two laboratory furne hoods. A schematic

representation of the type of {by-pass) fume hood used is given in

fig. 8.3a. These two furne hoods were part of a series of twelve

fume hoods covering one wall of the laboratory. The laboratory was

supplied with fresh air through a grille in one corner.

Our instrument was used to investigate two questions:

* Did the furne hoods meet the (generally accepted} requirement

of an average face velocity of 25 cm/s in the sash plane ?

* Was there any significant difference in behaviour of the fume

hoods close to and far from the supply grille ?

~· by-pa" t- 1:

I sash ) 5 +

4 +

3 +

2 +

1

l j

i ~ 1

+

+

+

+

2

k

?i 1 j

+

+

+

+

+

3

+

+

4

Fig. 8.3 Schematic side view of the fume hood (a),

+ +

+ +

5 6

the grid of mensurement points in the fume hood (b)

97

In order to check the safety of the fume bood the sash area was

divided into a grid of small areas, see fig. S.3b. At the centre

of each area the air velocity was measured, yielding a measure for

the flow and thus the average face velocity in the sash area.

8.3.2 Description of the experiments

Some preliminary experiments were first carried out to investigate

the direction of the air velocity. Using smoke as a tracer, it was

shown that the direction of the air velocity in the sash area was

mostly in the horizontal plane. This allowed us to use a

two-dimensional microanemometer and for practical reasons the

T2-90 was chosen.

In fig. 8.4 the position of the T2-90 in the fume bood is given.

The microanemometer was positioned in such a way that its central

point coincides with the i,j measurement point of the grid (i and

j were the horizontal and vertical index, resp.). For this central

point we took the geometrical middle of the middles of the two

pointers. All grid points were located in the sash plane.

plane of the sash

T air velocity

Ftg. 8.4 Top vtew of the posttton of the T2-90

Measurements were performed in the following way.

300 samples of the two output voltages were taken and averaged

over 30 seconds. This was repeated three times at intervals of 10

seconds and from the three values the 'overall' averaged Voutl and

98

V ou t 2 and the calculated. To

standard deviations o(V 1) and o(V t 2 ) were out ou calculate the corresponding magnitude (MA

2) and

direction (DI2 ) of the air velocity, eqns. 7.10 and 7.11 were used

respectively. Besides, we needed arelation between MA2 and U. For

this re lation we deduced a eaUbration curve from fig. 7. 7 by

restricting ourselves to the values of ~ at ó = 90 degrees so

that a single curve could be obtained. It should be noted here

that the position of the microanemometer in fig. 8.4 corresponds

to DI2

= 90 degrees in the case that the air veloei ties are

directed perpendicular to the sash plane.

To enable the average face velocity in the sash area of the fume

hood to be calculated, a measurement series was performed

invalving a measurement at each point of the grid. So a

measurement series consisted of thirty measurements. The average

face velocity was calculated as follows.

Each measurement point, characterised by i and j, was the centre

of an area AA1.J .. In this area the magnitude U .. and the direction

l.,J DI2 .. of the air velocity were measured. The flow . through

1, J • J the area AA .. can be written as

l.J

8.1

The average face velocity Ufa over the total area Afc(= I AA1j) is

For practical reasons Ui and Uj are introduced where

U. = ]. [

j=5 ] I U. j cos DI2i,J" AAi,J. /AJ.tot

j=l 1,

8.2

8.3

8.4

99

Four measurement series were performed under different

circumstances. Two grids were used, referred to as series I and

II, in studying the influence of choice of the points of the grid.

In studying the influence of the position of the pointers of the

microanemometer in the fume bood, one series (III) was performed,

in which the pointers were placed at the 'opposite' side of the

microanemometer, which implies that the situation in which the air

veloei ty is perpendicular to the sash plane, corresponds to a

value of DI2 = - 90 degrees. In this series the same grid was used

as in measurement series II. In studying the influence of the

supply grille on the face velocity. series IV was perform~ in a

second fume hood at the far end of the laboratory. The

microanemometer was positioned in the same way as in series III

and the same grid as in series II was used.

