Flow Meas Notes 0506 v04

8/8/2019 Flow Meas Notes 0506 v04

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flow meas notes 0506 v04.doc

The University of Edinburgh

School of Engineering and Electronics

Fluid Mechanics 3

Flow Measurement Methods

Tom Bruce1

February 2006

Summary

This short course aims to generate an awareness of the range of contemporary flow measurement

devices and methods available for application to both industrial and research flow problems in

Mechanical Engineering. Well-established mass and volume flow rate measuring devices are

reviewed, and the strengths and weaknesses of various meters and classes of meter are discussed.

Modern non-invasive methods - magnetic and ultrasonic - are also discussed.

Velocimetry (or anemometry) methods are then discussed, with a distinction drawn between

point measurement methods and 2-D methods. In the former category, Laser-Doppler

anemometry is described in detail. Under 2-D methods, Particle Image Velocimetry is described

in detail and a range of applications presented.

1Lecturer, School of Engineering and Electronics, University of Edinburgh, Kings Buildings, Edinburgh,

EH9 3JL, Scotland. Tel: +44 (0)131 650 8701, email: [email protected]


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flow meas notes 0506 v04.doc 2

1. Introduction

1.1 Rationale, Aims and Objectives

This short course was introduced in 93/94 to reflect a major research interest of the Fluid

Mechanics research group within the School.Fluid flow measurements are performed across the breadth of engineering, eg flows of oil, gas,

petrol, water, process chemicals, effluent are all necessarily and routinely measured. In the

research laboratory, advanced flow measurements are providing new insights into a wide range of

engineering flow problems in hydrodynamics (eg wave impact loading on coastal defences,

beach erosion) combustion (eg low NOx burners, IC engines), aerodynamics (eg wind turbine

optimisation and performance prediction) to list but a few.

The course aims to generate an awareness and understanding of the range of contemporary flow

measurement techniques available with the emphasis on devices and techniques with wide

application in Mechanical Engineering. It is the objective of the course that by its end, the

participant should be able

to describe the principles of operation of differential pressure, positive displacement, rotaryinferential, fluid oscillatory, electromagnetic and ultrasonic flow meters. to discuss advantages and disadvantages of the above meters for different applications. to design systems incorporating differential pressure meters. to describe the principle of operation of hot-wire anemometry. to describe the principles of Laser-Doppler Anemometry (LDA). to discuss the strengths, weaknesses and limitations of LDA. to design LDA systems to suit given experimental flow problems. to describe the principles of Particle Image Velocimetry (PIV). to discuss the strengths, weaknesses and limitations of PIV. to design PIV systems to suit given experimental flow problems.

1.2 Types of Measurement

Mass flow rate / volume flow rate

The most common industrial flow measurement requirement is a measure of the volume or mass

of fluid flowing per second through a given cross-section of a pipe. A wide range of devices exist

for these purposes reflecting the wide range of conditions which may prevail liquid flow, gas

flow, fluid temperature, pressure, viscosity, conductivity, the cleanliness of the fluid, the presence

of flow disturbance A selection of the most common and useful devices are presented in

Section 2.

Velocimetry (or Anemometry)

In many applications, particularly in the research laboratory, it is the actual local flow velocity

that is of interest rather than the total flow rate. Velocimetry methods fall into two broad

categories: those which measure the flow velocity at a single point and those which offer velocity

data over a 2-D plane or even a 3-D volume. Point measurement methods may provide very high-

resolution time histories of the velocity at a point. However, if a flow is neither steady nor

precisely repeatable or periodic, then single point methods cannot be used to build up a 2-D

velocity map in a point by point manner. 2-D methods are a recent addition to the armoury of

methods of flow measurement. Point measurement methods are described in Section 3. Section 4

is devoted to the description of 2-D methods.


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2. Pipe Flows: Measurement of Volume and Mass Flow Rates

2.1 Differential Pressure Flow Meters

Differential pressure flow meters all infer the flowrate from a pressure drop across a restriction in

the pipe. For many years, they were the only reliable methods available, and they remain populardespite the development of higher performance modern devices, mostly on account of

exceptionally well researched and documented standards.

The analysis of the flow through a restriction (Figure 2.1) begins with assuming straight, parallel

stream lines at cross sections 1 and 2, and the absence of energy losses along the streamline from

point 1 to point 2.

D1 Dt D2

2

1

Figure 2.1: A generalised restriction / differential pressure flow meter.

The objective is to measure the mass flow rate, &m . By continuity,

&m u A u A= =! !1 1 2 2

[2.1]

Bernoullis equation may now be applied to a streamline down the centre of the pipe from a point

1 well upstream of the restriction to point 2 in the vena contracta of the jet immediately

downstream of the restriction where the streamlines are parallel and the pressure across the duct

may therefore be taken to be uniform:

u p u p1

2

1 2

2

2

2 2+ = +

! ![2.2]

assuming that the duct is horizontal. Combining with [2.1] gives

& ( )mA

A

A

p p=

!

!

2

22

12

1 2

1

2" [2.3]

For a real flow through a restriction, the assumptions above do not hold completely. Further, we

cannot easily measure the cross-sectional area of the jet at the vena contracta at cross-section 2

where the streamlines are parallel. These errors in the idealised analysis are accounted for by

introducing a single, cover all correction factor, the discharge coefficient, C, such that

& ( )mCA

p pactualt

=

!

!

1

24 1 2

"

# where !"D

D

t

1

. [2.4]

Dt and At are the diameter and area of the throat of the restriction respectively.


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In summary, the principal advantages of the orifice plate are

it is simple and robust standards are well established and comprehensive plates are cheap may be used on gases, liquids and wet mixtures (egsteam)Its principal drawbacks are

low dynamic range: &max

m : &minm only 4:1 at best (see tutorial 1)

performance changes with plate damage or build up of dirt. affected by upstream swirl large head loss

Figure 2.4: Flow coefficients for orifice with corner taps.

