INSTRUMENTATION EQUIPMENT 2

FLOW MEASUREMENT
There are various methods used to measure the flow rate of steam, water,
lubricants, air, etc., in a nuclear generating station. However, in this module
will look at the most common, namely the DP cell type flow detector. Also
in this section we will discuss the application of a square root extractor and
cut-off relay plus the possible sources of errors in flow measurements and
different failure modes that can occur.

Flow Detectors
To measure the rate of flow by the differential pressure method, some form
of restriction is placed in the pipeline to create a pressure drop. Since flow in
the pipe must pass through a reduced area, the pressure before the restriction
is higher than after or downstream. Such a reduction in pressure will cause
an increase in the fluid velocity because the same amount of flow must take
place before the restriction as after it. Velocity will vary directly with the
flow and as the flow increases a greater pressure differential will occur
across the restriction. So by measuring the differential pressure across a
restriction, one can measure the rate of flow.

Orifice Plate
The orifice plate is the most common form of restriction that is used in flow
measurement. An orifice plate is basically a thin metal plate with a hole
bored in the center. It has a tab on one side where the specification of the
plate is stamped. The upstream side of the orifice plate usually has a sharp,
edge. Figure 1 shows a representative orifice plate.

 

A Typical Orifice Plate

When an orifice plate is installed in a flow line (usually clamped between a
pair of flanges), increase of fluid flow velocity through the reduced area at
the orifice develops a differential pressure across the orifice. This pressure is
a function of flow rate.
With an orifice plate in the pipe work, static pressure increases slightly
upstream of the orifice (due to back pressure effect) and then decreases
sharply as the flow passes through the orifice, reaching a minimum at a
point called the vena contracta where the velocity of the flow is at a
maximum. Beyond this point, static pressure starts to recover as the flow
slows down. However, with an orifice plate, static pressure downstream is
always considerably lower than the upstream pressure. In addition some
pressure energy is converted to sound and heat due to friction and
turbulence at the orifice plate. Figure 2 shows the pressure profile of an
orifice plate installation.

 

Orifice Plate Installation with Pressure Profile

one can see that the measured differential pressure
developed by an orifice plate also depends on the location of the pressure
sensing points or pressure taps.

Flange Taps
Flange taps are the most widely used pressure tapping location for orifices.
They are holes bored through the flanges, located one inch upstream and one
inch downstream from the respective faces of the orifice plate. A typical
flange tap installation is shown in Figure 3. The upstream and downstream
sides of the orifice plate are connected to the high pressure and low-pressure
sides of a DP transmitter. A pressure transmitter, when installed to measure
flow, can be called a flow transmitter. As in the case of level measurement,
the static pressure in the pipe-work could be many times higher than the
differential pressure created by the orifice plate.
In order to use a capsule that is sensitive to low differential pressure, a threevalve
manifoldhas to be used to protect the DP capsule from being overranged.
The three valve manifold is discussed in more detail in the section
on level measurement.

 

Orifice Plate with Flange Taps and Three Valve Manifold

Corner Taps
Corner taps are located right at upstream and downstream faces of the
orifice plates.

 

Orifice Plate with Corner Taps

Vena Contracta Taps
Vena contracta taps are located one pipe inner diameter upstream and at the
point of minimum pressure, usually one half pipe inner diameter
downstream .

 

Orifice Plate with Vena Contracta Taps

Pipe Taps
Pipe taps are located two and a half pipe inner diameters upstream and eight
pipe inner diameters downstream.
When an orifice plate is used with one of the standardized pressure tap
locations, an on-location calibration of the flow transmitter is not necessary.
Once the ratio and the kind of pressure tap to be used are decided, there are
empirically derived charts and tables available to facilitate calibration.

Advantages and Disadvantages of Orifice Plates
Advantages of orifice plates include:
• High differential pressure generated
• Exhaustive data available
• Low purchase price and installation cost
• Easy replacement
Disadvantages include:
• High permanent pressure loss implies higher pumping cost.
• Cannot be used on dirty fluids, slurries or wet steam as erosion will
alter the differential pressure generated by the orifice plate.