All the results of measurement series I are shown in fig. 8.5. To

explain this figure we use the coordinate system introduced in

fig. 8.3. The i-j plane with the grid is drawn in fig. 8.5. Around

each grid point we see a circle which is thought to repreaent a

local horizontal plane parallel to the 1-k plane. In such ei. circle

we can indicate a horizontal air veloei ty by an arrow wi th i ts

basis in the grid point. The length of this arrow represents the

magnitude of the air veloei ty. The drawn ei re les refer to air

veloeities of 25 cm/s. When there is uncertainty as to the

magnitude and direction of the air velocity, we can indi~te the

end points of the arrows by means of a shaded area. The centre of

the shaded area corresponds to Uij and the surface itself

represents Uij ~ o (Uij) at DI2ij ~ o(DI2ij).

From fig. 8.5 we see that the direction of the air velocity at

grid points 1.1, 2.1, 3.1, 4.1 and 5.1 is mostly directed outwards

from the fume hood. This was confirmed by other data, which showed

that, in other measurement series at 1.1 and 2.1 the direction was

the same. We also see that the measured air velocity is lower than

25 cm/s in many locations of the measurement grid.

100

..,

Fig. 8.5 : Air veLoeities in the sash area of a fume hood. For expLanation of the figure, see text. Note that the ftgure is rotated 90 degrees!

101

series 1 = 1 2 3 4 5 6 0fa

I 18.0 17.5 19.5 19.5 18.5 19.5 18.5

II 15.5 17.0 18.5 20.0 18.5 19.5 18.5

III 20.0 21.5 24.0 24.5 23.5 24.5 23.0

IV 20.5 19.5 21.0 21.0 22.0 23.0 21.0

series I II III

j =5 36.0 28.5 34.0 27.5

j = 4 23.0 22.0 27.5 22.5

j = 3 20.5 19.5 26.0 20.5

j = 2 18.5 17.0 22.0 19.0

j = 1 2.5 5.0 7.5 15.5

0ra 18.5 18.5 23.0 21.0

Tabl.e 8.1 : U., U. and Uf tn CIIVS L J Cl

ui. u j and u fa are presented in table 8.1 to characterise the

results of the four measurement series mentioned above.

8.3.4 Conclusions and discussion

The following remarks can be made about the resul ts shown in

table 8.1. hearing in mind that we used the T2-90 for our

measurements and that this only yields information on the air

veloeities in the horizontal plane.

* Table 8.1 shows that the air velocity is almost constant in the

horizontal plane : we see a general tendency that the air velocity

is somewhat higher at the right-hand side of the fume hood (marked

by high i values) than at the left-hand side.

102

* Table 8.1 also shows that the highest air veloeities are always

located at the top of the fume hood (marked by high j values).

* Comparison of series I and II shows that there is no significant

influence of the grid on the results of the average face velocity.

* From comparison of the resul ts of II and III we see that the

location of the pointers of the microanemometer significantly

influences the measured value of the air velocity. This influence

can be explained as follows. From the results of chapter 7 we can

conclude that the results of series II can lead to an

underestimation of the air velocity and those of series III to an

overestimation of the air velocity. We should note bere that the

T2-90 was calibrated at air veloeities lower than 15 cm/s in a

uniform air veloei ty and that extrapolation of the calibration

curve up to air veloeities of 40 cm/s was necessary. Also the fact

that the air velocity is not constant may have to be taken into

account.

* The comparison of the left and the right fume hood (series III

and IV) shows that the air velocity is lower in the left fume bood

than in the right hood, which could be caused by the location of

the fume hood with respect to the supply grille.

The most important conclusion of our experiments is that the two

fume hoods tested in this laboratory are found not to satisfy the

requirement of an average face veloei ty in the sash plane of

25 cm/s. The experiments suggest that in the bottom-Ieft corner of

the fume hood the air veloei ty is directed outwards. which can

bring about very dangerous situations.

103

8.4 AIR VELOCITIES IN A SURGICAL OPERATING TIJEATRE

8.4.1 Introduetion

The air in the operating theatre is the vehicle for bactetial and

gaseous contaminants which may be ei ther generated inside the

theatre or brought in from outside by the movement of people and

air. Since ma.ny of these airborne contaminants are harmful to the

patient, knowledge about air movements and, particularly, the

quantification of these air movements is very important. Therefore

air veloei ties in two types of operating theatres were measured

with a three-dimensional microanemometer {04-109) in a hospita! in

the vicini ty of Eindhoven. These two types of surgical theatres

differ in the way in which the clean air is brought into the

operating theatre: by means of a ceiling diffuser or by means of a

side-wall diffuser.

8.4.2 Description of the experiments

As already mentioned, the experiments in the operating theatres

were done with the three-dimensional microanemometer 04-109. The

measurements themselves were carried out in a way as is described

in §8.3.2, yielding 'overall' averaged values of V t of each OU

moving-coil meter.

