Fluid Mechanics 3 Flow Measurement Methods

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The University of Edinburgh

School of Engineering and Electronics




Fluid Mechanics 3

Flow Measurement Methods


Tom Bruce
1

February 2006





Summary


This short course aims to generate an awareness of the range of contemporary flow measurement
devices an
d 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
-
Do
ppler
anemometry is described in detail. Under 2
-
D methods, Particle Image Velocimetry is described
in detail and a range of applications presented.




1
Lecturer, School of Engineering and Electronics, University of Edinburgh, King’s Bui
ldings, Edinburgh,
EH9 3JL, Scotland. Tel: +44 (0)131 650 8701, email: Tom.Bruce@ed.ac.uk


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1. Introduction


1.1 Rationale, Aims and Objectives


This short course was introduced in 93/94 to refle
ct 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 routine
ly 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 en
gines), 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, rotary
inferential, flu
id 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 Velocim
etry (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 resear
ch 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 bui
ld 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 F
lows: 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 ava
ilable, and they remain popular
despite 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 str
aight, parallel
stream lines at cross sections 1 and 2, and the absence of energy losses along the streamline from
point 1 to point 2.



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


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









[2.1]

Bernoulli’s 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
ve
na 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:









[2.2]

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








[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




where

.

[2.4]

D
t
and A
t
are the
diameter and area of the
throat
of the restriction respectively.

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The discharge coefficient is empirically determined. If the restriction conforms to a standard
eg

BS1042, then C may be found from the standard (see below). The main influences on C are the
g
eometry of the restriction (
β
), the location of the pressure taps, and the Reynolds number
Re
.
Note that
Re
is based upon the pipe diameter,
not
that of the restriction.


For a given restriction,









[2.5]

where
is the value of C at highest Re, and
b
,
n
are constants, empirically determined. As
Re

increases,
C
becomes less sensitive to
Re

-
the flow is increasingly turbulent and thus the velocity
profile becomes flatter and flatter.


The three main restriction
devices are the
orifice plate, Venturi meter
and
flow nozzle
.



Orifice Plate








Figure 2.2. Tapping arrangements

(Furness, 1989).

Figure 2.3. Orifice profile

(Furness, 1989)


Orifice plates vary in the profile of the orifice and the location of
the pressure taps. Figure 2.2
shows the tapping arrangements covered by BS EN ISO 5167: flange taps, pipe taps (both
D
and
D
/2) or corner taps. Figure 2.3 shows a typical orifice, with a sharp, square edge on the
upstream

side. Installation of the plate ba
ck
-
to
-
front can introduce an error

20% in
!


Older standards (BS 1042) give
C
as a (relatively) simple function of pipe Reynolds number
Re

and diameter ratio
β
,
eg
for corner taps,





0.6% for 0.2 <
β
< 0.75 an
d 10
4
<
Re
< 10
7
.

The graph in Figure 2.4 shows this relation in terms of the
flow coefficient,
.

The current standard BS EN ISO 5167
-
2 gives more accurate (but much longer) equations for
C.


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In summary, the principal advantages of t
he 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 (
eg
steam)


Its principal drawbacks are



low dynamic range:
:
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, 1746

1822) 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 10
5
<
Re
< 10
7
is a useful approximation. BS EN ISO 5167
-
4 gives
more accurate Figures for particular details of an installation (ranges of
Re
,
β

etc
).


The main advantages of the Venturi over the orifice plate are



low head loss



less affected by upstr
eam flow disturbance



good performance at higher
β



even more robust



self
-
cleaning



less affected by erosion



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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 (manuf
acture 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,
eg
steam 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)




2% for 0.25 <
β
< 0.7
5 and 10
4
<
Re
< 10
7
.

Figure 2.8 shows this relation graphically. Figure 2.9 shows a comparison of permanent
ie
unrecovered head losses caused by the three designs of restriction flow meter that have been
considered.


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Figure 2.8: K for ASME long radiu
s flow nozzles.



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


Advantages:



better head loss characteristics than orifice plate



self
-
cleaning


Drawbacks:



higher cost than orifice plate



more sensitive to upstream disturban
ce 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
tapered
cross
-
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. Ba
ll
-
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
kno
wn 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
. Under
suitable 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 d
ynamic 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 al
so introduce a much greater
pulsing
into the
outlet stream, which may or may not be a concern.





Figure 2.10: The
Rotameter

(Furness, 1989)




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Figure 2.11: A
Sliding Vane
PD meter.

