Durst F. Fluid Mechanics: An Introduction to the Theory of Fluid Flows

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21.5 Basics of Hot-Wire Anemometry 665

a direct measure of the ﬂow velocity existing at the sensor at the moment

of measurement, i.e. a hot-wire anemometer can be built with a high time

resolution.

The basic element of hot-wire anemometry is a cylindrical sensor that can

be heated in a controlled way and whose electrical resistivity depends on the

temperature. The temperature and related resistivity change of the wire, due

to velocity changes, can be appropriately recorded electronically in a bridge

circuit. The probe itself represents a bridge arm of this bridge circuit. Of the

diﬀerent bridge circuits in practice, the Wheatstone bridge has proved to be

especially suited for hot-wire measurements.

From the heat loss of the sensor, which in the state of thermal equilibrium

has to be equal to the heat produced electrically over the wire:

Q = IE = I

R =

where I is the electric current, E is the applied voltage and R is the resistance

of the wire, the ﬂow velocity can be determined using two circuit variants.

From the need for measurements to have one dependent quantity to measure

the heat loss, one can either keep constant the electric current I,orthe

temperature of the sensor through the wire resistance R. In the ﬁrst case one

talks of the constant-current anemometer (CCA) and in the second case of

the constant-temperature anemometer (CTA).

In the constant-current operation of a hot-wire anemometry, the Wheat-

stone bridge is operated with a constant electric current. For this kind of

operation, the resistance of the energy source has to be large in comparison

with the total resistance of the bridge, in order to keep the current operating

the bridge constant at all measuring times. The temperature and resistance

changes of the hot wire, due to velocity changes of the ﬂuid ﬂow, induce in

the circuit in Fig. 21.12, an imbalance of the voltage at the vertical bridge

diagonal, e.g. the voltage between ports A and B. The resulting bridge output

signal is ampliﬁed and is then displayed as a measure of the ﬂow velocity of

the ﬂuid.

Compensation

Amplifier

Output to indicator for

measured resistance

Hot-wire

I=const.

R=R(U)

Fig. 21.12 Principal circuit of a constant-current anemometer for hot-wire

measurements

666 21 Introduction to Fluid-Flow Measurement

One disadvantage of the velocity measurements by constant-current hot-

wire anemometry is the small bandwidth of the system. This disadvantage

can be attributed to the thermal inertia of the hot wire. The upper frequency

of a hot wire of 5 µm diameter is approximately 100 Hz in constant-current

operation. By using very thin wires, the time constant can be reduced, but

thin wires are very sensitive to mechanical inﬂuences and can therefore easily

be destroyed by the ﬂow as a result of mechanical stresses.

Moreover, for the constant-current anemometry, operational diﬃculties ex-

ist. Due to the increasing heat losses to the ﬂowing ﬂuid at high velocities, the

supply current has to be increased at high velocities. On the one hand, this

leads to an increased sensitivity of the wire, i.e. the wire reacts more strongly

to occurring velocity changes. However, when carrying out measurements the

risk increases that the hot wire will burn, e.g. when the velocity decreases

suddenly in a ﬂow, the current cannot be removed fast enough from the wire

and, hence, the wire burns. Finally, the dependence of the time constant of the

hot wire on the mean ﬂow velocity makes an adjustment of the compensation

network to the corresponding ﬂow velocity necessary. When using hot-ﬁlm

probes in their constant current mode, which possess high time constants, a

compensation ampliﬁer with a complicated control circuit is required. This

special ampliﬁer has to have very precisely the opposite frequency response

to the hot-wire probe and therefore is hard to design and build in practice,

let alone its employment in measurements.

Nowadays, the constant-current operation of hot wires is employed almost

only for measurements of ﬂuid temperatures. For this application, the con-

stant heating power is reduced, in order to decrease the response of the probe

to the ﬂow velocity, so that almost exclusively temperature changes in the

ﬂuid lead to imbalances of the bridge. The bridge voltage at the horizontal di-

agonals in Fig. 21.13 is then a measure of the instantaneous ﬂow temperature.

The basic idea of constant-temperature anemometry (CTA) results in an

electronically achieved compensation of the thermal inertia of the probe by

a fast electronic voltage feedback, guaranteeing the operation of the sensor

at a constant temperature, i.e. at a constant wire resistance.