Venturi Meter

The Venturi meter (after Giovanni Venturi, 17461822) is designed to cause minimal head loss

as the flow passes the restriction. Figure 2.5 shows a typical arrangement. Like the orifice plate,

the Venturi is dealt with by a British / ISO standard (BS EN ISO 5167-4)

For a Venturi, C= 0.99 for 105


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Figure 2.5: The Venturi meter (Furness, 1989)

The disadvantages compared to the orifice are

occupies longer length of pipe more expensive (manufacture and installation)Flow Nozzle

In many respects, the flow nozzle is a compromise between the compact orifice plate and the

efficient Venturi. There are two standardised designs - Figures 2.6 and 2.7. Flow nozzles have

proved particularly suited to high velocity applications, egsteam metering.

Figure 2.6: The ISA flow nozzle.(Furness, 1989).

Figure 2.7: The ASME long radius nozzle(Furness, 1989)

For the ASME nozzle (see BS EN ISO 5127-3)

C= !0 99956 53

0 5

0 5.

.

Re

.

.

" 2% for 0.25 < < 0.75 and 10

4


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Figure 2.8: K for ASME long radius flow nozzles.

Figure 2.9: Comparison of permanent head loss caused by restriction meters.

Advantages:

better head loss characteristics than orifice plate self-cleaningDrawbacks:

higher cost than orifice plate more sensitive to upstream disturbance than Venturi.2.2 Constant Pressure Flow Meters


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This class of meter measure the flow by monitoring the

position of a moving element which moves such that the

pressure drop across it remains constant. The most

common design is the rotameter - actually the name of

the first major supplier of this type of meter.

Figure 2.10 shows a rotameter. The small float is free to

move up and down a tube of taperedcross-section which

increases upwards. Thus the area available for the flow

increases as the float is forced upwards until the pressure

difference to keep the float at rest is restored.

The actual relationship between flowrate, tube and float

characteristics depends upon the fluid density and

viscosity. Ball-floats are common in gas flow

applications.

The main selling points of the rotameter are that it is

cheap and simple. It is however not a high performance

meter; accuracy is unlikely to be better than 2-3% unless

the meter is individually calibrated. A further potential

drawback is that it must be mounted vertically and can

only cope with uni-directional flow.

2.3 Positive Displacement (PD) Flow Meters

This class of meter measure the flow by dividing the fluid into packets, each of a precisely

known volume. The number of such packets counted in a known time gives a precise measure of

the volume flow rate. They are also known as PD Meters or simply Displacement Meters. Undersuitable conditions, this class of device offers the highest performance of any mechanical meter,

achieved through careful manufacture to high tolerances.

Liquid Displacement Meters

The Sliding Vane meter, Figure 2.11, is among the most accurate PD meters - uncertainties in the

volume flow rate Q may be less than 0.2%. The dynamic range is also quite high, typically

20:1. The liquid is channelled smoothly into the measuring crescent, minimising head losses.

The vanes and channel are carefully machined to give smooth operation with very low leakage.

The number of rotations is usually counted mechanically.

Another PD meter in widespread use is the Oval Gear meter - Figure 2.12. Again, close

tolerances ensure minimal leakage. It is unlikely that an oval gear meter can approach the

accuracy of the sliding vane meter. They may also introduce a much greaterpulsing into the

outlet stream, which may or may not be a concern.

Figure 2.10: TheRotameter

(Furness, 1989)


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Figure 2.11: A Sliding Vane PD meter. Figure 2.12: An Oval GearPD

meter.

Figure 2.13: TheNutating Disc PD meter.

A further variation on this theme is the Nutating Disc meter (Figure 2.13). The incoming fluid

fills the chamber, alternately above and below the disc, driving the disc in a rocking, circularmotion - nutation (cfspinning top ?). There is a greater area over which leakage could occur than

for sliding vane or oval gear meters, so the accuracy is not in general so good, although meter life

is potentially longer.

Gas Displacement Meters

By far the most common gas PD meter is the Diaphragm meter, used worldwide to meter

domestic gas consumption (Figure 2.15).


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Figure 2.15: The domestic gas meter.

The two chambers are filled and emptied alternatively, controlled by a sliding valve as shown.

The motion of the diaphragm is connected mechanically to a counting mechanism and readout.Mechanical reliability is outstanding, but the design is really suited only to low flow rate, low

pressure gas flows. Mass production means that these are inexpensive devices.

Rotary gas meters operate in a similar manner to

oval gear meters for liquid flows. This type of

device is shown schematically in Figure 2.16.

Performance after calibration for a particular

application can be very good, 0.5%.

Dynamic ranges may be as great as 20:1.

Pressure may be as high as 80 atmospheres, but

moderately high temperatures (>600C) may cause

problems.

General Characteristics and Performance

At lowest flow rates, the friction of the moving parts may become significant and lead to the

meter running too slowly. Leakage is also most likely to be significant at lowest flows, again

leading to under-reading.

This class of meter all rely on moving parts with close tolerances, so sustained operation over

long periods is not their strength. A further consequence of their close tolerances is that they may

be sensitive to temperature changes, and almost certainly will not operate well is the flow is not

clean, ie has particulate matter entrained at all.

Figure 2.16:

The rotary gas meter.


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In summary, advantages of this class of meter include

inherent high accuracy and repeatability good operational experience high reliability insensitive to upstream flow conditions can perform well with viscous fluids devices for liquid and gas flowsAmong the drawbacks are

high performance designs are expensive unsuitable for use with dirty flows pulsation introduced into out flow applicable to uni-directional flows only applicable over limited ranges of temperature and pressure. head loss increases with flow rate and viscosity2.4 Rotary Inferential Flow Meters

This class of meter are all basically small hydraulic turbines running at zero load. The rotary

element rotates at an angular velocity which is proportional to flow rate. This rotation speed is

monitored by mechanical means, or better, by magnetic or optical methods.

The basic axial turbine flow meter is shown in exploded view in Figure 2.17.

Figure 2.17: Construction of anAxial Turbine flow meter.

The axial flow turbine has a bladed rotor running on bearings. The assembly is mounted on acentral shaft, which is itself held by hangerassemblies up and downstream. A magnetic pick up

senses the turbine blades as they pass, and the pulse frequency is the measure the flow rate. The

total number of pulses recorded measures total volume passed.

