Seminar Report

on

MEASUREMENTS IN UNSTEADY FLOWS

Submitted in the partial fulfillment of the requirements for the degree of

Bachelor of Technology in

Aerospace Engineering

By

Jitesh Chauhan 99D01001 Ashish Gupta 99D01003

Moble Benedict 99D01011

Department of Aerospace Engineering

Indian Institute of Technology Bombay

12 November 2002

1

CHAPTER 1

THE DYNAMICS OF CONTINUOUS MEASUREMENT OF

UNSTEADY FLOW

1.1 DYNAMIC PROPERTIES OF SYSTEMS FOR THE CONTINUOUS

MEASUREMENT OF UNSTEADY FLOW

Systems for the continuous measurement of unsteady flow have now been quite

widespread. They are utilized both industrially and in experimental research. There are

two ways of continuously measuring unsteady flow, depending on the task in hand :

(a) By determining the mean value of unsteady flow over some time interval from

t1 to t2.

(b) By continuously measuring rapidly varying flow and determining the

instantaneous value of the flow at any moment from t1 to t2.

The second instance of measuring unsteady flow is the more general.

The devices used measure unsteady flow function according to extremely varied

principles (mechanical, electrical, magnetic, optical and thermal). In all the continuous

measuring systems to be examined the primary transducer emits an electrical signal

which is the subject to appropriate conversion in secondary transducers and conversion

elements.

Flowmeters which do not use pressure difference when metering may be divided

into 2 groups.

(a) Mass flowmeters. Mass flowmeters are instruments applying the Coriolis

principle and gyroscopic effect, and also those using the force of inertia of a moving and

rotating flow of material. These flowmeters directly measure the mass of the flow, their

readings being independent of the physical parameters of the material.

(b) Volumetric flowmeters. These include turbine, electromagnetic, ultrasonic

flowmeters, and also to some extent the thermo-anemometers and ionization flowmeters.

These flowmeters react to the volumetric flow. In order to use their readings to assess the

flow by weight, corrections must be made for the density of the material.

2

The presence of a link of a metering chain is due to the need to perform definite

functions:

(a) The conversion of the unsteady flow rate or flow velocity into a primary

electric signal.

(b) Amplification and conversion of the primary signal.

(c) The recording of the measuring signal.

The structural schemes of most flow meters designed to measure unsteady flow have

three links: a detecting device, a transducer amplifier and a recording instrument. In such

measuring systems the flow acts directly on the detecting element of the emitter.

Continuous metering of unsteady flow may be effected using systems in which

the following measuring principles are applied.

(a) Continuous creation of an electrical intermediate parameter in the flow, whose

variation determines the velocity of the flow. These systems include inductive

flowmeters having a constant magnetic field and ionization flowmeters with

constant ionization of flow.

(b) Continuous creation of a mechanical intermediate parameter in the flow,

whose magnitude is proportional to the mass of the flow. Systems utilizing the

inertial properties of the medium include various flowmeters with spinning rotors

: flowmeters measuring the Coriolis force, gyroscopic and turbo-flowmeters.

(c) Continuous creation of a thermal intermediate parameter in the flow,

variations in which determine the velocity of the flow – calorimetric flowmeters.

(d) Introduction of a heated body into the flow under measurement, whose

thermal balance varies continuously depending on the velocity of the flow –

thermo anemometers.

(e) Introduction into the stream of a body which continuously detects the dynamic

pressure of the medium in motion.

In the discrete measurement of unsteady flow there is a periodic creation of an

intermediate parameter. It could be electrical, mechanical or thermal.

The primary transducers in electrical systems for continuous flow measurements

convert the sensed parameters into electrical signals. The primary elements may be

divided, in terms of power, into generator and modulator elements. No energy from a

3

source of supply is applied to primary generator elements; they form the electrical signal

by deriving the appropriate amount of energy from the flow. Magnetic-turbine type

transmitters may serve as an example of these elements. Modular elements, as distinct

from the generator type, consume power from the sources of supply and accordingly

modulate the size of the voltage (or current) in proportion to the amount of flow. The

electrical turbine transmitter is an example of such elements.

The quality of an element in a continuous measuring system may be characterized

by the magnitude and interrelationship of the input and output signals. On a change in the

input magnitude in the element a transient occurs whose nature depends on the elements

dynamic properties. These are a consequence of the presence in the element of inertial

parts which store energy. After a lapse of a certain time interval an equilibrium relation

is established between the input and output magnitudes which does not vary with time.

This is called the steady state of the element. The relation of the output magnitude to the

input magnitude for the element’s steady working mode is called its static characteristic.

1.2 FREQENCY CHARACTERISTICS OF CONTINUOUS MEASURING

SYSTEMS FOR UNSTEADY FLOW

When determining the percentage errors created by linear measuring systems in

measuring complicated functions, the errors may be considered as the sum of elementary

errors which arise in the individual measurement of the harmonic components of the

frequency spectrum of a complicated signal. This becomes possible through the fact that

in linear elements and linear systems where several disturbing effects are simultaneously

applied, their joint effect equals the sum of effects caused by each of the disturbing

elements in isolation. The properties of such continuous measuring systems are

determined by the amplitude and phase distortions occurring in response to the sinusoidal

varying signals at different frequencies. In this case the amplitude-frequency and the

phase-frequency characteristics may be used to describe the dynamic properties of

continuous measuring systems.

The amplitude-frequency characteristic is the relation showing how the amplitude

of the forced oscillations at the link’s output varies with frequency, if constant amplitude

harmonic oscillations are applied to the input.