I=I(U)

T,R=const.

Difference

voltage

servo

amplifier

Bridge current

Hot-wire

Fig. 21.13 Principle electrical circuit of a constant-temperature anemometer

21.5 Basics of Hot-Wire Anemometry 667

In the case of the balanced bridge, no voltage diﬀerence exists between the

entrance ports of the servo-ampliﬁer. Velocity changes in the ﬂow, however,

result in temperature and corresponding resistance changes of the hot-wire

sensor, which cause voltage diﬀerences at the servo-ampliﬁer input ports.

The exit of the servo-ampliﬁer is back-coupled to the vertical parts of the

bridge, as shown in Fig. 21.13, with a polarity such that the bridge ad-

justs itself automatically to the new heat transfer situation. Through this

back-coupling, a signal is generated which is not inﬂuenced considerably by

the thermal inertia of the sensor, i.e. the upper frequency of the hot-wire

anemometer response is raised by several orders of magnitude compared with

constant-current operation of a hot wire. The upper frequency can reach up

to approximately 1.2 MHz at high ﬂow velocities. This upper frequency of the

constant-temperature anemometer is essentially determined by the frequency

response of the feedback ampliﬁer and not by the time constant of the wire.

Advantages of constant-temperature operation are the above-mentioned

large bandwidth and the possibility of choosing high operating temperatures

of the sensor, to obtain a very high sensitivity to velocity changes. A dis-

advantage is the unstable behavior of the servo-ampliﬁer in some extreme

operational cases.

21.5.2 Properties of Hot-Wires and Problems

of Application

As measuring sensors for hot-wire measurements, usually hot wires with a

cylindrical form, with typical diameters of a few µm and a length larger

than 200 times the wire diameter, are used. For hot-wire sensors, the wire is

mounted between the tips of special supports to which the wire is soldered or

welded. Because of this, certain mechanical demands are required to permit

the wire to be placed between the tips of the two supports (prongs). The

stated diameters and lengths of hot wires employed are a compromise between

the required mechanical strength and the upper frequency of the measuring

system. Typically, measuring wires with a diameter of 5 µmandalengthof

1–2 mm are employed for ﬂow measurements.

Special measuring requirements, in diﬀerent velocity ﬁelds, place diﬀerent

requirements on hot-wire probes and make the employment of appropriate

sensors necessary, usually possessing special probe geometries. Thicker wire

sensors are employed when a higher mechanical stability is required; thinner

wires are employed when higher frequencies are required.

The dominating and for hot-wire probes decisive property of the sensor

material is the dependence of the electrical resistance on temperature. This

dependence can be stated as follows:

R = R

[1 + α

(T − T

)+α

(T − T

)

+ ···], (21.6)

668 21 Introduction to Fluid-Flow Measurement

where R is the wire electrical resistance at the operating temperature T , R

is the corresponding value at the reference temperature T

,andα

and α

are the thermal resistance coeﬃcients. Preferred are hot-wire materials with

values as high as possible and extremely small α

values. In such cases

the square term in (21.6) can be neglected, so that the electrical resistance

changes practically linearly with temperature. For platinum as an example,

the values for the resistance coeﬃcients are

=3.5 × 10

−3

−1

; α

= −5.5 × 10

−7

−2

(21.7)

and for tungsten

=5.2 × 10

−3

−1

; α

=7.0 × 10

−7

−2

. (21.8)

In Fig. 21.14, the variations of the electrical resistance with temperature are

given for some pure metals.

During hot-wire measurements, the temperature along the hot wire usually

diﬀers which is explained in detail later; the measured resistivity has a mean

value R =

[R(z)/A(z)]dz. A(z) is the hot-wire cross-section and z the

coordinate along the hot wire, i.e. in direction of the ﬂow of the electric

current. R(z) can therefore be considered the local resistance of the hot wire.