The driving torque of the fluid is resisted by mechanical bearing friction, fluid drag and magnetic

drag, all of which effects vary with flow rate. The relation between flow rate and the rotation

speed may be written

Q K= .!

whereKis the meter factorwhich must be calibrated for a given meter.


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Figure 2.18: A performance curve for a turbine meter.

Figure 2.18 shows how K would typically vary with flow rate. The actual shape of such a

characteristic curve will depend upon a multitude of parameters, eg flow rate, viscosity, bearing

design, blade roughness, blade sharpness, inlet flow profile... and must be determined for every

meter individually. The best meters incorporate flow-straightening vanes upstream of the meter.

Simplification of the axial turbine meter is possible by using a mechanical pick up to drive a

counting system. Such meters are clearly less accurate, and so may be manufactured to lower

tolerances. The cost is lower, and they are also more suited to dirty flows.

The propeller meter is essentially an axial turbine

meter modified in some way to reduce the cost of

production and installation to be reduced. Figure

2.19 shows one particular design in which the

bearing assembly is moved outside the flow and the

bladed propeller is inclined to the flow.

Performance is clearly poorer than for an axial

turbine meter, but the cost is much less. 2%

linearity over the operating range would be typical.

General Advantages and Drawbacks

Strengths RI flow meters include

excellent short term repeatability can indicate flow rate and total flow directly excellent transient response relatively low head losses designs available for liquid and gas flows reliability is good in lubricating fluids wide flow ranges and linearity are possible use over wide temperature and pressure ranges is possibleDrawbacks include

necessity to calibrate to establish performance sensitive to inlet flow profile and swirl sensitive to changes in viscosity small designs have poor dynamic range sufficient back pressure required to prevent cavitation2.5 Fluid Oscillatory Flow Meters (or vortex meters)

Figure 2.19:

A propeller meter.


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The basis of fluid oscillatory meters is the process of vortex shedding from a bluff body exposed

to a flow. Early work in fluid mechanics established that, at Reynolds numbers above about 500,

continuous vortex shedding takes place, with the generation of a vortex street in the wake

downstream of the bluff body. Further, the vortex shedding pattern is largely independent of the

fluid density, the frequency of shedding depending only upon the shape of the body, the

viscosity, and the flow speed. For a given shape of body in a fluid of a given viscosity, the

Strouhal Number, S(Vincenz Strouhal, who first investigated ringing of wires in 1878!) is given

by;

Sf d

u=

.

wherefis the frequency of the vortex shedding, dis a characteristic dimension of the bluff body,

and u is the flow velocity.

Figure 2.20: Strouhal number vs. Reynolds number for circular and triangular section

bluff bodies..

Figure 2.20 shows how the Strouhal number varies with Reynolds number for vortex shedding

from bluff bodies of triangular and circular cross-sections. Clearly, for the circular body, S 0.2

over the range 500


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body. The shedding of a vortex from the lower side of the bluff body generates a lift on the body.

Similarly, shedding from the upper side causes the body to experience a lift force in the opposite

direction. Thus the shedding of a continuous street of vortices, alternately from upper and lower

surfaces induces a periodically varying lift force on the object which may be measured by a force

sensor in the body. Possible sensors include piezo-electric, thermal or mechanical devices.

The flowrate in a channel of diameterD, for a bluff body of characteristic dimension dis given

by

QD f

S d

kd

D= !

"#$

%&'

(

(

.

. .

4

41

4

where Sis the Strouhal number,fis the vortex shedding frequency and kis a shape factorfor the

bluff body (taking account of width and aspect ratio). Figure 2.22 illustrates a range of shapes

proffered by manufacturers of these flowmeters.

Relatively recent arrivals, these meters are now competing with DP meters in many areas, eg

water, steam and air. Linearity may be as good as 0.5%, and achieved dynamic ranges 15:1 (cf

Orifice meter, 4:1 at best).

Pros and Cons

No moving parts, crevices or seals - suitable for applications where high flow cleanliness isimportant (egsemiconductor manufacture)

May be used with liquids or gases. Insensitive to fluctuations in temperature, pressure or density. Digital output. Very sensitive to swirl or pulsation in incoming flow. Limited range of sizes available. No standards yet, and limited operational experience.2.6 Electromagnetic Flow Meters

Figure 2.23: Illustration of Faradays Law - a primitive generator.

When a conductor is moved through a magnetic field (Figure 2.23), a voltage is induced across

the conductor. This voltage (emf) e is proportional to the field strength B, the velocity u of the

conductor and the length lof the conductor:

uBe l=

This is the basis of the electromagnetic flowmeter, ormagmeter. For the magmeter, the conductor

is the flowing fluid, a field is applied across the pipe, and the induced voltage is therefore a

measure of the velocity with which the conductor is moving. Clearly, non-conducting fluids such


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as hydrocarbons cannot be metered by these means. For a pipe of diameterD,

e k B u D= . . .

where k is a constant of proportionality. Figure 2.24 illustrates the components of a magnetic

flowmeter. The output signals may be very small and quite noisy, but modern electronics can

cope cheaply and relatively easily with the necessary signal conditioning.

Figure 2.24: An electromagnetic flowmeter.

This family of meters appear in a remarkable range of sizes suitable for pipe bores from 3mm to

3m, with the result that they have found applications ranging from the metering of blood flow in

arteries to the metering of flows in large hydroelectric schemes. Typical applications include

water distribution and inorganic chemical process monitoring. They also work well with non-

Newtonian fluid flows such as liquid metal flows, sewage sludge...

Performance is good: 2-3% uncertainties are easily achieved; 0.5% achievable with the most

sophisticated designs.Pros and Cons

Obstructionless, so zero head loss. No moving parts. Wide size range. Insensitive to profile distortion or swirl. Insensitive to changes in pressure, viscosity, temperature and density. Linear output with flowrate. Bi-directional operation no problem. Dynamic range ~10:1. Works only with conducting fluids. Works with liquids only. Errors larger than good PD or RI devices. Electrodes may foul with some process liquids.