4

The phase-frequency characteristic is the relation showing the variation with the

frequency of the phase shift between the harmonic oscillations applied to input of the link

and those obtained at the output.

Frequency characteristic are essentially static in nature, since for each value of the

frequency they indicate relations obtaining during steady state operation. The amplitude-

frequency and phase-frequency characteristics show the manner in which a link reacts to

periodic disturbances of different frequencies. The elements of continuous measuring

systems possess certain selective properties, so that out of the entire frequency spectrum

of the variation of flow to be measured, they transmit without distortion only frequencies

located definite bands of frequency range.

1.3 ACCURACY OF MEASUREMENT OF UNSTEADY FLOW

Errors which occur in measuring unsteady flow may be divided into static and

dynamic. Static errors are those which arise during measuring of magnitudes which do

not vary in time. Errors occurring during measurement of magnitudes which do vary in

time are known as dynamic.

Errors may also be classified as those due to the method and those due to the

apparatus, though our opinion is that, when considering continuous measuring systems

for unsteady flow, it is more rational to classify errors into static and dynamic.

One of the most important questions arising in the measurement of unsteady flow

is that of the dynamic accuracy. In most continuous measuring systems the dynamic

accuracy is governed by what is called the “inertia factor” of the system, i.e. the ability of

a measuring system to react rapidly to all variations of flow. The question of dynamic

accuracy in such systems is important, since in many cases dynamic accuracy obtainable

is the principal selection criterion for a system required to measure rapidly varying

magnitudes.

In the measurement of a constant flow (not varying with time) a continuous

measuring system is completely characterized by a static amplification factor (or gain).

The factor is proportional to the tangent of the angle of slope of static characteristic

relative to the abscissa. In the case of measuring unsteady flow, the instantaneous

dynamic factor of the system is not constant in value, but varies with time. Its

5

instantaneous magnitude basically depends on the amplification factor of the individual

harmonics and their relative disposition at a given moment. Since the overall dynamic

amplification factor of the system has definite variation with time, the measuring signal

follows the variation of magnitude to be measured with certain deviations. These

variations in the amplification factor of the system with time also cause the occurrence of

dynamic error when measuring unsteady magnitudes.

A system can measure a varying magnitude without any dynamic error in the case

where its dynamic amplification factor constant. This is possible in the ideal case when

the variation to be measured falls within the distortion-free-pass-band of the system, and

furthermore when, for all frequencies within the pass-band of the system, constant and

equal amplification factors occur in the absence of phase shift. Since in overwhelming

majority of cases when measuring varying magnitudes these conditions cannot be entirely

satisfied, corresponding dynamic errors arise. The magnitude of dynamic error depends

both on the nature of the physical processes underlying the measuring system and on the

parameters of the components (resistance, inductance and capacitance) composing the

measuring system.

The magnitude of errors introduced by the primary element is accordingly

amplified. In the other event of errors being introduced by subsequent elements of the

system, these errors suffer no amplification as in the first case.

The following parameters exercise an indirect influence on the sensing element of

a flowmeter: temperature and pressure of the medium, external magnetic and electrical

fields, and vibrations. The most substantial effect on the reading of a flowmeter is

exercised by the parameters of the substance under measurement via the sensing element.

In the transmission of a measuring signal, noise is superimposed on it, it becomes

necessary to separate signal from noise. This is achieved by the means of filters.

1.4 CALIBRATING CONTINUOUS MEASURING SYSTEM FOR UNSTEADY

FLOW

In order to determine an actual variation of flow with time from the measured

signal obtained, the appropriate transient relations must be available. For this purpose

frequency characteristics may be used for continuous measuring systems which may be

6

considered linear over the measuring range. The use of a statically calibrated relation to

determine the flow quantitatively is possible only when the amplitude-frequency and

phase- frequency characteristics of the system do not vary throughout the measured

frequency range, beginning with static mode. Thus in the general case the dynamic

calibration of the linear continuous measuring systems for unsteady flow boils down to

determining experimentally their frequency characteristics. For this purpose flow pulses

are formed on special installations, the pulses having a definite regular variation in time.

The principle of such a device is shown in Fig.7. A rotary valve is set in motion

by an electric motor having a variable rotation speed. The signal which controls the

electric motor is formed by a special electronic signal generator. The measuring signal

obtained from the flowmeter passes to an oscilloscope, to which is simultaneously

applied an electrical signal corresponding to the true variation of the flow. With such a

device one can determine the frequency characteristics of flowmeters and over the range

of frequencies of pulsating flow which can be generated by means of the rotating valve.

Thus the amplitude and phase distortions can be evaluated from one oscillogram on

which is recorded the reaction of flowmeter to a pulsating flow of increasing frequency

7

CHAPTER 2

CONTINUOUS MEASURING SYSTEMS FOR MASS FLOW The principle of action is based on imparting to the flow material to be measured

an additional movement, in order to excite in it intermediate measuring parameters. The

possibility of creating intermediate parameters in a given case is due to the tendency of a

flow of material (owing to its inherent inertia) to maintain a motion imparted to it.

Depending on the actual additional motion communicated to the flow (by a rotating or

oscillating unit) a Coriolis force, gyroscopic effect or an inertial torque is set up in the

sensitive element, proportional to the mass of flow of the substance. If a vibrating

element is used instead of a rotating unit, the working principle of the instrument is

unchanged.