Another important parameter for the sensitivity of the anemometer is the

overheating relation β

=(T −T

)/T

, where again T is the hot-wire temper-

ature and T

the reference temperature in K. Of more practical importance is

the relation β

=(R −R

)/R

,whereR is the resistance of the sensor at the

operating temperature T and R

the resistance at the reference temperature

. From the above, the following holds: β

= α

(with α

= 0). In prac-

tice, one chooses the operating temperature of the hot wire as high as possible,

in order to obtain a high sensitivity for the velocity changes and also a re-

duction of the inﬂuence of the ﬂow-medium temperature. As a rule, tungsten

-200

200

400

600

800

1000

100

Temperature °C

Resistivity, microhm-cm

Iron

Nickel

Platinum

Copper

Silver

Tungsten

Fig. 21.14 Temperature-resistivity behavior of hot-wire materials

21.5 Basics of Hot-Wire Anemometry 669

wires coated with platinum tolerate temperatures up to 200–300

◦

C. At high

ﬂow temperatures, sensors made of platinum and a 10% platinum-rhodium

alloy are employed, permitting operating temperatures up to 750

◦

Measurements of ﬂow velocities of ﬂuids impose requirements which make

the employment of special sensors necessary. These sensors consist of dif-

ferently shaped elements of quartz glass, on to which thin-ﬁlm layers (e.g.

nickel) have been coated. Film probes can be shaped conically, like a wedge,

or can have other shapes, so that they fulﬁll the requirements enforced by

diﬀering measurement problems. Film sensors are moreover coated with a

quartz layer for protection, so as to be less sensitive towards environmen-

tal inﬂuences. In addition, the quartz layer provides electrical insulation

for the ﬁlm sensor and thus makes it applicable to electrically conductive

ﬂuids.

In ﬂuid ﬂow measurements, use can be made of diﬀerent types of probes

with hot-wire or hot-ﬁlm elements, in order to measure wall-shear stress in-

formation in addition to carrying out local velocity measurements. Shear

stress sensors are formed as ﬂat heating elements, as shown, e.g. in Fig. 21.15,

among other sensor shapes. For measurements in liquids, sensors of thin metal

ﬁlms are provided with a protective layer (insulation), in order to avoid elec-

trolytic interactions between the sensor and measuring ﬂuid. All of this makes

Quartz rod

30°

0.060 Inches

(1.50 mm) dia.

Gold lm electrical leads

Alumina or quartz coated platinum lm

0.004" x 0.040"(0.10 mm x 1.0 mm) each side

Quartz rod

0.050 Inches

(2 mm) dia.

Gold lm electrical leads

Approx. 0.010" (0.25 mm)dia.

Quartz costed platinum

lm band

40°

0.040"

(1.0 mm)

Gold plating denes

sensing length

Gold plated stainless

steel supports

Quartz coated platinum

lm sensor on glass rod

(0.002" dia.)

(0.051 mm dia.)

Hot-lm sensors based on glass

support and plexiglass cotter

Quartz rod (50µ)

Platin lm (0.1µ)

Quartz protection

Cross section

Fig. 21.15 Diﬀerent probe types for measurements in liquids

670 21 Introduction to Fluid-Flow Measurement

it clear that ﬂow-measurement technology nowadays employs hot elements

extensively, in order to measure ﬂuid mechanically relevant quantities, when

carrying out experimental ﬂow investigations.

The employment of hot-ﬁlm technology for ﬂow measurements in ﬂuids re-

quires special skills and much care from the experimentalist, in order to obtain

reliable velocity measurements. The above-mentioned special designs of ﬁlm

sensors are required because of the special properties of liquids. The most im-

portant of these properties disturbing the execution of hot-ﬁlm measurements

are as follows:

1. The boiling temperature of ﬂuids is low.

2. Organic ﬂuids can decompose.

3. Fluids generally possess electrical conductivity.

4. Fluids dissolve gases and these can be set free.

5. Fluids are usually more contaminated than gases.

6. In water and other ﬂuids salts are dissolved.

7. Tap water contains algae, bacteria and microorganisms.

In order to be able to obtain reproducible results when doing measurements

in ﬂuid ﬂows, the above-mentioned special properties of ﬂuids have to be

taken into account.