The maasurement series consisted of 60 or SO measurement points

forming a three-dimensional grid characterised by three indices:

i, j and k. The location of the measurement points in the grid and

the location of the grid in the operating theatre with regard to

the oparating table is shown in fig. 8.6. It should be noted bere

that the grid shown in fig. 8.6 is that used in the oparating

theatre with the ceiling diffuser {SO points). The grid '\lSed in

the other oparating theatre has only 60 points because no

measurements were taken at k = 3.

104

Fig. 8.6 The tocation of the grid mensurement points with regard to the operating tabte in the operatf.ng theatre with the ceiting diffuser

For the data processing, eqn 7.18 is used to calculate the

corresponding magnitude. Only one provisional cal i bration series

was carried out in our calibration unit at U 1

< 130 mm/s for the cy relation between MA4 and U. The pos i tion of the microanemometer

with regard to the direction of the air velocity was restricted to

the values of e 1 = e2 = 0 {see §7.4.2). We represent the direction

of the velocity by ui. uj and uk. these being the components of

the air velocity in the i,j and k direction, with

8.5

105

8.4.3 Experimental results

I The results of the measurements in the operating theatre w~th the

ceiling diffuser are shown in fig. 8. 7 and those of the operating

theatre with the side-wall diffuser are presented in fig. 8.8. To

explain these figures we use the coordinate system given in

fig. 8.6. In fig. 8.7 (fig. 8.8 is similar) a figure is given for

each value of i in which the corresponding plane parallel to the

j-k plane is drawn. At each maasurement point an arrow is drawn

which represents the velocity components Uj and Uk. Around each

measurement point a circle is drawn: the radius of this circle is

a measure for the third component of the velocity Ui. The

direction of this third component is given by the +/- sign in the

vicini ty of the circle. An arrow indicating an air veloei ty of

5 cm/s is drawn at the right hand side of the figure. It bas to be

noted that the presentation of the air veloeities is restricted to

values larger than 1 cm/s.

We see in both figures 8. 7 and 8.8 that the magnitude of :the air

velocity is mostly less than 10 cm/s. The air velocity generally

consists of three components, none of which can be neglected. We

also see that, in the case of the operating theatre with the

ceiling diffuser, the air veloeities are generally directed

upwards in the vicinity of the operating table. In the case of the

operating theatre with the side-wall diffuser, the air veloeities

are generally directed from the operating table. The magnitude of

these air velocities, however, is very small and rarely exceeds

8 cm/s.

106

'

@ 1::.:4

0- l \ i ~ f 1 t t

~:wr+ Ö+ Ó-1=3

(!>-

6- <:9-C)-

t 1 0- 9-; t

G)+ 1=2

f '

4 t t ~- r (!)-t t

"" t

K t ! cJ+

1 1::.1 I

(!)- t t t 5 cmjs

2 3 4 5 ....... J

Fig. 8.7 : Air veLoeities in an operating theatre with a ceiLing diffuser. For expLanation of the figure, see text

107

4

Kt 2

1

! 0

0+ Q+

Q+

Q+

(j} ~

0+ Cf (!)-

0+ ~+

f

6- 4)-

2

0+

0-

11

11· 3 -....

J

l 0+ I= 4

\ 0)-

1

0- 1=3

Q- 0-

0-

, ..... I= 2

o-- o-

,t o- I= 1

0- f § cm/s 4 §

Fig. 8.8 : Air veloeities in an operattng theatre with a side-wall diffuser. For explanation of the figure, see text

108

8.4.4 Discussion

It was shown in the previous paragraph that our D4-109 is a very

suitahle instrument with which three-dimensional air veloeities in

operating theatres can he measured. We have to mention bere that,

hefore any definitive eonclusions can he drawn as regards the

actual magnitude of the air velocity, further consideration will

have to he given to the calihration of the D4-109 at other values

of e 1 and e2 .

We may however conclude that the flow patterns in the operating

theatres compare very well with those expeeted. The fact that the

air veloeities in the vicinity of the operating tahle were

directed upwards means that possible contaminants were directed

towards the operating tahle, which should be a bacteria-free clean

zone. Henee our experiments confirm that these types of air supply

in operating theatres are less sui ted for the provision of the

clean zones with fresh air. This implies that the required

asceptic level of the clean zone bas to he achieved hy an

appropiate number of changes per hour of the air.