The most important feature of this group of flowmeters is that they ensure the

direct measuring of the true value of mass flow in a non-steady flow of the substance,

regardless of the properties and the state of the substance (pressure, temperature, density,

viscosity, etc.). A desirable quality of these flowmeters is that they cause only small

pressure losses.

The group under consideration comprises:

(1) continuous measuring systems for mass flow using Coriolis force;

(2) those using gyroscopic couple;

(3) those using inertial moment of a rotating flow.

2.1 SYSTEMS FOR CONTINUOUSLY MEASURING MASS FLOW BY THE

CORIOLIS FORCE

A liquid mass-flowmeter with a rotating T-shaped element acts on the following

principle. The liquid flows through a double T-shaped which revolves at a constant

angular velocity (Fig. 8a). The tube system consists of two parts (1 and 2), joined by

flexible connections. The T-shaped tube is mounted on a torsion element 5, which

permits it to move through a certain angle relative to the rotating case 4, to which the

remainder of the rotating tubing is rigidly fixed. The system is joined to the stationary

tubing by means of sealing muffs. The rotor is at a constant speed by an electric motor

through the gearing 3. Under the action of Coriolis acceleration, as the liquid passes

8

through tube 1 a moment develops whose magnitude is proportional to the flow of liquid.

The moment can be measured by various electrical transmitters, a particular one for these

being the strain gauge, which is glued to the torsion element and measures the

deformation. The measuring signal is tapped off the rotor by slip rings and fed to the

measuring circuit; the magnitude of the measuring signal is in linear proportion to the

mass flow up to the limit of elasticity of the material of which the torsion element is

made.

The Coriolis force exerted on the rotating tubing by a liquid (Fig. 8b) can be

expressed by the following formula.

dP = ρ F dr a,

where ρ is the density of the liquid;

F is the area of cross-section of the tube;

R is the radial distance of the liquid element from the axis of rotation;

a is the Coriolis acceleration, which has the same value for any part of the liquid

present in the tube 1 (a = 2 w v);

v is the speed of liquid in the tube.

The magnitude of the mass flow rate through the tube is G = ρ F v. After the appropriate

substitution we obtain

9

dP = 2 G w dr

The moment about the axis of rotation developed in one radial tube 1 under the action of

Coriolis force is

M = ∫ 2 G w r dr = w (r22 – r1

2) G

It follows from the above formula that the magnitude of the measured moment is

unaffected by the properties of the liquid or the shape of the driving tube. The sole

requirement for this moment to develop is radial motion of the liquid in the rotating

channel, while the rotor can be designed to a great variety of patterns.

The defects inherent in the majority of flowmeters in which the flow is measured

by the magnitude of Coriolis force, are due to the use of sealed rotating joints, and are

entirely absent in an instrument employing an electrical rotor driven through the

hermetically sealed wall of a branch pipe. The design of such an instrument is as follows

(Fig .12). The rotating tube 2, with one central and several radial channels, is mounted in

low friction bearings 3 in the casing 1. The element 2 is made in the form of the rotor of a

synchronous electrical motor 4; it is rotated by means of an electrical field created by the

windings of the stator 5 situated outside the body.

When the rotor revolves at constant speed, the liquid travels along the rotating

radial channels from centre to periphery and then returns to the axis of the rotor along the

stationary channel 6, situated in the casing. During its motion in the rotating radial

channels, a Coriolis acceleration and the corresponding forces develop in the liquid.

Since the liquid, on emerging from the rotor, passes into the stationary channels, the

power spent on imparting to it a Coriolis acceleration is not returned to the rotating

system but is carried off with the stream. This power is proportional to the mass flow of

material, and may be written as

N = G (r22 – r1

2) w2

where G is the mass flow

r2 and r1 are the respective radii of the rotating channels of the rotor

In the flowmeters of the type in which the liquid returns to the rotor axis along the

revolving channels the power required to turn the rotor does not depend the amount of

flow. If conditions are created in such a device that for returning the liquid to the rotor

axis along the stationary channels, thus obviating an electric motor with a sealed shaft, it

10

is impossible to measure the flow by the power with sufficient accuracy because the

revolving rotor is connected through sealed joints in which the power used to overcome

friction has a value which in a number of cases greatly exceeds that needed to create

Coriolis force in the stream.

In the case where the rotor is driven by a rotating magnetic field passing through

the wall of the body, however the flow may be measured directly from the power

consumed to form Coriolis accelerations in the stream. This is due to greatly reduced

mechanical friction of the system.

In a flowmeter working on the principle under discussion, flow can also be

measured directly by the value of the torque developed in the stator of the electric motor.

In this case the stator of the electric motor, situated outside the connecting tube, is

designed to be able to rotate slightly in relation to the axis of the connecting tube.

Rotation of the stator is resisted by a force gauge which detects a torque arising in it.

When Coriolis forces develop on the uniformly rotating vane, a corresponding torque is

set up on it in the opposite direction to that of rotation, and with a value proportional to

the flow rate of material. A torque of equal value and opposite sign arises on the stator of

11

the electric motor and is detected by a force gauge. The measuring signal created at the

latter will therefore be proportional to the flow rate.

2.2 GYROSCOPIC CONTINUOUS MEASURING SYSTEMS FOR MASS FLOW

A gyroscopic mass flowmeter with a revolving rotor has the following structure.

The stream of liquid or gas passes along a special tube of complicated shape, rotating at

constant speed. The gyroscopic effect thus caused, proportional to the mass flow of the

substance, will tend to rotate the whole revolving system relative to the axis B-B (Fig.

19b). The size of this moment will be measured by some sort of transmitter.