Because of point 1 above, when carrying out hot-ﬁlm measurements, the

operating temperature of the sensor has to stay below the boiling temper-

ature of the ﬂow medium, as otherwise boiling of the ﬂuid at the heated

sensor occurs. For practical reasons, it is important to consider that lower

operating temperatures, compared with the boiling temperature, have to be

chosen for the mean temperature of the hot ﬁlm. As the temperature distri-

bution of commercially available cylindrical hot-ﬁlm probes, having a length

of only 20–30 times their wire diameter, show a steep temperature max-

imum in the wire center, as can be deduced from measurements with an

infrared detector (Fig. 21.16). It is this maximum temperature that must

not exceed the boiling temperature when carrying out hot-ﬁlm measure-

ments in liquids. When the temperature distribution along the wire is not

taken into consideration when setting the overheating temperature, the boil-

ing temperature of the ﬂuid can easily be exceeded locally in the probe

center and evaporation of the ﬂuid can occur. This leads to local modiﬁ-

cations of the heat transfer between sensor and ﬂuid and thus to erroneous

measurements.

Organic ﬂuids decompose (point 2) after exceeding a critical temperature,

lower than the boiling temperature. This can lead to depositions on the probe

surface, which usually result in decreases in the anemometry output voltages.

Electrical conductivity of a ﬂuid (point 3) leads to electrolysis at the sen-

sor surface of uncoated and, hence, unprotected ﬁlms. Due to unprotected

exposure of the sensor to the liquid, gas bubbles (H

or O

bubbles in water)

are generated and the sensor material is worn away from the wire surface

as a result of electrolysis, which is manifested by an increase in the cold

21.5 Basics of Hot-Wire Anemometry 671

300

250

200

150

100

515

10 20

0.0 0.2 0.4 0.6 0.8 1.0

Temperature °C

0.0 0.2 0.4 0.6 0.8 1.0

times wire diameter

Temperature °C

300

250

200

150

100

10 50 90

30 70

= z/l

times wire diameter

Fig. 21.16 Temperature distributions along the hot wires (Champagne et al., 1967).

Left : length of a hot wire having a diameter of 400 µm in two overheating relations.

Right :lengthofahotwireof99µm diameter

resistance of the sensor. The increased electrical resistance due to the wear-

ing away of sensor material, caused by the locally weakened cross-section of

the wire, leads to an increase in the local probe temperature, which in turn

intensiﬁes the electrolysis at this point, until ﬁnally the wire or ﬁlm sensor

breaks. Therefore, sensors working in electrolytes always require a thin quartz

layer for protection, in order to separate the wire or ﬁlm from the electrically

conductive ﬂow medium.

There is also a decrease in the heat transfer between the sensor surface and

the ﬂuid, caused by degassing of the gases dissolved in the liquid (point 4).

This inherently leads to non-reproducible velocity measurements. Once a gas

bubble has deposited at the sensor surface, usually the formation of further

bubbles takes place very quickly. They modify the heat release to the ﬂowing

medium, and thus the evaluation of the measurements can no longer be based

on the carried out calibration. This can be remedied by degassing the ﬂow

ﬂuid before the measurement. In the simplest case it is already suﬃcient to

leave the ﬂuid to stand quietly for some time, so that small air bubbles are

discharged by rising in and leaving the ﬂuid. However, it is better to bring

about degassing by heating or by creating an under-pressure above the ﬂuid

surface before starting the measurements.

Dirt particles also deposit on the sensor used in ﬂuids (point 5) and modify

thus the heat transfer between sensors and the ﬂuid ﬂow. Therefore, the ﬂuid

should be kept as clean as possible during one series of measurements. This

can be eﬀected by continuous ﬁltration with suﬃciently small ﬁlter pores.

Covering the ﬂow channel with a protective cover is also recommended, in

order to avoid the continuous entry of dirt. Contaminated sensors have to be

cleaned. Dust can be removed mechanically, e.g. by brushing it oﬀ. It is also

672 21 Introduction to Fluid-Flow Measurement

usual to rinse the probes in methanol to remove depositions of dirt in this

way, or to clean the sensor in an ultrasound bath.

The most commonly used liquid in ﬂuid mechanics is water. The salts

dissolved in water generally lead to depositions on the sensor surface (point

6). Calcium carbonate is an essential part of the layers deposited on hot-ﬁlm

sensors. Calciﬁcation of the sensor is substantially stopped if the operating

temperature of the sensor is below 60

◦

Finally, tap water contains algae, bacteria and microorganisms (point 7).

In measurements with hot wires and hot ﬁlms, slimy depositions can form

on the sensor surface and thus lead to deterioration of the heat transition. In

order to minimize these depositions, the ﬂow channel should be set up in a

dark room and not be exposed to solar or light radiation. Moreover, adding

small amounts of borax is also recommended to stop the development of algae

and microorganisms.