Venturi Tubes
For applications where high permanent pressure loss is not tolerable, a
venturi tube (Figure 6) can be used. Because of its gradually curved inlet
and outlet cones, almost no permanent pressure drop occurs. This design
also minimizes wear and plugging by allowing the flow to sweep suspended
solids through without obstruction.

 

Venturi Tube Installation

However a Venturi tube does have disadvantages:

• Calculated calibration figures are less accurate than for orifice plates.
For greater accuracy, each individual Venturi tube has to be flow
calibrated by passing known flows through the Venturi and
recording the resulting differential pressures.
• The differential pressure generated by a venturi tube is lower than
for an orifice plate and, therefore, a high sensitivity flow transmitter
is needed.
• It is more bulky and more expensive.
As a side note; one application of the Venturi tube is the measurement of
flow in the primary heat transport system. Together with the temperature
change across these fuel channels, thermal power of the reactor can be
calculated.

Flow Nozzle
A flow nozzle is also called a half venturi. Figure 7 shows a typical flow
nozzle installation.

 

Flow Nozzle Installation

The flow nozzle has properties between an orifice plate and a venturi.
Because of its streamlined contour, the flow nozzle has a lower permanent
pressure loss than an orifice plate (but higher than a venturi). The
differential it generates is also lower than an orifice plate (but again higher
than the venturi tube). They are also less expensive than the venturi tubes.
Flow nozzles are widely used for flow measurements at high velocities.
They are more rugged and more resistant to erosion than the sharp-edged
orifice plate. An example use of flow nozzles are the measurement of flow
in the feed and bleed lines of the PHT system.

Elbow Taps
Centrifugal force generated by a fluid flowing through an elbow can be used
to measure fluid flow. As fluid goes around an elbow, a high-pressure area
appears on the outer face of the elbow. If a flow transmitter is used to sense
this high pressure and the lower pressure at the inner face of the elbow, flow
rate can be measured. Figure 8 shows an example of an elbow tap
installation.
One use of elbow taps is the measurement of steam flow from the boilers,
where the large volume of saturated steam at high pressure and temperature
could cause an erosion problem for other primary devices.
Another advantage is that the elbows are often already in the regular piping
configuration so no additional pressure loss is introduced.

 

Elbow Tap Installation

Pitot Tubes

Pitot tubes also utilize the principles captured in Bernoulli’s equation, to
measure flow. Most pitot tubes actually consist of two tubes. One, the lowpressure
tube measures the static pressure in the pipe. The second, the highpressure
tube is inserted in the pipe in such a way that the flowing fluid is
stopped in the tube. The pressure in the high-pressure tube will be the static
pressure in the system plus a pressure dependant on the force required
stopping the flow.

                                                    Pitot Tube

Pitot tubes are more common measuring gas flows that liquid flows. They

suffer from a couple of problems.

The pressure differential is usually small and hard to measure.

The differing flow velocities across the pipe make the accuracy dependent
on the flow profile of the fluid and the position of the pitot in the pipe.

Annubar
An annubar is very similar to a pitot tube. The difference is that there is
more than one hole into the pressure measuring chambers. The pressure in
the high-pressure chamber represents an average of the velocity across the
pipe. Annubars are more accurate than pitots as they are not as position
sensitive or as sensitive to the velocity profile of the fluid.

                                             Annubar

Square Root Extractor

Up to now, our flow measurement loop can be represented by the
installation shown in Figure 9. The high and low-pressure taps of the
primary device (orifice type shown) are fed by sensing lines to a differential
pressure (D/P) cell. The output of the D/P cell acts on a pressure to milliamp
transducer, which transmits a variable 4-20 ma signal. The D/P cell and
transmitter are shown together as a flow transmitter (FT).