The measuring device works as follows. If a force F (Fig. 19a) is applied to the

axis of the rotating disc, then under the action of the moment of precession the axis will

begin to move in a plane perpendicular to the vector of the force. Conversely, if the disc

rotating about its axis is caused to rotate also in a plane passing through its axis, then a

force F will occur on the axis of the disc.

If the rim of the rotating disc is replaced by an annular tube (Fig. 19b) along

which a liquid is continuously passing, and it is uniformly turned about the axis A-A, a

gyroscopic moment occurs relative to the axis B-B, whose value is proportional to the

mass flow through the annular tube.

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2.3 TURBO-FLOWMETERS

The working principle of a turbo-flowmeter designed to measure the unsteady

flow is as follows. Located coaxially in the body of the instrument are two impellers,

mounted some distance apart (Fig. 29). Round the periphery of both impellers there are

channels, whose axes are parallel to those of the impellers. There is a certain amount of

radial clearance between the body and the vanes. Liquid enters the body, passes

consecutively through the channels in both the impellers and issue from the instrument

through the outlet tube. The upstream impeller is set in rotation by an electric motor at

constant angular velocity. The second impeller is fixed to an elastic element.

The rotating impeller creates a certain inertial moment in the liquid so that the

flow of liquid under torsion exerts a pressure on the blades of the fixed impeller, causing

it to rotate through a certain angle until equilibrium ensues between the moment acting on

the impeller, and what arises through torsion of the elastic element. The value of the

moment and consequently the deformation of the elastic element, are proportional to the

mass flow of liquid.

All the turbo-flowmeters under discussion, compared with other mass flow

meters, possess the following advantages: (a) small dimensions and weight; (b) low

hydraulic loss. In addition these instruments contain no sliding contacts in the measuring

circuit, which is also an extremely great advantage.

The driving impeller in turbo-flowmeters may be driven by means of an external

rotary magnetic field. In this case the rotating impeller is designed as the rotor of a

synchronous electric motor, the windings of whose stator is arranged externally directly

on the branch pipe of the flowmeter. The rotating magnetic field, creator by the stator

winding, passes through the metal tube of the instrument and sets in rotation the rotor

through which longitudinal channels have been drilled parallel to the flow axis. When the

driving impeller is actuated in this manner, the turbo-flowmeter will have the following

positive qualities.

1. The absence of rotating sealed couplings, which is very important when

measuring the flow of corrosive liquids and liquids under pressure.

13

2. A substantial simplification of the flowmeter, by mounting the stator on the

branch-tube of the flowmeter, because of the absence of any special electric motor

and a corresponding mechanical transmission.

3. A substantial reduction in weight and dimensions of the flowmeter for the same

reasons.

2.4 THE COMPARISON OF MASS FLOWMETERS

In order to create an intermediate measuring parameter in mass-flowmeters, an

additional movement is imparted to the substance to be measured. Through this

movement accelerations and forces arise which are proportional to the mass flow of the

substance under measurement. Mass-flowmeters are made both with rotating and

oscillating sensitive elements. In the instruments having rotating sensitive elements the

formation of the intermediate measuring parameter proceeds continuously, so that they

constitute continuous-measurement instruments. The dynamic ranges of flowmeters

whose sensitive elements are mounted on elastic couplings are governed by the natural

oscillating frequency of the corresponding oscillating systems.

In mass-flowmeters having oscillating sensitive elements, the inertial forces are

produced in the flowing substance in the same manner as with a uniformly revolving

rotor, though their value varies in time according to the law of variation of velocity of the

oscillating element. The force oscillating frequency of the system is chosen in most cases

equal to the natural oscillating frequency of the sensitive element.

14

CHAPTER 3

CONTINOUS MEASURING SYSTEM FOR VOLUMETRIC FLOW Continuous measuring systems for volumetric flow include the following: turbine,

ultrasonic, induction, thermal, those which continuously ionize the flow and those which

mark the flow in various ways.

3.1 TURBINE-TYPE FLOWMETER

Turbine-type flowmeters belong to the velocity flowmeters, in which the kinetic

energy of the stream under investigation is used to produce a torque on the measuring

vane. The measurement of unsteady flow by the speed of rotation of a rotor is affected by

two principal factors: variation in the velocity of the flow, and in its density.

The working principle of turbine-type flowmeters designed to measure unsteady

flow is as follows. A well-balanced light rotor is placed in the flow to be measured and

revolves in low-friction bearings. Under the pressure of the moving flow, the rotor

revolves, doing do at a rate proportional to the speed of flow. The vanes may be made

axial or tangential.

The rotational speed of the rotor may be measured in various ways:

electromagnetically, photo-electrically, by radioactivity etc. To measure the mass flow,

turbine flowmeters must be equipped with density pick-ups and the appropriating

correcting systems.

A. Turbo-magnetic flowmeters:

In this type of flow meter the speed can be measured simply and with great

accuracy by counting the rate at which turbine blades pass a give point, using a magnetic

proximity pickup to produce voltage pluses. By feeding these pulses to an electronic

pulse-rate meter, one can measure flow rate; by accumulating the total number of pulse

during a time interval, the total flow is obtained. These measurements can be made very

accurately because of their digital nature. If an analog voltage signal is desired, the pulses

can be fed to a frequency-to-voltage converter. The two types of turbo-magnetic

flowmeters are shown in the fig below.