Figure 2.12: An
Oval Gear
PD
meter.



Figure 2.13: The
Nutating Disc
PD meter.


A further variation on this t
heme 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, circular
motion
-
nutation (
cf
spinning 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 con
sumption (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.
Me
chanical 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 mann
er 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 (>60
0
C) 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 al
so 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 tole
rances 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 flows


Among 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 viscosity


2.4 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 ba
sic axial turbine flow meter is shown in exploded view in Figure 2.17.



Figure 2.17: Construction of an
Axial Turbine
flow meter.


The axial flow turbine has a bladed rotor running on bearings. The assembly is mounted on a
central shaft, which is itsel
f held by
hanger
assemblies 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 flu
id 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


where
K
is the
meter factor
which must be cali
brated 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, visc
osity, 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 po
ssible 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 prope
ller 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 possible

Drawbacks 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 p
ressure required to prevent cavitation

2.5 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 s
hedding 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;


where
f
is the frequency of the vortex shedding,
d
is 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 <
Re
< 2x10
5
. The principle of the vortex shedding m
eter is to measure this
shedding frequency, so such a meter has a potential to measure flows over an enormous dynamic
range,

400:1. A similar situation pertains for the triangular body, for which
S


0.15 over

200
<
Re
< 10
5
.




Figure 2.21: The vorte
x shedding flowmeter

Figure 2.22: Bluff body shapes...

Figure 2.21 illustrates the principle of a flowmeter based upon vortex shedding from a bluff

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body. The shedding of a vortex from the lower side of the bluff body generates a lift on the body.
Similarl
y, 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 wh
ich 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 diameter
D
, for a bluff body of “characteristic dimension”
d
is given
by




where
S
is the Strouhal number,
f
is the vortex shedding frequency and
k
is a
shape factor
for 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
-
sui
table for applications where high flow cleanliness is
important (
eg
semiconductor 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 inco
ming flow.



Limited range of sizes available.



No standards yet, and limited operational experience.


2.6 Electromagnetic Flow Meters



Figure 2.23: Illustration of Faraday’s Law
-
a primitive generator.


When a conductor is moved through a magnetic fiel
d (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


of the conductor:


This is the basis of
the electromagnetic flowmeter, or
magmeter
. 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
-
conductin
g fluids such

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as hydrocarbons cannot be metered by these means. For a pipe of diameter
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 a
nd 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 3
mm 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 monitori
ng. 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 he
ad 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 onl
y 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 (
eg
1%) 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. F
igure 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 trans
ducer 1 to 2,
, partially opposed by
the flow, and from transducer 2 to 1,
, partially assisted by the flow, are given by


and


The flow velocity
u

«
c
,
so the difference
between the times of flight is



Thus
Δ
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

100

s, and
Δ
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 pi
pe.



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 f
requency 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 sca
tterers
travelling with the flow (
eg
dirt particles, bubbles), and the scattered sound wave detected by a
receiver. The
frequency shift
is then a measure of the flow speed. A possible arrangement is
shown in Figure 2.26.



Figure 2.26: The Doppler flowme
ter

The Doppler shift frequency is given by


where
c
is the sound speed in the fluid and
θ
is the angle between the transmission direction and
the pipe axis. (The theory of Doppler shifting is covered in more detail in Section 3).

Bec
ause 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 frequenc
ies 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


due to restriction in the flow.



Long term reliability.



Gas and liquid.



Extr
emely 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 m
easured.



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 affec
ted 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 d
esigns
-
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.



flow

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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 t
o changes in temperature, pressure and density.



Sensitive to upstream flow disturbance.


Electromagnetic meters




Faraday’s Law: Voltage induced across conductor (conducting fluid) moving in magnetic
field

speed of conductor,
ie
flow rate

induced voltag
e 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” m
eters




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 applicati
ons 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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3. Anemometry / Ve
locimetry
-
Point Measurement Methods


3.1 Introduction


Section 2 has reviewed a wide range of devices for measuring the total flow rate in pipes. In this
Section, we concentrate on methods for measuring the actual fluid flow velocity
at a single point

i
n the flow. Methods suitable for velocimetry over a two
-
dimensional field of points are held
back until Section 4.


Whereas most applications of the flowmeters of Section 2 are clearly in the industrial arena, the
focus tends to shift to the engineering re
search laboratory as attention is turned to
anemometry

(UK term) or
velocimetry
(US
-
imported term).