109

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111

J.K. Kurz and J.C. Olin: A new instrument for airflow maasurements. Flow, its maasurement! (1971), pp. 765-772.

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C.H. Massen, M.J.F.P. Pluijm, J.T.H. Lammers, E. Robens and j.A. Poulis: The influence of conveetien on weighing, Thermochimica Acta 103 (1986), pp. 45-49.

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112

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113

In this thesis a new type of microanemometer is presented. The

instrument is developed in a cooperation project between the

facul ties of Physics and Archi tecture. Building and Planning at

the Eindhoven Uni ver~> i ty of Technology. This microanemometer is

based on the principle of the measurement of the (moment of;) force

exerted on the pointer of a moving-coil meter by the airr'low. By

sending a current through the coil the Lorentz couple serves as

retroactive couple. In the case of equilibrium, the feedback

current is a measure of the air velocity (chapter 3).

For calibration of the microanemometers in practice and

establishment of the lowest detection limit, a calibration unit

capable of producing air veloeities as low as 1 mm/s up to air

veloeities of about 15 cm/s is presented in chapter 4.

The influence of the microanemometer in the eaUbration unit on

the air veloei ties in the vicini ty of the microanemometer is

calculated numerically {chapter 5). Therefore the Navier Stokes

equations by the Finite Element Metbod using the Penalty Function

Approach were solved.

Calibration of the microanemometers in the calibratio.n unit

resul ted in a lowest detectable air veloei ty of approx. · 1 mm/s

(chapter 6). which is two decades lower than that qf most

commercially available anemometers. By varying the lengtht of the

pointer of the microanemometer. both the lowest and highest

detectable air velocity can be adjusted. resulting in air

veloeities measurable even up toa few mis.

In chapter 7 the si mul taneous measurement of several veloei ty

components using a number of moving-coil meters with their

pointers in different directions is described.

Finally. the applicabi li ty of the microanemometers is tested in

practice. For this purpose introductory measurements were carried

out in fume hoods and in operating theatres.

114

SAJIEJWA'ITING

In dit proefschrift wordt een nieuw type micro-anemometer

beschreven, dat in een samenwerkingsverband tussen de faculteiten

der Technische Natuurkunde en Bouwkunde van de Technische

Universiteit Eindhoven ontwikkeld is. Deze micro-anemometer is

gebaseerd op het principe van het meten van het door de

luchtstroom uitgeoefende moment op de wijzer van een

draaispoelmeter. Dit moment wordt gecompenseerd door het

Lorentz-koppel door een stroom door het spoeltje van de

draaispoelmeter te sturen. In evenwichtssituatie is de grootte van

de stroom een maat voor de windsnelheid (hoofdstuk 3).

Een ijkopstelling met een bereik van ca. 15 cm/s tot 1 mmls is

gebouwd om de micro-anemometers te testen en de laagst te

detecteren snelheid te bepalen (hoofdstuk 4).

Om de invloed van de aanwezigheid van de micro-anemometer op het

snelheidspatroon in de ijksopstelling te bekijken, zijn met behulp

van de Eindige Elementen Methode de Navier-Stokes vergelijkingen

opgelost (hoofdstuk 5).

Daadwerkelijke ijking van de micro-anemometer in de opstelling

resulteerde in een laagst detecteerbare snelheid van ca. lmmls,

hetgeen twee decades lager is dan bij de meeste commercieel

verkrijgbare anemometers. Door de lengte van de wijzer van de

micro-anemometer te varteren kan het snelheidsbereik veranderd

worden, hetgeen o.a. resulteerde in het meten van snelheden van

enkele meters per seconde (hoofdstuk 6).

In hoofdstuk 7 worden de 'mul ti -dimensionale' micro-anemometers

beschreven waarmee gelijktijdig meerdere snelheidscomponenten

gemeten kunnen worden. Hierbij wordt gebruik gemaakt van een

enkele micro-anemometer met daarin een aantal draaispoelmeters

aangebracht waarvan de wijzers in verschillende richtingen wijzen.

Tot slot worden in hoofdstuk 8 enkele inleidende practische

toepassingen van de ontwikkelde micro-anemometer beschreven.

Daartoe werden o.a. metingen , in zuurkasten en in operatiekamers

verricht.