15

Figure 1 Axial Turbine Flowmeter (Magnetic)

Figure 2 Tangential Turbine Flowmeter (Magnetic)

B. Turbo-optical flowmeters:

To measure the speed of a liquid of a sufficient transparency, one may use turbo-

optical flowmeters. In a turbo-optical flowmeters, the rotor is similar to that in the turbo-

magnetic flowmeter, except that the device measuring the speed of rotation of the rotor is

based on an optical principle. As the rotor 1 rotates, its blades intersect a beam of light

16

passing from the incandescent lamp 2 to the photoelement 3, thus alternately opening and

closing the passage of the light to the photoelement (Fig 3).

Figure 3 Turbo-optical flowmeter

At the electrodes of the photoelement pulsating electrical signals are produced as

a result, whose frequency is proportional to the flow of liquid through the flowmeter.

C. Turbo-radioactive flowmeter:

These flowmeters are constructed as follows. A balanced rotor (axial or tangential) is

placed in the flow to be measured and rotates under the pressure of the fluid. In one or

more of the blades radioactive isotopes with gamma-radiation are paced in the form of a

solid insert. The flowmeter is externally screened to prevent radiation. There is an

aperture in the screen for the outlet of the radiation into the external medium.

Opposite the aperture is placed a radiation indicator, coupled to a suitable

recording device. At the moment when the blade with the radioactive isotope is in the line

with the opening in the screen and the indicator, the radiation is detected by a counter.

The frequency of the radiation pulses falling on the counter is governed by the rotational

speed of the rotor, i.e. by the flow of fluid passing through the flowmeter.

17

3.2 ULTRASONIC FLOWMETER

Small-magnitude disturbances are propagated through a fluid at a definite velocity

(the speed of sound) relative to the fluid. If the fluid also has a velocity, the absolute

velocity of pressure-disturbance propagation is the algebraic sum of the two. Since flow

rate is related to fluid velocity, this effect may be used in several ways as the operating

principle of an “ultrasonic” flowmeter. The term ultrasonic refers to the fact that, in

practice, the pressure disturbance usually are short bursts of sine waves whose frequency

is above the range audible to human hearing, about 20,000 Hz. A typical frequency might

be 10 MHz.

The various methods of implementing the above phenomenon all depend on the

existence of transmitters and receivers of acoustic energy. A common approach is to

utilize piezoelectric crystal transducers for both functions. In a transmitter, electrical

energy in the form of a short burst of high-frequency voltage is applied to a crystal,

causing it to vibrate. If the crystal is in contact with the fluid, the vibration will be

communicated to the fluid and propagated through it. The receiver crystal is exposed to

these pressure fluctuations and responds by vibrating. The vibration motion produces an

electrical signal in proportion, according to usual action of piezoelectric displacement

transducers. For crystal to be an efficient transmitter of acoustic energy, its diameter D

must be large compared with the wavelength λ of the oscillation. The conical beam

projected from a circular crystal has a half-angle α given by sin α = 1.2λ/D; thus the

desired small angles also require a small λ/D ratio. Since compactness requires

reasonably small (~ 1 cm) values of D, we need to use wavelength on the order of 1 mm.

Figure 4 shows the most direct application of these principles. With zero flow velocity

the transit time to of pulse from the transmitter to the receiver is given by

cLto =

where L = distance between transmitter and receiver and c = acoustic velocity in fluid. If

the fluid is moving at a velocity V, the transit time t becomes

2cLVt =

and we define ∆t = to – t, then 2cLVt ≈∆

18

Thus, if c and L are known, measurement of ∆t allows calculation of V. While L may be

taken as constant, c varies, for example, with temperature; and since c appears as c2, the

error caused may be significant. Also, ∆t is quite small since V is a fraction of c.

Figure 4 Ultrasonic Flowmeter

Since the measurement of to is not directly provided for in this arrangement, the

modification is required. In the figure 5 two self-excited oscillating systems are created

by using the received pulses to trigger the transmitted pulses in a feedback arrangement.

The pulse repetition frequency in the forward propagation loop is 1/t1 while that in the

backward loop is 1/t2. The frequency difference is ∆f = 1/t1 - 1/t2, and since

t1=L/(c+Vcosθ) and t2=L/(c-Vcosθ), we get

LVf θcos2

=∆

Figure 5 Ultrasonic Flowmeter

This is independent of c and thus not subjected to errors due to changes in c.

19

CHAPTER 4

THERNAL SYSTEM FOR MEASURING UNSTEADY FLOW In thermal automatic monitoring system the rate of flow is measured either by the

cooling of a heated body placed in the flow or by the transfer of heat energy between two

points situated along the flow. There are two main classifications of the system, first

Thermo-anemometers and second, calorimetric flow meter.

4.1.1 THERMO-ANEMOMETER

The principle is based on the relation between the quantity of heat lost by a heated

measuring element and the rate of the ambient flow. This is further classified in two

groups. The first group comprises those in which the thermo element is connected as one

of the arms directly to a measuring bridge. These thermo-elements may be made with

their thermo element at either constant or variable temperature. The rate of flow is

measured by the variation of resistance in the thermo element for a current of constant

magnitude, or by the variation in the strength of the current for a thermo-element with its

resistance and temperature constant.

The second group contains instrument in which the receptor consist of a heated

filament and a thermocouple or thermistor, designed to measure the temperature of the

filament itself. In this instance the rate of flow is measured by the variation in the

filament temperature for constant power or current. The second group as a rule possesses

enormously greater inertia than the first.

The sensitive element of the thermo anemometer is made of platinum, tungsten or

nickel wire or 0.005 to 0.3mm diameter. As the diameter of the filament decreases so

does the inertia.