In general, the disadvantageous inﬂuences outlined in points 1–7 result

in non-reproducible velocity measuring results and require regular recalibra-

tions of the sensors employed for ﬂow measurements in ﬂuids. The same

holds for corrosive changes, structural changes and other uncontrollable in-

ﬂuences to which the wire or ﬁlm material is exposed in the experiments,

or during storage between experiments. Only by continuous surveillance of

the calibration of the probes can negative inﬂuences on the measurements be

excluded.

21.5.3 Hot-Wire Probes and Supports

As already mentioned, the actual sensor, in the case of hot-wire probes, is

mounted between the two tips of two prongs acting as holders, and the wire

ends are, as a rule, soldered on these wire holders. The prongs of the probe

are inserted in a ceramic body acting as probe holder. Normally the hot wire

is a platinum-coated tungsten wire.

In order to reduce the heat conduction from the hot wire to the cold holder

tips and to be able do deﬁne the active sensor length more precisely, copper-

plated or gold-plated probes have been developed, in which the sensor ends

welded on to the prongs are copper-plated or gold-plated (Fig. 21.17). Thus

Gold layer

Holder of hot-wire

Prongs

- component

Hot-wire

Electric connection

Fig. 21.17 Single-wire gold-plated sensor with prongs and probe ﬁlter

21.5 Basics of Hot-Wire Anemometry 673

the temperature distribution along the active sensor length is more uniform

than with non-plated probes. Because of the larger distance of the prongs

from the measuring point, the ﬂow ﬁeld in the region of the active sensor

part is less disturbed. The described single-wire probes can show diﬀerent

conﬁgurations, according to the application purpose. Probes with equally

long, straight prongs, where the hot wire forms an angle of 90

◦

with the axes

of both prongs, are employed for measurements of mean ﬂow velocities and of

the velocity ﬂuctuation in the main ﬂow direction. Figure 21.18 shows such

a hot-wire sensor, which is oriented in the ﬂow such that it is measuring the

U velocity component, indicated in Fig. 21.18.

Probes with unequally long straight prongs, where the hot wire forms an

angle of 45

◦

with the axes of the two prongs, serve for measuring Reynolds

shear stresses. They are used sequentially with straight probes, as shown in

Figs. 21.18 and 21.19. Additional measurements with ±45

◦

then yield u



, v



and u



, i.e. all elements of the Reynolds stress tensor.

Straight hot-wire sensor is

placed into the flow to

measure the

U -component

perpendicular to the wire

w = Parallel to the wire

= Perpendicular to the

wire and prongs plane

Prongs lie in

the u-w-plane

Fig. 21.18 Straight hot-wire probe for measurements of the

U component and u



ﬂuctuations in a turbulent ﬂow

Prongs to lie in

u-w-plane

(U + u)

With innclined hot-wires,

with respect to the flow

direction, correlation

measurements of velocity

fluctuations can be

carried out.

Fig. 21.19 Inclined probe for measurement of combined u



and u



term

674 21 Introduction to Fluid-Flow Measurement

Single-wire probe X-wire probe 3-wire probe

4-wire probe Boundary layer probe

Different probes are used

depending on the quantity

to be measured

Fig. 21.20 Diﬀerent types of hot-wire probes

Hot-wire

Hot-wire I

The hot-wires

lie in the plane parallel to

the x-z-plane of the coordinate system

Probe-axis

Fig. 21.21 X-probe for simultaneous measurement of the second velocity component

In Fig. 21.20, diﬀerent probe holders, also for multiwire probes, are shown,

giving a good overview over those wires used today for ﬂuid velocity

measurements.

For determining the ﬂow direction in a plane, where two velocity com-

ponents are located in this plane, and carrying out measurements in one

measuring operation, so-called X-probes are used with two wires or ﬁlms

standing perpendicular to one another, as shown in Fig. 21.21. The wires are

mounted parallel to the x–z plane and thus consist of two combined “inclined

probes” with a probe inclination of ±45

◦

, as shown in Fig. 21.19.

The following velocity relationships result for wires A and B:

gem

= U cos α + W sin α

gem

= U cos α − W sin α