115

NAWOORD

Dit promotie onderzoek is uitgevoerd in het kader van een

interafdetingsproject van de facuLteiten Technische NatWJ-rkunde

(vakgroep Analyse van Fysische llleetmethoden) en Bou:uhunde

(vakgroep Fysische Aspecten van de Geboullde Omgeving} van de

Technische Universiteit Eindhoven.

Het moge duidelijk zijn dat dit proefschrift alleen tot stand ,kon

komen dankzij de vele nuttige en vaak onmisbare . bijdragen van

anderen. Met recht geldt hier dat 'het succes vete vaders kent'.

Een ieder die mij gedurende de laatste uier Jaar hierbij

behulpzaam is geweest wiL ik hiervoor dan ook van harte bedanken.

ALtereerst mijn promotoren prof. ].A. Poutis en prof.

] . Vorenkamp en mijn copromotor dr. C.H. llla.ssen.

De overige basts-leden van het project, te weten

dr. ]. Lammers, ir. C. Nieuwvelt en W. v.d. Ven

Het experimenteLe gedeelte van dit proefschrift kon steehts tot

stand komen door de medewerking van vete stagiaires en

afstudeerders. Merkwaardig dat juttie werk niet vermeld mag

worden in de referentie Lijst.

Mijzelf beperkend tot de afstudeerders, noem ik :

Tim v.d. Hagen, Ad v.d. Kieboom, Art Pitmeyer, Guido Bars,

Frank van Riet, Ertk 1fo.as en Rene Leenen.

Gerard Hamers voor de electronica assistentie en de

stappen-motor print.

dr. R. van Dongen en prof. G. Vossers, bij wie ik en miJn

afstudeerders meerdere maten voor theoretische ondersteuning

terecht konden.

dr. A. u. Steenhoven voor de numerieke ondersteuning bij de tot

standRaming van hoofdstuk 5 en tevens dr. F. v.d. Vosse voor

hun hulp en geduld bij de vragen van Ad.

ir. G. Dekker en A. Kemper voor hun hulp bij de ontwikkeling

van het terugkoppeL-systeem.

116

Een speciaal 100ord van dank aan de leden van de werkplaats:

M. Bogers die als 'fijn-mechanisch' vakman toch niet

afgeschrikt werd door de waanzinnige afmetingen van de

gebouwde ijkopstelling en daarnaast ook constructeur van

diverse prototypes van microanemometers was.

H. Hetter voor zijn constructieve ideeen en atle

'klusjesmannen' (Jan van Asten, Henk van Helvoirt, Frank

van Hoof, Rien de Koning en Gerard Wijers) die vaak ook de

'net·niet' klusjes witden behandelen.

Voor de grafische vormgeving, tips en bijdragen aan de tay·out

van het proefschrift dank ik Guido Sars en P. Magendans

(voorkant), H. Pouwels, ]a.n Millenaar (fig. 4.1) en Ruth

Gruyters, die sommige figuren nog netter maakte.

drs. E. Swaan voor de aangeboden gelegenheid de

twee-dimensionale micro-a.nemomemeter te testen in de zuurkasten

van de faculteit der Scheikundige Technologie.

De medewerkers van de technische dienst en het o.k. personeeL

van het Diaconessenhuis te Eindhoven voor hun hulp bij de

metingen met de drie·dimensionat micro-anemometer in de o.k.'s

H. Keuten en R. Bugel voor de soft-ware assistentie en de

ontwikkeling van de 'portable' meetbus die bij de praktijk

metingen gebruikt werd.

Tot slot bedank ik iedereen die ik hierboven eventueel over het

hoofd gezien zou hebben en druk hen op het hart dat er van boze

opzet geen sprake is geweest.

Martin Pluijm

117

mRRIClJUJlf VITAE

6 januari 1959

sept. '71 - juni '77

sept. '77- okt. '83

26 okt. '83

sept. '83 - jan. '84

28 apr. '86

10 okt. '86

jan. '84 - dec. '87

118

geboren te Heerlen

G!Jifti'Ulsium 13

Berrardinuscollege te Heerlen

Technische Hogeschool Eindhoven,

afdeling der Technische Natuurkun4e

groep Analyse van Fysische Meetmethoden

o.l.v. prof. dr. ]. A. Poulis

Onderwerp: Bepaling van de momentane

flow ut t de vorm. van een een t.v. curve

Onderwijsbevoegdheid Natuurkunde

WetenschappeLtik assistent bij "A.F.M"

Onderwijsbevoegdheid Wtskunde

AanvulLend Examen Bedrijfskunde

Promotie-onderzoek tn het Rader ~ het

interafdelingsproject: Het ontwt~Len

van een nieuw type micro-anemometer.

behorende bij het proefschrift van

M.J.F.P. Pluijm

Eindhoven, 11 december 1987

1. De in dit proefschrift beschreven ijkopstelling is tevens geschikt

voor het ijken van bestaande anemometers in het snelheidsgebied

lager dan 20 cmls. Zij levert dan betrouwbaardere resultaten dan

verkregen worden met behulp van een extrapolatiemethode.