3.2 Pitot
-
Static Tubes


The humblest of devices for measuring flow velocity directly is the Pitot
-
static tube. Figure 3.1
shows the principle of operati
on.


Figure 3.1: Principle of Pitot
-
Static tube.


We apply Bernoulli’s equation to a streamline which meets the tip of the tube. The flow is steady,
so there is no flow in the tube. Thus there is a stagnation point, so
u
2
= 0. Th
e pressure difference
p
2

-

p
1
is the difference between the
impact
or
stagnation pressure
at the tip of the tube,
p
2
, and
the
static pressure
in the body of the fluid,
p
1
. From Bernoulli,




Figure 3.2: Pitot
-
Static tube; detail.


The most common practical design based upon the above is shown in Figure 3.2. A pair of
concentric tubes is used: the inner tube measured the impact pressure, the outer tube has a
number of tiny tappings, flush with the tube, to measure the static pressu
re.


Accuracy is crude, but these devices do provide a very simple and fast estimate of flow velocity.
They are clearly not well suited to dirty flows in which their tappings may become blocked.


3.3 Hot
-
Wire Anemometry


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The basis of these devices is tha
t 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 diameter


m, so very high spatial resolution is possible. Wires are u
sually
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 flo
w 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 change
s. 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 wh
ere 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 a
nd 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 LD
A 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 t
he 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 (
L
ight
A
mplification by
S
timulated
E
mission of
R
adiation) 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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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
f
is given by


where
h
is Planck’s 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. I
n 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
-
a
population inversion
. There is a tendency for these electrons to drop back to their lower
energy state, and in doin
g 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 d
ivergence of the beam is always present. The
beam cannot be focused to a point, but only to a
beam waist
of thickness 2
w
o
, Figure 3.4.




Figure 3.4: Laser beam waist.

The beam waist thickness is given by


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

Example:

λ
= 514nm,
w
0
= 12mm,
θ
= 0.014 mrad


w
= 25mm at

1000m from waist.



λ
= 514nm,
w
0
= 1mm,
θ
= 0.164 mrad


w
= 25mm at

6m from waist.



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23

Common Lasers

Solid
-
state lasers



Ruby

λ
= 669 n
m

E
up to 1.5 J/pulse (15 ns)

phase coherence 2
-
5m



NdYAG

λ
= 1064 nm

E
up to 0.3 J/pulse (8
-
20 ns)

phase coherence 1
-
3m

Gas lasers



He
-
Ne

λ
= 632.8 nm

powers 0.1
-
50 mW

phase coherence 300
-
400mm



Argon ion

λ
= 514.5 nm

powers 1
-
20 W


phase coherence 1
-
100mm


Optics Basics

Speed of light in a vacuum:
c
0

= 3.0 x 10
8
ms
-
1


Speed of light in a medium of refractive index
n
,
c = c
0
/
n
.

:
f
= frequency (Hz)
independent of medium
,
λ
= wavelength (m)

:
k
= wavenumb
e
r
(m
-
1
)

Interference:

Figure 3.5 shows how the wavefronts associated with two laser beams cross. When two peaks
coincide, there is
constructive interference
and a local maximum of intensity results. When a
peak and a trough coincide, they cancel and a loc
ally dark area results
-

destructive interference
.



Figure 3.5: Interference of laser beams.

From the geometry of the system, it can be seen that the bright areas form lines, as do the dark
areas, giving rise to a pattern of al
ternating dark and bright
fringes
. From the geometry of the
system,, the separation of the light fringes is given by




The Doppler Effect






The Doppler effect applies equally to light waves as in its familiar form with sound waves
,
eg
the
change in tone of a siren as it passes the listener.


flow

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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.




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

When the receiver
R
is stationary, th
e number of waves received in a time
t
is


However, if the receiver is moving with a velocity
u
at an angle
α
to the direction of the wave
propagation as shown in the Figure, then the
catch up
speed of the waves is reduced, and the
n
umber of waves received in a time
t
is now



where
is a unit vector in the direction of the wave propagation. Thus the frequencies for
stationary and moving observers,
f
0
and
f
1
are given by t
he number of waves received per unit
time,
ie

,


and so the
frequency shift
is


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


c/λ


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25

The Differential Dopple
r Method




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
θ
, crossing at the measurement point. (The purpose of the
Bragg Cell
is 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 det
ector,
eg
a photomultiplier and lens
system. 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, a
nd 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

α
= 90
o

-

θ
/2. Therefore the particle receives light at a sh
ifted frequency. The light from the lower
beam will be shifted to a frequency


since cos
α
= cos (90
o

-

θ
/2) = sin
θ
/2 .
The shifted frequency is lower because a component of
the particle’s velocity is away from the source.