If, rate of the flow, v varies, both the current strength I and resistant of the thermo

element R vary. Since the output signal in this kind of instrument is usually expressed in

the form of a voltage drop on the measuring bridge, an independent variation of current

and resistance makes such a measurement impossible. To eliminate one of the variables,

the instrument’s power supply circuit must be designed so that the size of the current

passing through heated thermo-element always remains constant, regardless of its

resistance. In this case the rate of flow can be determined by the potential difference at

20

the ends of the thermo- element, the temperature of the flow and the characteristics of the

material of the thermo-element. The main drawback of the thermo-anemometer is that

their readings depend substantially on the temperature of the flow being measured.

The filament is subjected to an aerodynamic load, which depends on the ratio of

the length of the wire to its diameter, and to a shock load occurring when it is bombarded

by solid particles borne along with the flow. If the vibration load does not damage the

filament, it will cause its resistance to pulsate, which may introduce substantial errors

into the measurement. Higher is the temperature of the thermo element, the more

sensitive is the instrument, and less its reading are affected by fluctuation in the

temperature of the flow being measured. The heating range of the thermo-element

normally lies in the range of 400-5000C. If the axis of the heated filament is

perpendicular to the direction of the airstream, the stream exerts the maximum effect on

the filament else it would have some cosθ component. The transfer of the heat depends

on the rate of flow, temperature difference between the body and medium.

4.1.2 HOT WIRE ANEMOMETER

The hot-wire anemometer increases VOUT until the power dissipated in the wire

sensing element, and hence its temperature and resistance, has risen to the point where

the bridge at equilibrium. Air movement past the wire would cool it, but VOUT increases

compensate for the increased dissipation restoring the wire to its equilibrium temperature.

The equilibrium behavior of the system is independent of the heat capacity of the wire.

However, the dynamic response, and noise figure, are both improved by minimizing the

size of the wire. Anemometry will refer to the use of a small, electrically heated element

exposed to a fluid medium for the purpose of measuring a property of that medium.

Normally, the property being measured is the velocity. Since these elements are sensitive

to heat

Transfer between the element and its environment, temperature and composition changes

can also be sensed.

Typical dimensions of the wire sensor are 0.00015 to 0.0002 inches (0.0038 to

0.005 mm) in diameter and 0.040 to 0.080 inches (1.0 to 2.0 mm) long. This is the type of

21

hot wire that has been used for such measurements as turbulence levels in wind tunnels,

flow patterns around models and blade wakes in radial compressors.

4.1.3 HOT FILM ANEMOMETER

The hot film is used in regions where a hot wire probe would quickly break such

as in water flow measurements. The hot-film sensor is essentially a conducting film on a

ceramic substrate. The sensor shown in Figure 2 is a quartz rod with a platinum film on

the surface. Gold plating on the ends of the rod isolates the sensitive area and provides a

heavy metal contact for fastening the sensor to the supports. The metal film thickness on

a typical film sensor is less than 1000 Angstrom units, causing the physical strength and

the effective thermal conductivity to be determined almost entirely by the substrate

material. Most films are made of platinum due to its good oxidation resistance and the

resulting long-term stability. The ruggedness and stability of film sensors have led to

their use for many measurements that have previously been very difficult with the more

fragile and less stable hot wires. This type of anemometer also facilitate advantages over

hot wire anemometer like,

1) Better frequency response (when electronically controlled) than a hot wire of

the same diameter because the sensitive part of the sensor is distributed on the surface

rather than including the entire cross section as with a wire.

22

2) Lower heat conduction to the supports (end loss) for a given length to diameter

ratio due to the low thermal conductivity of the substrate material. A shorter sensing

length can thus be used.

3) More flexibility in sensor configuration. Wedge, conical, parabolic and flat

surface shapes are available.

4) Less susceptible to fouling and easier to clean. A thin quartz coating on the

surface resists accumulation of foreign material. Fouling tends to be a direct function of

size.

figure 3, probe as a bridge branch

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4.2 PROBE SHAPES

In addition to the cylindrical shape, hot films have been made on cones, wedges,

parabolas, hemispheres, and flat surfaces. Cylindrical film sensors that are cantilever

mounted are also made. This is done by making the cylindrical film sensor from a quartz

tube and running one of the electrical leads through the inside of the tube.

4.2.1 SINGLE ENDED SENSOR

This is an important modification for fluidic applications since they can be made

very small and inserted into very small channels. Also, for omni-directional

measurements (e.g., meteorology applications when the vertical flow can be ignored), it

permits unobstructed flow from all directions.

4.2.2 CONE SHAPE SENSOR

This sensor is used primarily in water applications where its shape is particularly

valuable in preventing lint and other fibrous impurities from getting entangled with

sensor. The cone can be used in relatively contaminated water, while cylindrical sensors

are more applicable when the water has been filtered.

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figure 5, cone probe

4.2.3 FLUSH MOUNTED PROBE

Flush mounted probe which has been used for sensing the presence of flow with

no obstruction in the fluid passage, detecting whether the boundary layer is laminar or

turbulent, and measurements of shear stress at the wall. It makes a very rugged probe

when compared with other anemometer type sensors.

figure 6, flush probe

4.2.4 WEDGE SHAPED PROBE

The wedge shaped probe shown in Figure 7 has been used for both gaseous and

liquid applications. It is somewhat better than cylindrical sensors when used in

25

contaminated water and is certainly stronger than cylindrical sensors for use in very high

velocity air or water where there is a large load on the sensor due to fluid forces.