 

                      A Flow Loop with Orifice Plate

This simple system although giving an indication of the flow rate (Q), is actually transmitting a signal proportional to the differential pressure (ΔP).

However, the relationship between the volume of flow Q and ΔP is not

linear. Thus such a system would not be appropriate in instrumentation or
metering that requires a linear relationship or scale.
In actuality the differential pressure increases in proportion to the square of
the flow rate. We can write this as: ΔP   ∝   Q2
In other words the flow rate (Q) is proportional; to the square root of the
differential pressure.
Volumetric Flow Rate = Q   ∝    Δ P
To convert the signal from the flow transmitter, (figure 9 above) to one that
is directly proportional to the flow-rate, one has to obtain or extract the
square root of the signal from the flow transmitter. Figure 10 illustrates the
input - output relationship of a square root extractor.

Square Root Extractor Input and Output

The square root extractor is an electronic (or pneumatic) device that takes
the square root of the signal from the flow transmitter and outputs a
corresponding linear flow signal. Several methods are used in the
construction of square root extractors. However, it is beyond the scope of
this course to discuss the actual circuitries.
A typical square root extractor installation is shown in Figure 13. This
system would produce a 4-20-ma signal that is linear with the flow rate.

 

A Typical Square Root Extractor Installation

 Square root extractors are usually current operated devices so they can be
connected directly in the 4-20 mA current loop of a flow transmitter. The
output of the square root extractor is again a 4-20 mA signal. This signal is
directly proportional to the flow-rate in the pipe-work.
The signal from the square root extractor usually goes to a controller.
The controller (which can be regarded as an analog computer) is used to
control the final control element, usually a valve.

Cut-off relay
Square root extractors do have a drawback. At low values of input, very
small changes in the input (differential pressure) to the extractor will cause a
large change in the square root output (flow indication). This system is
described as having high gain at values close to zero input. Observe figure
14 below, which is an expanded version of figure 12 at the lower end. The
amount of change from zero pressure to A and from A to B is identical.
However, for the same input change (ΔP), the gain at low input is greater.

 

Square Root Extractor Graph Expanded View

To illustrate the effect of the very high gain in the square root extractor at
low scale values consider a typical situation. A pipe valve is closed and the
zero flow produces a 4 mA output from the flow transmitter. If due to noise,
temperature or other disturbances, the input drifted from 0% to 1% (i.e.,
from 4 mA to 4.16 mA), the output would have changed from 0% to 10% (4
mA to 5.6 mA). It is obvious that this significant error sent to the controller
has to be eliminated.
For this reason, square root extractors are equipped with cut-off relays. The
setting for the relay can be adjusted from 6% to 10% of output. Shown in
Figure 15 is a response curve for a cut-off relay set at 7% output. In this
case, any input signal below (0.07)2 or 0.49% would be ignored by the
extractor. The output of the extractor would remain at 0% as long as input is
below 0.49%.
When the input exceeded 0.49%, the output would resume its normal curve,
starting at 7%.

 

Response Curve for Extractor with 7% Cut-Off Setting

Density Compensating Flow Detectors

It must be remembered that a DP transmitter used for flow measurement,
measures differential pressure, not the volume or mass of flow. We have
shown that differential pressure instruments require that the square root
differential pressure be taken to obtain volumetric flow Q:
Volume of Flow =Q ∝ ΔP / ρ
For compressible vapour such as steam, it is more important to know the
mass of the flow W rather than the volume. To determine the mass of a
liquid/gas the density (ρ = mass per unit volume) must also be obtained.
Mass of Flow =W = ρQ ∝ ρΔP
We also know that density varies directly with pressure and inversely with
temperature:
ρ α K pressure/temperature
The coefficient K (which can be obtained from tables) depends on a number
of variables including the pipe size and the characteristics of the fluid/gas. It
is sufficient to say that if the process temperature and static pressure is
known, then the density can be obtained.

 

Density Compensating Flow Detector

The density compensating flow detector (shown schematically in
figure 16) is a necessity for steam flow between the boilers, re-heaters and
the turbines, where the mass (weight) of the steam is more important than
the volume.