The ligh
t 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 particle’s velocity towards the source.
The shifted frequency is therefore


The particl
e scatters the light that is incident upon it: the scattered light is made up of two
frequencies,
f
1
and
f
2
. The particle’s velocity has no component in the direction of the receiver,
so the light entering the detector is at the same frequencies at whi
ch it was scattered from the
particle,
f
1
and
f
2
.

The final stage is to establish the shift in frequency in order to establish the particle’s velocity.
When two waveforms of similar frequencies are combined, a
beating
effect is seen (demo with
overlayi
ng transparencies with lines drawn at spacings differing by 5%). The beat frequency is
simply the difference between the component frequencies






flow

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26



Figure 3.8: Fringe pattern formed at beam intersection.

A more visual but less rigoro
us 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
τ
taken to pass from one bright fringe t
o the
next. A particle travelling at speed
u
through a fringe pattern with spacing
δ
will produce flashes
of light at a frequency given by


but we know


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


This visual alternative formulation is useful in visualising the effect of
frequency shifting
,
discussed below.


Practical Implementation

LDA systems are generally bought “off the shelf”.
Dantec
(based in C
openhagen) 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 th
ird 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 u
sed to good effect.

Most systems are laid out as sketched in Figure 3.8
-
a
forward scatter
arrangement. This requires
optical access to both sides of the test volume. An alternative is to work in
back scatter
mode,
detecting light scattered back in the di
rection 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 splitt
ing and alignment.



Multi
-
Component LDA


flow

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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 veloc
ity 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 to
measure 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
particle’s motion and therefore the fluid velocity.
Frequency shifting
is a trick to overcome this
limitation. Basically, the fring
e 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 particle’s backward
motion, 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, relat
ive to the moving fringe pattern.

This apparent
shifted
velocity is then measured, and the known shift subtracted to give the true
flow velocity.

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


so the apparent measured velocity is


The actual velocity is recovered by subtracting the shift velocity,
u
shift
, from the measured,
shifted velocity, u’




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4. Particle Image Velocimetry


4.1 Summary


This c
hapter reviews the Particle Image Velocimetry (PIV) flow measurement method. All
stages in the process of obtaining PIV flow maps are described. The underlying principles are
introduced in Section 4.3. The acquisition phase of PIV is divided into illumin
ation (Section 4.5)
and image acquisition (Section 4.6). The analysis phase
-
extracting the velocity data from the
PIV flow record
-
is discussed in Sections 4.4 and 4.5. The chapter concludes with a review of
applications and brief look at the future of
the PIV technique.


4.2 Motivation


Non
-
intrusive flow measurement techniques are becoming an increasingly familiar part of
laboratory experiments in fluid dynamics. Since its inception in 1966, Laser Doppler
Anemometry (LDA) has progressed, and aided b
y developments in other technologies, notably in
lasers, fibre
-
optics and computers, it is now a most useful tool under a wide range of conditions.
LDA is, however, fundamentally a point measurement technique; the time evolution of flow
velocity can be me
asured with great accuracy at a point, but if a map of an area of the flow is to
be obtained, it must be built up point by point. Thus this leads to a requirement that the flow be
either steady or accurately repeatable, neither of which conditions holds f
or most interesting
engineering flow problems. PIV gives a quantitative map of instantaneous flow velocities over a
large field.


4.3

Basic Principles


The basic principle of PIV is very simple: tiny tracer particles in the flow are illuminated and
their pos
itions recorded photographically or by video at two successive instants. The
photographic or video “flow record” of the whole 2
-
d field is then divided into a grid of cells and,
in each cell, the distance moved by the tracer particles from the time of the
first image being
recorded to the second is determined. Knowing this distance travelled and the time taken, the
velocity of the flow in that cell is therefore measured. This is done for every cell, giving a 2
-
d
map of the “instantaneous” velocity field at
the time of the recording.


Thus it can be seen that implicit in the method are two basic assumptions; that the flow field as a
whole does not change over the time between first and second exposures, and that the velocity in
each cell is uniform. In any r
eal flow of interest, neither assumption will hold fully and the extent
to which they hold is always an important consideration.