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2.7 Ultrasonic Time of Flight Flow Meters

The ultrasonic time of flight meter is in its relative infancy. It is probably the only type of

meter capable of high performance (eg1%) with bores of >3m. The basis of operation is the

measurement of the difference in the time of flight of sound waves propagated in opposite

directions, with and opposing the flow. Figure 2.25 illustrates the arrangement.

Figure 2.25: Time of flight ultrasonic flowmeter.

The sound propagates at velocity c through the liquid, which is moving at velocity u. Referring to

Figure 2.25, it can be seen that the transit times from transducer 1 to 2,21!

t , partially opposed by

the flow, and from transducer 2 to 1,12!

t , partially assisted by the flow, are given by

( )ucd

tcos

1.

sin21

!

="

and( )uc

dt

cos

1.

sin12

+=

!

The flow velocity u c, so the difference between the times of flight is

21221

cot2

c

duttt =!=""

Thus t is proportional to u. The time difference may be very small: eg for water flowing in a

100mm diameter pipe at 1ms-1

, the transit times are 100s, and t 100ns. Thus if a

performance to 1% is sought, timing will have to be good to 1ns - so even now, complex

electronics is required.

These meters have been used successfully on water flows, clean process fluid flows and on

natural gas pipelines. As with electromagnetic meters, ultrasonic meters cover the whole

spectrum of sizes from mm up to an 11m bore application on a hydro scheme.

Pros and Cons

Non-invasive - zero head loss. Gas or liquid flows possible. Bi-directional applications possible. Wide range of sizes. May simply be clamped to pipe. Sensitive to velocity profiles. Long term stability unproven. Not suitable for dirty flows.


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2.8 Doppler Ultrasonic Meters

The basis of operation of this class of flowmeter is that if sound of a given frequency is reflected

from a moving object, the frequency of the reflected sound is shifted by an amount proportional

to the speed of the moving object (cf passing ambulance, driving past players of bagpipes in

Glencoe laybys...). In these maters, ultrasound is transmitted into a flow which contains scatterers

travelling with the flow (egdirt particles, bubbles), and the scattered sound wave detected by a

receiver. The frequency shiftis then a measure of the flow speed. A possible arrangement is

shown in Figure 2.26.

Figure 2.26: The Doppler flowmeter

The Doppler shift frequency is given by

f f f f u

c D trans rec trans= ! " 2 cos#

where c is the sound speed in the fluid and is the angle between the transmission direction and

the pipe axis. (The theory of Doppler shifting is covered in more detail in Section 3).

Because the velocity profile across the pipe will not, in general, be uniform, a range of

frequencies will be received related to the velocity profile that exists in the pipe. Usually, the

peak frequency is sought - this smearing of received, shifted frequencies degrades the accuracy of

these devices.

Pros and Cons

Non-invasive - zero head loss. Bi-directional applications possible. Liquids or gases. Wide range of sizes. May simply be clamped to pipe. Works with dirty or aerated flows. Sensitive to velocity profiles. Flow must contain ultrasound scatterers. Long-term stability unproven. Low accuracy.


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2.9 Summary

Differential Pressure (DP) meters

Flow rate !p due to restriction in the flow.

Long term reliability. Gas and liquid. Extremely well documented standards. Moderate accuracy; 1% - 5% Low dynamic range; 3:1 - 4:1 Sensitive to temperature and pressure changes. Sensitive to upstream flow disturbances.Orifice Meter:

Simple and cheap construction. Large head loss. Error-prone in dirty flows.Venturi: Bulky and expensive. Very low head loss. Not susceptible to sedimentation in dirty flows.Flow Nozzle:

Compromise between Orifice and Venturi.

Positive Displacement (PD) meters

Fluid volume measured directly cumulative volumes measured. Short-term reliability. Clean flows only. Different designs for gases and liquids. Very accurate; better than 1% Moderate dynamic range, up to 10:1 No calibration required. Devices suited to limited ranges of pressures and temperatures. Not affected by upstream disturbances. Introduces pulsation into downstream flow.Rotary Inferential (RI) meters

A propeller rotates at a rate proportional to the flow rate. Remote detection possible. Short-term reliability. No standard possible - wide range of designs - calibration necessary. May be very accurate - expensive designs may do better than 1%. High dynamic range; up to 50:1 Designs for extremes of temperature and pressure. Sensitive to upstream disturbance.


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Fluid Oscillatory meters

Vortex shedding from a bluff body - flow rate frequency of shedding. Long-term reliability. Suitable for gas and liquid flows. Moderate dynamic range; 15:1 possible No moving parts or seals - suitable for applications where flow cleanliness is important. Insensitive to changes in temperature, pressure and density. Sensitive to upstream flow disturbance.Electromagnetic meters

Faradays Law: Voltage induced across conductor (conducting fluid) moving in magneticfield speed of conductor, ie flow rate induced voltage across duct.

Long-term reliability. Can be used only with conductive liquids - no gases. Moderate to good accuracy; better than 1% when installed correctly. Moderate dynamic range; 10:1 Application possible in extreme conditions of temperature, pressure and flow rate. Demanding applications in dirty flows, corrosive liquids, non-Newtonian liquids possible. Wide range of pipe sizes. Bi-directional flows OK. Non-invasive - zero head loss. Insensitive to upstream disturbances.Ultrasonic Time of Flight meters

Sound propagated with and against the flow. Difference in time of propagation flow rate. Long-term reliability. Clean gases and liquids. Very accurate. Large dynamic range. Bi-directional flows OK. Extremely large pipe sizes possible. Non-invasive - may be just clamped to pipe. Sensitive to pressure and temperature changes.Ultrasonic Doppler meters

Ultrasound scattered from moving scatterers in flow. Shift of frequency speed of scatterer. Non-invasive - zero head loss. Bi-directional applications possible. Liquids or gases. Wide range of sizes. May simply be clamped to pipe. Works with dirty or aerated flows. Sensitive to velocity profiles. Flow must contain ultrasound scatterers. Long-term stability unproven. Low accuracy.