4.3 CONSTANT TEMPERATURE ANEMOMETER (CTA)

It works based on the fact that the probe’s resistance will be proportional to the

temperature of the hot wire. The bridge circuit shown in Figure 3 below is set up by

setting the adjustable resistor to the resistance you wish the probe and its leads to have

during operation. (The other two legs of the bridge have identical resistance.) The servo

amplifier tries to keep the error voltage zero (meaning the resistances of the two lower

legs of the bridge match). It will adjust the bridge voltage such that the current through

the probe heats it to the temperature, which gives the selected resistance. When we put

the probe in a flow, the air (or water) flowing over it will try to cool it. In order to

maintain the temperature (resistance) constant, the bridge voltage will have to be

increased, Thus, faster the flow, higher the voltage. A very fine hot wire by itself cannot

respond to changes in fluid velocity at frequencies above about 500 Hz. By compensating

for frequency lag with a non-linear amplifier this response can be increased to values of

300 to 500 kHz.

4.4 CALORIMETRIC FLOW METERS

The principle is based on the heat transfer by the flow of material. This is divided

into three groups,

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1) Devices operating by the application of constant power to the heater, and with

measurement of the amount by which the flow is heated, depending on the velocity.

2) Those which operate by heating the flow to constant temperature and by

measuring the amount of energy applied to the heater and depending on the velocity of

flow.

3) Those in which the temperature of the heater varies sinusoidal in time. In these

devices the rate of flow is measured by the amount of phase shift of the signals obtained

at the meter and those applied to the heater.

The measuring elements used in calorimetric flow meters are thermocouples or

resistance thermometers, which have relatively low dynamic properties. The measuring

frequency range of these instruments is small. In calorimeters operating with a constant

temperature difference of the flow before and after the heater, the flow is measured by the

amount of power consumed by the heater. When the flow temperature varies, the

measuring bridge goes out of equilibrium and varies the current strength in the heater to a

value at which a pre-set degree of heating of the gas is restored. The inertial errors

created by such a system are governed by the thermal inertia of the temperature

measuring devices employed, and also by the heater operating in a pulsating mode. The

measuring errors substantially decrease as the distance between the heater and the

measuring devices is reduced. The equation for the thermal balance is given as,

q = QCp∆t

where, Q is the flow of gas:

q is the heat consumed in heating the gas

∆t is the temperature difference of the gas before and after the heater.

Cp is the thermal capacity for constant pressure.

Heat is transferred to the flow by an electrical heater, hence,

q = KU2/R2

Q = KU2/RCp∆t2,

Where R is the resistance to be heated, through which passes a current of strength I with a

voltage drop U. K is the thermal equivalent of the electrical energy.

The calorimetric method of measuring the flow of a liquid or a gas can be so

designed that the heating and measuring elements are not introduced into the flow, but

27

are mounted on the outer surface of the flow meter tubing. The flow is measured by the

transfer of heat by the boundary layer of the substance flowing in the tube. It should be

noted that the dynamic sensitivity of this method is poor, since the motion of the

boundary layer follows that of the main flow with a certain time lag, and also because of

the relatively large thermal inertia of the walls of the branch tube. the static response of

such a measuring system is linear.

The mode in which the heater of thermal flow meter operates may be either steady

or pulsating, and in later case an intermediate parameter is periodically formed in the

flow. The readings of the flow meters with continuous heating of the flow, and which

measure by the amplitude method, depends greatly on the pressure of the medium being

measured, since the conditions of heat transfer alter considerably with a change of

pressure. The dynamic properties of calorimetric flow meters are governed by the thermal

inertia of their elements. The dynamic properties of the flow meters improves as the

masses of these elements is reduced, though the strength of the elements also diminished.

The dynamic properties of calorimetric flowmeters are far lower than for thermo

anemometers.

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CHAPTER 5

CONTINOUS MEASURING SYSTEM WITH CONTINUOSLY

IONIZED FLOW Automatic monitoring systems with continuously ionized flow includes,

1) Flow meters with continuous ionization of the flow by radioactive irradiations.

2) Ionization anemometers with a glow discharge.

The characteristic feature of this group of devices is that their primary transducers

produce an intermediate electrical parameter in the flow, from whose value the velocity

of the flow can be found.

5.1 FLOW METERS WITH CONTINOUS IONIZATION OF THE FLOW BY

RADIOACTIVE IRRADIATION

It consists of two electrodes 1 and 2, attached to the inner surface of the tubing. A

layer of radioactive material is deposited on electrode 2, which emits α or β particles

which ionize the gaseous flow passing between the electrodes. Owing to the potential

difference (100-300V) applied to the electrodes, and ion flux is formed in the inter-

electrode space. The ions so formed travel in the space between the electrodes at a

velocity determined by two components. The component v1 of the velocity of the ions,

which is directed along the lines of force, is determined by the strength of the electrical

field H and the mobility of the ions k (v1 = kH). The second component of the velocity of

the ions is the speed of the flow v.

The gaseous flow carries away from the inter-electrode space a certain quantity of

ions, the number of ions swept away increasing with a rise in the velocity of flow. This

causes diminution in the current in the measuring circuit, and at some value of the rate of

flow, when all the ions are swept away, current will cease altogether in the circuit. These

instruments may be constructed either with a plane or cylindrical ionization chamber. The

ionizer employed may be, e.g., radioactive polonium deposited on one of the electrodes.