In the early years of PIV (1980s), the usual approach was to illuminate the flow stroboscopically
and to record a double
-
or m
ultiple
-
exposure photograph of the flow,
ie
holding the camera
shutter open long enough such that each tracer particle is illuminated twice and therefore gives a
pair of images on the flow record. This is PIV using the
autocorrelation
method.


With develo
pments in still image video technology, the complication of arranging for the
stroboscopic illumination of a plane within the flow can be avoided by exposing the first and
second images as successive frames recorded by a CCD
2
camera or on two separate CCD
arrays.
The movement of the tracer particle images over the time between the exposure of the first frame
and the second can then be analysed to give the velocity map. This is the
cross
-
correlation

method. Cross
-
correlation has a number of significant advan
tages over autocorrelation and is
now almost universally the preferred approach.





2

charge
-
coupled device

-
a video array chip


flow

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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 parame
ters 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, bu
t 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 i
nformation 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 t
aken of
exactly
the same field
in 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 carr
y 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 a
nd robust approach.


The cross
-
correlation function
C(
Δ
x,
Δ
y)
is arrived at by comparing the base and cross images
given by intensity distributions
I
base
(x, y)
and
I
cross
(x, y)
. In physical terms, the function is moving
the cross image relative to the ba
se image, seeking the best match between the intensity patterns.




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.



flow

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


The clearly visible peak in the function indicates the offset in
x
and
y
between the base and cross
images at which the best correlation between the images was found. Once the soft
ware has
calculated the cross
-
correlation function, it locates this peak and records the
Δ
x,
Δ
y
values.
Knowledge of the optical magnification and the time interval between images allows
Δ
x,
Δ
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 divergen
ce of their beams
allows thin sheets to be formed, and because the energy density in the beam is very high,
eg
we
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 achieve
d 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.




flow

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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 section
through the flow.



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

A practical criterion is that the cross plane velocity v
z
should be small enough such that the cros
s
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 m
ajor 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 considerati
ons 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 sui
table 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 reflec
tive at the
wavelength of the laser, and small enough to follow the flows studied (typical particle diameters
are

70

m). Importantly, it is also quite inexpensive
-
the cost to seed a flume containing six
tonnes of water is

£2
-
£5.


For air flows of h
igh 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 an
d 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 d
istortions 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 si
mply 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!



flow

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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 p
ulsed 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 digita
l 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 choic
e 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 t
he
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 imag
es 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 t
han 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 over
a few pixels can be measured to “sub
-
p
ixel” 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, d
i
is determined by three factors: the particle diameter, d
p
, the
magnification (recorded:actual size) M, a
nd the lens aperture used. defined by its “f
-
number
3
”, f
#

:


where d
spot
is the diffraction
-
limited image size
-
the smallest image that can be recorded by a
lens working at the given f
-
number, f
#
,


Thus for lar
ger 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,
eg
an
aperture of
f/8 implies that the aperture is 1/8
th
of the focal length. In this case the “f
-
number” f
#
= 8.


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in the flow gives a particle im
age 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 extr
emely 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 M
agnification


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 general
another 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 (
eg
32 x 32 pixel) interrogation region on the flow record. The
implicit assumpt
ion 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 variou
s settings of camera aperture and laser power is required for a new
application. 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 parti
cle images. Using
f
/4 or
f
/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 po
sitional 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 x
1
and x
2
(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 x
3
position, the distance from camera to measurement plane defines the magnification. The
magnification is chosen as a compromise between t
he 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,
ϕ
1
,
ϕ
2
and
ϕ
3
. The
pitch

ϕ
1
and
yaw

ϕ
2
axes must be set so that the camera image pl
ane 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
roll
axis
ϕ
3
needs t
o 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 import
ant 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 camera

2.

the internal workings of the camera

If the camera is mounted o
n 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,
eg
upon 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 an
absolute 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,
eg
a 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 t
he 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 exp
eriments,
eg
of 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 po
wer station combustion chamber


Coastal Engineering



Beach erosion /accretion



Wave impacts on breakwaters



Flow around seabed pipelines


Offshore Engineering



Wave enhancement due to structure blockage



Oceanic internal waves



Deep water breaking waves


Wind En
ergy



Measurement of wake behind a wind turbine


Heat Transfer



Recirculation in horizontal kettle reboilers


Fire Safety



Flow of fumes and smoke out of burning buildings