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The basis of these devices is that the heat transfer away from a small heated wire, placed in a

fluid flow, is related to the local flow velocity at the wire. The wire itself is typically only 0.1mm

to 2mm long, and of diameterm, so very high spatial resolution is possible. Wires are usually

Tungsten, Platinum or Nickel. The wire is mounted on a thin arm inserted into the flow - the

method is therefore intrusive.

In most designs, the current through the wire is kept constant, and the change in resistance is the

measure of the local flow velocity. It is possible to record a time history of the flow velocity at a

particular point, and very high time resolutions -up to 50 kHz - are possible - though clearly such

rates require highly sophisticated electronics to track wire resistance changes. Two or three wires

may be arranged orthogonally to give an estimate of two or all three velocity components.

Hot wire anemometry is fundamentally a single point method, so finds most applications in flows

whose structure is well known a priori, and where the interest is in the time variation of velocity

at a point, eg in wind tunnel studies of vortex shedding, or in measurements of turbulent

intensities.

3.4 Laser Doppler Anemometry (LDA)

Introduction

The early development Laser Doppler Anemometry (LDA) dates back to the very end of the 60s,

when low power continuous wave (CW) lasers began to become available at costs which were

not astronomical. Since then it has developed into a sophisticated and robust tool suited both to

research laboratories and industrial applications. Developments in electronic and computer

processing have improved data gathering and reduction beyond measure, and optical

developments, notably in fibre-optics, have opened up many new application possibilities.

The basis of LDA is not complicated, but a short digression into some properties of light and of

laser beams will prove useful.

Laser Basics

All objects emit thermal radiation - a continuous range of frequencies with the peak wavelength

of the spectrum depending upon the temperature of the body. Hotter bodies emit a distribution of

radiation peaked at shorter wavelengths = higher energy radiation. The radiation from the Sun

peaks at about 500 nm wavelength - green light - corresponding to a temperature of around 6000

K. Photons from thermal sources are emitted over a wide range of wavelengths and in all

directions.

The radiation from a laser (Light Amplification by Stimulated Emission ofRadiation) is quite

different in character. Photons emerge with identical energies, ie identical wavelengths, identical

phases, and all travelling in the same direction.


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E = 0

N

NE =!

1

2

thermal source laser source

Figure 3.3: Thermal and Laser light sources.

Figure 3.3 illustrates the fundamental difference between thermal and laser radiation. Quantum

mechanics dictates that electrons orbiting the nuclei of atoms cannot have any arbitrary energy,

but must be in one of a number of discrete energy states. If the electron absorbs a quantum of

radiation - just the right amount of energy - then it moves up to the next discrete energy level.

Equally, it may emit radiation, and in doing so, lose energy and fall back one or more levels. The

energy associated with a photon of light of frequency fis given by

E h f = .

where h is Plancks constant: h = 6.63 x 10-34

Js.

In a collection of atoms in a normal state, electrons are continuously jumping between a large

number of different states, separated by a range of different energies - they continuously absorb

and emit over a range of energies and therefore frequencies. In a laser, it is arranged by some

means that a large number of atoms have a higher proportion of electrons in a particular, raised

state - apopulation inversion. There is a tendency for these electrons to drop back to their lower

energy state, and in doing so, they all emit photons of exactly the same energy corresponding to

the energy difference between the levels.

Lasers have a unique ability to form light beams with high energy concentrations. However, the

quantum nature of photons means that a small divergence of the beam is always present. The

beam cannot be focused to a point, but only to a beam waistof thickness 2wo , Figure 3.4.

!

2w0

lens

Figure 3.4: Laser beam waist.The beam waist thickness is given by

!"

#=

.w0

Thus efforts to bring the beam to sharper focus result in increased divergence.

Example: = 514nm, w0 = 12mm, = 0.014 mrad w = 25mm at 1000m from waist.

= 514nm, w0 = 1mm, = 0.164 mrad w = 25mm at 6m from waist.


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A receiver moving towards a stationary source of a sound wave will encounter the wave crests at

a greater frequency than if (s)he were to be standing still. Similarly, if (s)he were to be moving

away from the source of the waves, the crests would arrive at the receiver at an apparently lower

frequency. The same effect applies to light.

s !

uno. of waves per second = c/"

Figure 3.6: The Doppler effect - stationary source, moving receiver.

When the receiverR is stationary, the number of waves received in a time tis

N f t c t0

= =.!

However, if the receiver is moving with a velocity u at an angle to the direction of the wave

propagation as shown in the Figure, then the catch up speed of the waves is reduced, and the

number of waves received in a time tis now

( )N ct

1 = ! component of u in direction of propagation"

( )! = " N c t 1

1

#u s.$

where $s is a unit vector in the direction of the wave propagation. Thus the frequencies forstationary and moving observers, f0 and f1 are given by the number of waves received per unit

time, ie

fc

0=

!, ( )f c

1

1= !

"u s.$

and so thefrequency shiftis

! f f f = " = =0 1

1

#

$

#u s

u

.$cos

where is the angle between the direction of the wave propagation and the receiver.

c/


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The Differential Doppler Method

laser!/2

beam splitter

photodetec

u

Figure 3.7: Set up for differential Doppler method.

The optical arrangement is sketched in Figure 3.7. A laser beam passes into a beam-splitter from

which two beams emerge. Via an arrangement of mirrors, these two beams are made to converge

at an angle , crossing at the measurement point. (The purpose of the Bragg Cellis discussed

later in the Section). The light from these beams is then scattered by any particle moving with the

flow -flow seeding- and the scattered light picked up by a detector, ega photomultiplier and lenssystem. Only light scattered in the direction of the detector is recorded - the main, unscattered

beams pass through the system.

We can consider the scattering particle as first a receiver of the incoming laser light, and then a

(re)transmitter of the light to the detector. The first process - transmittal of light from a stationary

source to the moving particle - is just the situation shown in Figure 3.6, with

= 90o

- /2. Therefore the particle receives light at a shifted frequency. The light from the lower

beam will be shifted to a frequency

f f1 0

2= !

u sin"

#

since cos = cos (90o - /2) = sin /2 . The shifted frequency is lower because a component of

the particles velocity is away from the source.