For measuring the flow of substances which corrode the radioactive coating, a device is

used, in which a plate with the isotopes deposited on it is covered with a special

corrosion-proof protective film. This device will be corrosion proof, so that steady

29

radioactive emission will take place over a longer interval than in the case of a

radioactive isotope placed openly in the flow.

The accuracy of this method is comparatively poor, since, the ion flux depends

not only on the rate of flow, but also on the mobility of the ions and the recombination

rate constant, which to a great extent are governed by the state of the gaseous medium.

When measuring the velocity of a gas, the range of flight of the α particles depends on its

temperature, pressure and humidity. The devices may be used to measure pulsating flow

with an average velocity from 0 to 100m/min.

Among the disadvantages of continuous ionization of flow should be included the

direct relation of the readings of the measuring instrument to the magnitude of the supply

voltage and to the decay of the radioactive isotope.

5.2 IONIZATION ANEMOMETERS WITH A GLOW DISCHARGE

Ionization anemometer with a glow discharge, which are also called gas resistance

instruments, are usually made in the form of a probe on which platinum electrodes are

mounted. Under the action of a fairly large potential difference between the two platinum

electrodes, with a clearance of 0.1-0.2m, a glow discharge is obtained. The gaseous flow

whose rate is being measured affects the conditions under which the ionized particles

pass between the electrodes, which are detected as a variation in the resistance of the

discharge gap. The ion flux varies inversely as the rate of flow. If a device is used to

maintain the current between the electrodes constant, the potential difference between the

electrodes varies as the rate of flow. The sensitivity of the glow discharge anemometer is

governed by the blowing out of ions from the spark gap, the effect off the temperature

and pressure of the medium, the effect of gas cooling on the thermo-ionic properties of

the electrodes and mechanical deformation of the electrodes caused by pressure of the

flow or its cooling effect on the electrodes when heated by the discharge. In anemometer

with a fixed current passing through the ionization gap, the source of energy of the glow

discharge may be either d.c. or a.c. sources, which ensure a fixed value of the current

strength of the order of 10mA. A great disadvantage of the flow discharge anemometer

using a d.c. source is the blasting of the material of the cathode and a subsequent voltage

30

increase because of the increased gap. This fault is absent in the a.c. source either at

relatively low or at high frequencies.

The accuracy of the measurement depends to a large extent on the amount and

uniformity of the natural ionization of the flow being measured. The anemometer has low

inertia and high sensitivity. Disadvantages include the unsteadiness of the reading and the

blow out of the charge. The instrument we have been using are used to determine the

local velocity of the flow, so that when measuring the flow through a tube of given

section, the profile of the distribution of velocities must be taken in to account.

31

CHAPTER 6

MISCELLANEOUS

6.1 SYSTEM OF DIGITAL MEASUREMENT OF UNSTEADY FLOW USING

VARIOUS FLOW MARKERS

In several cases, unsteady velocity and flow must be measured in high speed

stream, in to which for a great many reasons measuring elements cannot be introduced,

for these purposes systems are employed which operate by forming measuring markers

directly in the stream being metered. The markers so produced constitute an integral part

of the flow, and experiences all its variations of velocity. The marker can be ionic,

radioactive, optical or thermal. The working principle is based on the flow markers and

on measuring the time of motion of the marker together with the flow between two points

on the tubing. When the flow s measured by means of such devices, the profile of the

distribution of velocities over the channel cross section must be taken care. In order to

measure the velocity, two types of the electronic circuits are employed and this gives

continuous measurement of the time interval during which the flow marker travels with

the stream from its point of formation to that of registration. These are open loop and

closed loop circuits. Different classifications are,

Flow markers and mediums:

Type of markers Method of marker

formation

Medium to which

methods apply

Ionic Spark ionization of flow

Gases at low

temperature and

humidity in the

absence of external

ionization of flow.

Ionic

Ionization of flow by

modulated radioactive

emission

Gases at low

temperature and

humidity in the

absence of external

ionization of flow.

32

Radioactive Introduction of the radio

active isotopes into flow

Gases and liquids

of any physical

properties.

Optical, opaque Introduction of opaque

substance into flow

Transparent liquid

and gases

Optical, radiating

Introduction into flow of

radiating substances of

given spectral composition

High temperature

gases

Thermal Periodic heating of part of

flow

Liquids not at high

temperature

Vortex

Creation of rotating vortex

in flow by periodic

switching of magnetic field

Conducting liquid

Table 1.1

6.2 INSTRUMENTS WHICH MEASURES FLOW BY VELOCITY PRESSURE

For measuring unsteady flow of liquids and gases, devices are used which

determine the flow by the velocity head. They include manometric and immersion

flowmeters.

Immersion flow meters are instruments whose sensitive element is a body which

detects the dynamic pressure of the current flowing about it, and which acts on a

measuring element. These instruments can be divided into systems of constant pressure

drop and systems in which velocity pressure is measured directly. The instruments of this

group used for measuring pulsating flow include low inertia devices in which the velocity

pressure set up by the current on the sensitive element is determined directly. Flow is

measured in these devices by the amount of movement of the body under action of

velocity pressure or by the amount of the corresponding force. Flow meter also devised to

measure flow by the velocity pressure, without introducing any immersed body into the

flow. They measure the amount of velocity pressure on the branch-tube wall as the flow

changes direction at right angle.

Flow meter of the manometric group include instruments in which the pulsating

flow is determined by pressure difference before and after a fixed perforated diaphragm,

33

at two points of Venturi tube inserted in the flow, or obtained by mean of a Pitot tube.

Various differential electrical pressure pick-ups are employed for measuring the pressure

difference: capacitive, inductive, and others.