Process Conditions
As previously stated, the measurement of flow using any of the devices
described above is purely inferential. It relies on the signal from a
differential pressure (D/P) cell to obtain an inferred flow measurement. This
flow measurement could be either the volume or mass of the liquid/gas. In
either case the instrumentation can be affected by the process conditions.
The three main parameters are:

Fluid Temperature
The temperature of the flow quantity has a dramatic effect on the flow
measurement. Under the right conditions the liquid can either boil
(producing gas pockets and turbulence) or freeze (producing blockages and
distorted flow patterns) at the sensors.
At the onset of temperature related flow instrumentation problems the meter
readings will become unstable. Gas pockets (causing intermittent low
pressure) at the high pressure sensing lines will cause apparent low flow
fluctuations. This is more predominant in orifice and flow-nozzle
installations. Turbulence at the low-pressure sensor will usually increase as
the temperature increases to cause a more stable but incorrect high flow
reading.

Temperature also affects the density of the liquid/gas, as per the following
relationship (where K is a constant for the liquid/gas).
The mass flow (i.e., pounds of steam per minute) varies inversely with
temperature and must be compensated for using a density compensating
flow detector.
The elbow tap sensor uses centrifugal force to detect flow and is most
sensitive to density changes. The flow readings will increase as the
temperature decreases.

Fluid Pressure
As we have just seen, pressure also affects the density of the fluid/gas. For
the elbow tap previously mentioned, the flow readings will increase as the
process pressure increases.

ρ α K pressure/temperature

For all types of D/P flow sensors, mass flow will of course increase as the
pressure increases. To obtain the correct measurement of mass flow, a
density compensating flow detector must be used as described previously.

Flow Measurement Errors
We have already discussed the pros and cons of each type of flow detector
commonly found in a generating station. Some, such as the orifice, are more
prone to damage by particulate or saturated steam then others. However,
there are common areas where the flow readings can be inaccurate or
invalid.

Erosion
Particulate, suspended solids or debris in the piping will not only plug up the
sensing lines, it will erode the sensing device. The orifice, by its design with
a thin, sharp edge is most affected, but the flow nozzle and even venturi can
also be damaged. As the material wears away, the differential pressure
between the high and low sides of the sensor will drop and the flow reading
will decrease.

Over ranging Damage to the D/P Cell
Again, as previously described, the system pressures are usually much
greater than the differential pressure and three valve manifolds must be
correctly used.

Vapour Formation in the Throat
D/P flow sensors operate on the relation between velocity and pressure. As
gas requires less pressure to compress, there is a greater pressure differential
across the D/P cell when the gas expands on the LP side of the sensor. The
flow sensor will indicate a higher flow rate than there actually is. The
turbulence created at the LP side of the sensor will also make the reading
somewhat unstable. A small amount of gas or vapour will make a large
difference in the indicated flow rate.
The opposite can occur if the vapour forms in the HP side of the sensor due
to cavitation or gas pockets when the fluid approaches the boiling point. In
such an instance there will be a fluctuating pressure drop across the D/P cell
that will give an erroneously low (or even negative) D/P reading.

Clogging of Throat
Particulate or suspended solids can damage the flow sensor by the high
velocities wearing at the flow sensor surfaces. Also, the build-up of material
in the throat of the sensor increases the differential pressure across the cell.
The error in flow measurement will increase as the flow increases.

Plugged or Leaking Sensing Lines
The effects of plugged or leaking D/P sensing lines is the same as described
in previous modules, however the effects are more pronounced with the
possible low differential pressures. Periodic maintenance and bleeding of
the sensing lines is a must. The instrument error will depend on where the
plug/leak is:
On the HP side a plugged or leaking sensing line will cause a lower reading.
The reading will become irrational if the LP pressure equals or exceeds the
HP sensing pressure.
On the LP side a plugged or leaking sensing line will cause a higher reading.