The light from the upper beam, when received by the particle will also be shifted, but in this case

to a higher frequency since there is a component of the particles velocity towards the source.

The shifted frequency is therefore

f f2 0

2= +

u sin!

"

The particle scatters the light that is incident upon it: the scattered light is made up of two

frequencies, f1 and f2 . The particles velocity has no component in the direction of the receiver,

so the light entering the detector is at the same frequencies at which it was scattered from the

particle,f1 and f2 .

The final stage is to establish the shift in frequency in order to establish the particles velocity.

When two waveforms of similar frequencies are combined, a beatingeffect is seen (demo with

overlaying transparencies with lines drawn at spacings differing by 5%). The beat frequency is

simply the difference between the component frequencies

f f f beat

= ! =2 1

22 u sin "

#


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!/2

"

fringe spacing#

u

Figure 3.8: Fringe pattern formed at beam intersection.

A more visual but less rigorous way to view the set up is to think in terms of the fringe pattern

formed by the intersecting beams, sketched in Figure 3.8. A particle moving through this volume

will be illuminated at intervals given by the time taken to pass from one bright fringe to the

next. A particle travelling at speed u through a fringe pattern with spacing will produce flashes

of light at a frequency given by

f

u

u= = =

1 1

! " "

but we know

!"

#=

2 2sin

so we arrive at the same result for the frequency of the light received at the detector:

fu

=

2

2

!

"sin

This visual alternative formulation is useful in visualising the effect offrequency shifting,

discussed below.

Practical Implementation

LDA systems are generally bought off the shelf. Dantec (based in Copenhagen) and TSI Inc.

(USA) are the market leaders. The beam splitting and convergence optics are generally packaged

into one black box, the detector plus its optics into another, and the signal processing carried out

by sophisticated electronics in a third black box, usually linked to a PC or workstation.

The seeding of the flow for LDA is not usually a problem: only in the cleanest conditions in

water flow experiments are there no suitable scatterers present. In gas flows, corn oil droplets

have been used to good effect.

Most systems are laid out as sketched in Figure 3.8 - a forward scatterarrangement. This requiresoptical access to both sides of the test volume. An alternative is to work in back scattermode,

detecting light scattered back in the direction of the incoming beams. This set up has the

disadvantage that the much more light is scattered forward than back, so for a given laser power,

there is much less light scattered to the detector. However, optical access is required from only

one side, making it well suited to use with fibre optics - two fibres are used - one to carry the

laser light to the measurement volume, and the second to carry the back-scattered light to a

detector. A tiny optical head on the end of the fibre does the beam splitting and alignment.

Multi-Component LDA


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A second pair of laser beams of different wavelength can be arranged to intersect at the

measurement volume at right angles to the first pair, and therefore give a measurement of a

second component of the flow velocity at that point. Similarly, all three velocity components can

be measured with three pairs of intersecting beams which are mutually perpendicular.

Two component fibre LDA systems based upon an Argon ion laser make use of the two principal

wavelengths of laser light - the beam is split into a green beam and a blue beam, and one used tomeasure each velocity component. The back scattered light from both components is carried

down the one fibre before being separated again by the detector optics.

Frequency Shifting - the Bragg Cell

In the form described above, it is clear that LDA cannot distinguish the direction or sense of the

particles motion and therefore the fluid velocity.Frequency shiftingis a trick to overcome this

limitation. Basically, the fringe pattern is given its own velocity, and if this velocity is larger than

the largest velocity that the flow might have, then particles will always appear to be crossing the

fringes in the same direction.

Put another way, if the fringes are moving back at a speed greater than the particles backwardmotion, then the particle will overtake the fringes, ie will be going forwards relative to the fringe

pattern. A particle which was going forwards anyway will appear to be going forwards even more

quickly, relative to the moving fringe pattern.

This apparent shiftedvelocity is then measured, and the known shift subtracted to give the true

flow velocity.

The device which supplies this shift is called aBragg Cell. The new measured frequency is

! = + f f f beat beat shift

so the apparent measured velocity is

! =!

u f"#

. beat

22.sin

The actual velocity is recovered by subtracting the shift velocity, ushift , from the measured,

shifted velocity, u

( )u u u f f = ! " = ! "shift beat shift

#

$2 2.sin


28/35


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As will be understood by the end of this Section, consideration of the method of analysis of a

flow record to give a velocity map dictates much in the selection of the parameters in the

experimental set-up for the recording of the flow records. Thus the analysis methods are

discussed first - cross-correlation in Section 4.4, and autocorrelation in Section 4.5. This is the

reverse of the historical development of the method, but autocorrelation is perhaps more easily

explained once the principle of cross-correlation analysis is understood.

General objectives for any analysis system can be laid down quite simply. We have a flow

record or successive records containing velocity information over a large field. We wish to be

able to define a grid of points over this area, and at each point, interrogate a small area of the

photograph to establish the most common (most correlated) particle image separation.

Additionally, we require that this process be highly accurate, fast (ie hours are not taken to

analyse one flow record), and, apart from initialising a run, completely automated.

4.4 Cross-Correlation PIV Analysis

The basis for cross-correlation analysis are two PIV flow records taken ofexactly the same fieldin a flow separated by a (usually short) time interval.

Figure 4.1: Typical interrogation areas from successive flow records.

Figure 4.1 shows typical interrogation areas from two successive records - selected small cells

within base and cross images, in this case of 32 x 32 pixels. A number of approaches may be

taken to finding the distance moved by the tracers between frames. For example, if the number

density of particle images is low, one approach might be to carry out some image processing to

establish the positions of all images and in some way try to pair the images. With a higher

density of images a method based on finding the cross-correlation of the images within the

interrogation areas is a very efficient and robust approach.

The cross-correlation function C(x, y) is arrived at by comparing the base and cross images

given by intensity distributionsIbase(x, y) and Icross(x, y). In physical terms, the function is movingthe cross image relative to the base image, seeking the best match between the intensity patterns.