- Dit proefschrift, hoofdstuk 4

- A.E. Perry : Hot-wire anemometry. Oxford Univ. Press (1982)

t

2. Bij het berekenen van snelheidsvelden in de ijkopstelling rondom

de micro-anemometer met de eindige elementen methode kan een

aanzienlijke tijdwinst behaald worden door beginschattingen te

gebruiken die verkregen worden uit analytische uitdrukkingen voor

test-stroomfunctiepolynomen.

-Dit proefschrift, hoofdstuk 5

- C.Y. Chow : An introduetion to computational fluid mechanics.

]ohn Wiley 8 Sons, New York (1979)

3. Ten onrechte zou men kunnen veronderstellen dat de

ormauwkeurigheid, waarmee de grootte van de windsnelheid bepaald

kan worden met de in dit proefschrift beschreven meetprocedure,

afneemt met de wortel uit het aantal wijzers. Een 'optimale'

twee-dimensionale micro-anemometer bestaat uit vier draaispoel­

meters waarvan de wijzers onderling hoeken van 90 graden maken.

- Dit proefschrift, hoofdst.uk 7

4. De 'gemiddelde raamsnelheid' is een onbetrouwbare norm om de

veiligheid van zuurkasten aan te toetsen.

- Dit proefschrift, hoofdstuk 8

- Arbeidsinspectie, Publicatieblad P 130-1 (1980)

5. Gezien de loopbaanontwikkeling van de natuurkundig ingenieur dient

de faculteit der Technische Natuurkunde te overwegen om het

begeleiden van stagiaires door afstudeerders in het

onderwijsprogramma op te nemen.

6. De bewering van Tsanis, dat er in zijn ijkopstelling sprake is van

een 'absolute quiescent environment', is misleidend.

- I. K. Tsonis : Catibration of hot -wire anemom.e ters at uery Law

uetocities. DANTEC Informatian, ~ (1987), pp. 13-14

7. De door Van der Hart aanbevolen gezamenlijke commercieel­

technische beroepsopleiding voor in de richtingen elektrotechniek,

werktuigbouwkunde, informatica en chemische technologie

afgestudeerde ingenieurs, zou ook voor afgestudeerde natuurkundige

ingenieurs toegankelijk moeten zijn.

- H.W.C. u.d. Hart : CommercieeL technicus geuraagd.

Rapport Stichting C.T.O. (1986)

8. Bij het meten van oppervlaktespanningen aan lucht-vloeistof

grensvlakken met de Wilhelmy-plaat methode kan een aanzienlijke

verbetering bereikt worden door het gelijktijdig meten van de

contacthoek aan de Wilhelmy-plaat.

- H. 1. Schut ze 8 G. Schoppe Beruehrungs l.oses !fessen uon

OberfLaechenspannung und RandwinkeL eines Flutdes mtt dem

Interferenzmikroskop. Jenaer Rundschau 2 (1981}, pp. 222-224

P. Giel.es : Ifethods af measurem.ent for the euaLuatian af monol.ayer

praperties, deuetapment and appl.tcations, Thesis T.U.E. (1987}

9. Het verdient aanbeveling te onderzoeken in boeverre de in dit

proefschrift bescbreven micro-anemometer ook als flow-meter

gebruikt kan worden.

10. Het feit dat de leerlingen tijdens het HAVO/VWO natuurkunde­

eindexamen gebruik mogen IIIBken van BINAS, waarin 'alle'

natuurkundige formules staan, strookt niet met de doelstellingen

van het natuurkunde-onderwijs.

-Concept Examenprogramma. natWLrkunde VWO en HAVO, 'f.E.N. (1986}

- BINAS Informatieboek Vi'OI'HAVO V()Or het ondenDtjs tn de

natWLnDetenschappen, 'fol.ters NoordJwff Grontngen {1986}

11. Het valt te betreuren dat 'het' Limburgs volkslied in bet

Nederlands geschreven is.