C x y I x y I x x y y dxdybaseIA

cross( , ) ( , ). ( , )! ! ! != " "##

The cross-correlation function in Figure 4.2 is a typical result of the cross-correlation of partner

interrogation areas in base and cross images.


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Figure 4.2: The cross-correlation function arising from IAs shown in Figure 4.1, above.

The clearly visible peak in the function indicates the offset in x andybetween the base and cross

images at which the best correlation between the images was found. Once the software has

calculated the cross-correlation function, it locates this peak and records the x, y values.Knowledge of the optical magnification and the time interval between images allows x, y

subsequently to be scaled to give a velocity vector relating to the location of the interrogation

area.

4.5 Illumination Systems for PIV

Illumination for must usually also define a 2-d plane or sheet through the flow. The source of

the light is typically a pulsed laser. Lasers are used because the low divergence of their beams

allows thin sheets to be formed, and because the energy density in the beam is very high, egwe

may need enough energy to image a 50 m tracer particle with a camera 1 m away within a few

microseconds.

PIV illumination is usually achieved either by an expanded beam method (Figure 4.3). The

pulsing of the illumination may be achieved by employing a pulsed laser or (more historically)

combining a high speed shutter with a continuous wave (CW) laser.

Figure 4.3: Expanded beam / pulsed laser illumination for PIV.


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The width of the light sheet generated by either method described above will be a compromise:

If the plane is too thick, then the measurement zone is moving away from being a 2-d sectionthrough the flow.

If the plane is too thin, then even very small out-of-plane motion may make it unlikely that aparticle stays in the illuminated plane for long enough to record an image pair.

A practical criterion is that the cross plane velocity vz should be small enough such that the cross

plane distance travelled between illuminations is less than 1/4 of the thickness of the sheet. This

is known as the out-of-plane criterion.

4.6 PIV Image Acquisition

4.6.1 Introduction

The process of acquiring good PIV flow records involves two major stages. The first is selecting

appropriate hardware for the application eg, illumination, seeding and camera, and the second is

using this hardware to best effect. This Section addresses both of these stages.

4.6.2 Hardware

The hardware considerations may be divided into three broad (and somewhat interdependent)

areas: illumination, flow seeding and camera. The illumination system preferred for the

application of PIV to hydrodynamics has been discussed (Section 4.5).

Seeding

The selection of a suitable flow seeding is very important. The seeding used in hydrodynamics

experiments at Edinburgh is conifer pollen. This meets the most important criteria for a suitable

seeding: once soaked with water, it is almost exactly neutrally buoyant, quite reflective at thewavelength of the laser, and small enough to follow the flows studied (typical particle diameters

are 70m). Importantly, it is also quite inexpensive - the cost to seed a flume containing six

tonnes of water is 2 - 5.

For air flows of high and low speeds, hollow glass spheres have proved a very successful

seeding. Diameters are 10 - 20 m. Such small particles have a tiny terminal velocity in air, and

so do not rapidly fall to Earth under gravity.

Generally now, a wide range (sizes and densities) of synthetic seed particles are available from

PIV equipment suppliers.

Camera and Lens (Still Image Video or Conventional Photography)

The choice of the camera and lens is also important. The lens should be a flat-field lens in order

that distortions of the image plane are minimised. Choosing a lens of longer focal length reduces

the apparent effect of any out-of-plane motions of particles in the field, but increases the

difficulty of achieving a really sharp focus and makes the process more sensitive to vibrations.

In the early years of Edinburgh PIV, a Hasselblad 500 EL/M camera was the mainstay of PIV

measurements in hydrodynamics. In the early 90s, it was joined by a Kodak MegaPlus still

image video camera (what would now be called simply a digital camera). It was a

monochrome camera with 4 Mpixels (2048 x 2048 pixels resolution). It cost over 20k - compare

this with the cost of a colour 4 Mpixel digital camera today!


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Over the last ten years, PIV acquisition has become dominated by specialist PIV cross-correlation

cameras. These cameras enable pairs of images to be acquired at (at least) conventional video

frame rates, ie 25 base/cross image pairs taken per second. These cameras are built to interface

easily to the trigger for a pulsed laser so that they synchronise easily with the flow illumination.

Standard resolutions are now very good - typically 4Mpixels (2k 2k pixels) with cameras

offering up to 10 Mpixels beginning to become available (at a price!).

Very high speed digital cameras have also been used successfully for PIV. Frame rates of up to

30kHz have been used, though at some cost in spatial resolution.

4.6.3 Recording the Flow Records

After the selection of the hardware, the important issues remaining are the choice of camera

position, achieving the correct seeding density, optimising the focus and optimising the exposure

parameters to give good, high contrast flow images

Seeding

The optimum seeding density is determined by considering the subsequent analysis of the

photograph. In typical applications in the wave flumes at Edinburgh, the local flow velocity at a

point on the flow record is averaged over a 32 x 32 pixel interrogation area (IA). Thus the

seeding density should be high enough that there will always be several (5 to 15) tracer particles

in each IA on the flow record. Experience is perhaps the best guide to getting an optimum level

of seeding; once good results have been obtained, the successful level of seeding can be repeated.

The size of the images of the seeding should also fall within reasonable, intuitive bounds. Seeing

images which fill a substantial part of the IA would be too large to offer a good correlation

between base and cross images. Similarly, if the image is so small as to be less than one pixel in

size, then the analysis will only ever be able to see particle image movements of whole units of

pixels (ie 1 pixel; 2 pixels; 3 pixels etc) whereas the shift (base to cross) of an image spread overa few pixels can be measured to sub-pixel accuracy.

The seeding should also be of a size that forms images of the desired size. The size of a particle

image on the recording medium, di is determined by three factors: the particle diameter, dp , the

magnification (recorded:actual size) M, and the lens aperture used. defined by its f-number3, f#

:

d M d d i p spot = +2 2 2

where dspot is the diffraction-limited image size - the smallest image that can be recorded by a

lens working at the given f-number, f# ,

( )d M fspot = +2 44 1. #!

Thus for larger magnifications, larger particles and larger apertures (smaller f-numbers), the size

of the diffraction-limited image becomes less significant, and the size of the recorded image

approaches that which would be expected on the basis of the magnification alone.

Illumination Interval

Like the optimisation of seeding density, the choice of illumination interval is dictated by

consideration of the subsequent analysis. The interval should be set such that the largest velocity

3

The working diameter or aperture of the lens is usually given in terms of the lens focal length, f, eganaperture of f/8 implies that the aperture is 1/8

thof the focal length. In this case the f-number f# = 8.


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in the flow gives a particle image separation on the flow record(s) which is the largest suitable for

the analysis system. Typically, if both particle images in a pair are to stand a good chance of

falling within a single interrogation area, then the criterion

max. image separation < 1/3 dimension of interrogation area

serves as a guide. Normally an accurate estimate of the largest velocities can be made, but it may

be necessary to try different intervals in order to optimise the choice.

Focus

Achieving a really sharp focus is extremely important if good PIV photographs are to be

obtained, and can be quite difficult, especially when a large lens aperture or long focal length lens

are being used. Tests in which the focus is varied can provide a route to optimisation.

Photographic Magnification

The magnification from the measurement zone to the image depends upon the focal length of the

lens and the distance from the camera to the measurement zone. Its selection is in generalanother compromise. It is often desirable to measure as large a region as possible, but it is again

important to consider the analysis phase. The velocities are calculated from averaging particle

image displacements over a small (eg32 x 32 pixel) interrogation region on the flow record. The

implicit assumption is that particle image displacements over this small region are uniform: if

there is a strong displacement gradient present, errors are introduced and the resulting data point

may be at best inaccurate and at worst, spurious. Therefore the size of the area imaged onto the

flow record is typically limited to that which will result in displacement gradients of less than

5% over any interrogation area, limiting systematic error from this source to less than 1%.

Exposure

In general, tests trying various settings of camera aperture and laser power is required for a newapplication. The quality of the resulting flow records may then be assessed under analysis and

the best settings finalised.

If there is scope for choosing an aperture setting, it should be remembered that the largest

apertures (smallest f numbers) give the poorest depth of field, so focusing is more difficult.

However, if the particle image size is diffraction limited, the smaller apertures (larger

f numbers) will result in larger particle images. Usingf/4 orf/5.6} is usually a good compromise.

Camera Positioning and Alignment

The geometric relation between the measurement plane in the flow and the PIV image plane in

the camera may be generally specified by six coordinates - three positional and three angular(Figure 4.7). The selection of these coordinates corresponds to the positioning and alignment of

the camera.

The position of the camera in x1 and x2 (Figure 4.4) is determined by the characteristics of the

measurement zone. In the simplest cases, the camera field of view will be centred on the centre

of the measurement zone. However, if there is some feature in the measurement zone which

partially obstructs the view such as a test object or a free surface, then the selection of the camera

position may demand some care if as much as possible of the region of interest is to be imaged.

The x3 position, the distance from camera to measurement plane defines the magnification. The

magnification is chosen as a compromise between the size of the measurement area and the

resolution of the velocity map.


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Figure 4.4: Camera alignment

Aligning the camera fixes the rotational degrees of freedom, 1 , 2 and 3 . Thepitch 1 andyaw 2 axes must be set so that the camera image plane is parallel to the measurement plane. If

this is not achieved precisely, not only will a systematic distortion of the image plane result, but

also it may prove impossible to maintain a sharp focus over the whole of the plane. The rollaxis

3 needs to be set if the object and image planes are not to be rotated relative to one another.

Vibration

The sharpness of the particle images recorded on the film is an important factor in the

signal-to-noise ratio of the resulting data. Therefore it is important to consider possible sources of

mechanical vibration in the recording system and how they might be minimised. Two possible

sources can, in general, be identified:1. the mounting of the camera2. the internal workings of the cameraIf the camera is mounted on a good quality tripod, itself standing on a solid lab floor, there should

be little or no problem from this quarter. However, if the camera is mounted otherwise, egupon a

moving stage in an image shifting system, or if the tripod rests on a floor which vibrates for any

reason, related to the experiment or not, then steps may have to be taken to minimise or at least

quantify the effect of vibration.

Registration

In general, it is desirable or necessary to be able to relate a position on the flow image to anabsolute position in the real measurement plane. This requires some form of registration mark,

visible on the photograph, whose actual real world coordinates are known. If there is an object

visible in the flow, ega cylinder, then this may present few problems. Otherwise, the use of some

additional marker in the measurement plane, or even in another known plane, will be necessary.

Calibration

Finally, provision should be made to measure the photographic magnification from the laboratory

frame to the image frame. Again, it may be possible to measure this directly from the image of

an object of known size in the measurement zone. However, in most cases, it may be preferable

to take a dedicated calibration photograph before the start of a run of experiments, egof an object

or grid of accurately known dimensions.


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4.6.4 Errors in PIV Measurement

A summary of the errors inherent in the acquisition phase of autocorrelation PIV is presented in

Skyner [1992], from which the table below is reproduced.

factor typical random error systematic error

illumination interval 0.2 %

photographic magnification 0.3 %

photographic distortion 0.0 - 0.3 %

illumination plane flatness 0.0 - 0.3 %

illumination plane thickness 0.1 %

seeding not following flow 0.0 - 1.0 %

combined errors 0.4 % 1.0 - 1.6 %

4.7 Applications

A random selection of applications with which the Edinburgh group has been associated...

Combustion

Flow in power station coal burners (live flame tests) Flow of pulverised coal into power station combustion chamberCoastal Engineering

Beach erosion /accretion Wave impacts on breakwaters Flow around seabed pipelinesOffshore Engineering

Wave enhancement due to structure blockage Oceanic internal waves Deep water breaking wavesWind Energy

Measurement of wake behind a wind turbineHeat Transfer

Recirculation in horizontal kettle reboilersFire Safety

Flow of fumes and smoke out of burning buildings

Documents

Flow Meas Notes 0506 v04