The
tubes within a Coriolis flowmeter are shaken at their mechanical resonant
frequency to maximize their shaking motion while minimizing electrical power applied
to the force coil. The electronics module uses a feedback loop between the
sensor coils and the shaker coil to maintain the tubes in a continuous state of
resonant oscillation. This resonant frequency changes with process fluid density,
since the effective mass of the fluid-filled tubes changes with process fluid
density, and mass is one of the variables influencing the mechanical resonant
frequency of any elastic structure.
Note
the “mass” term in the following formula, describing the resonant frequency of
a tensed string:
Where,
f
= Fundamental resonant frequency of string (Hertz)
L
= String length (meters)
FT
= String tension (newtons)
μ
= Unit mass of string (kilograms per meter)
A
fluid-filled tube is a close analog to a tensed string, with tube stiffness
analogous to string tension and liquid density analogous to unit mass. So long
as the spring constant (tube stiffness) is known, the resonant frequency of the
tubes’ vibration serves to indicate the unit mass of the tubes, which in turn represents
fluid density given the known internal volume of the tubes.
Temperature
changes have the potential to interfere with this density measurement because temperature
affects the elasticity of metal (Young’s modulus). This is why all Coriolis
flowmeters are equipped with RTD temperature sensors to continuously monitor
the temperature of the vibrating tube(s). The flowmeter’s microprocessor takes
this tube temperature measurement and uses it to compensate for the resulting
elasticity changes based on prior modeling of the tube metal characteristics.
In other words, the flowmeter’s microprocessor continuously updates the force variable
(FT ) representing tube stiffness in the resonant frequency equation so that
the frequency will always be a reliable indicator of unit mass (fluid density).
This temperature measurement happens to be accessible as an auxiliary output
signal, which means a Coriolis flowmeter may double as a (very expensive!)
temperature transmitter in addition to measuring mass flow rate and fluid
density.
The
ability to simultaneously measure three process variables (mass flow rate,
temperature, and density) makes the Coriolis flowmeter a very versatile
instrument indeed. This is especially true when the flowmeter in question
communicates digitally using a “Fieldbus” standard rather than an analog 4-20
mA signal. Fieldbus communication allows multiple variables to be transmitted by
the device to the host system (and/or to other devices on the same Fieldbus
network), allowing the Coriolis flowmeter to do the job of three instruments!
An
example of a Coriolis mass flowmeter being used as a multi-variable transmitter
appears in the following photographs. Note the instrument tag labels in the
close-up photograph (FT, TT, and DT), documenting its use as a flow
transmitter, temperature transmitter, and density transmitter, respectively:
Coriolis
flowmeter capabilities and limitations
Even
though a Coriolis flowmeter inherently measures mass flow rate, the continuous
measurement of fluid density allows the meter to calculate volumetric flow rate
if this is the preferred means of expressing fluid flow. The relationship
between mass flow (W), volumetric flow (Q), and mass density (ρ) are quite
simple:
All
the flowmeter’s computer must do to output a volumetric flow measurement is taken the mass flow measurement value and divide that by the fluid’s measured
density. A simple exercise in dimensional analysis (performed with metric units
of measurement) validates this concept for both forms of the equation shown
above:
Coriolis
mass flowmeters are very accurate and dependable. They are also completely
immune to swirl and other fluid disturbances, which means they may be located
nearly anywhere in a piping system with no need at all for straight-run pipe
lengths upstream or downstream of the meter. Their natural ability to measure
true mass flow, along with their characteristic linearity and accuracy, makes
them ideally suited for custody transfer applications (where the flow of fluid represents
products being bought and sold).
The
American Gas Association (AGA) formalized the use of Coriolis mass flowmeters
for the measurement of natural gas with their Report #11. This standard is
equivalent to AGA #3 for orifice meters, AGA #7 for turbine meters, and AGA #9
for ultrasonic meters.
Perhaps
the greatest disadvantage of Coriolis flowmeters is their high initial cost,
especially for large pipe sizes. Coriolis flowmeters are also more limited in
operating temperature than other types of flowmeters and may have difficulty
measuring low-density fluids (gases) and mixed-phase (liquid/vapor) flows. The
bent tubes used to sense process flow may also trap process fluid inside to the
point where it becomes unacceptable for hygienic (e.g. food processing,
pharmaceuticals) applications. Straight-tube Coriolis flowmeter designs, and
designs where the angle of the tubes is slight, fare better in this regard than
the traditional U-tube Coriolis flowmeter design. However, an advantage of
U-shaped tubes is that they aren’t as stiff as straight tubes, and so
straight-tube Coriolis flowmeters tend to be less sensitive to low flow rates
than their U-tube counterparts.
Thermal
flowmeters
The wind chill is a phenomenon common to nearly everyone who has ever lived in a cold
environment. When the ambient air temperature is substantially colder than the
temperature of your body, heat will transfer from your body to the surrounding
air. If there is no breeze to move air past your body, the air molecules
immediately surrounding your body will begin to warm up as they absorb heat from
your body, which will then decrease the rate of heat loss. However, if there is
even a slight breeze of air moving past your body, your body will come into
contact with more cool (unheated) air molecules than it would otherwise,
causing a greater rate of heat loss. Thus, your perception of the surrounding
temperature will be cooler than if there were no breeze.
We
may exploit this principle to measure mass flow rate, by placing a heated
object in the midst of a fluid flow stream, and measuring how much heat the
flowing fluid convects away from the heated object. The “wind chill”
experienced by that heated object is a function of true mass flow rate (and not
just volumetric flow rate) because the mechanism of heat loss is the rate at
which fluid molecules contact the heated object, with each of those molecules
having a definite mass.
The
simplest form of the thermal mass flowmeter is the hot-wire anemometer, used to
measure air speed. This flowmeter consists of a metal wire through which an
electric current is passed to heat it up. An electric circuit monitors the
resistance of this wire (which is directly proportional to wire temperature
because most metals have a definite temperature coefficient of resistance). If
air speed past the wire increases, more heat will be drawn away from the wire
and cause its temperature to drop. The circuit senses this temperature change
and compensates by increasing current through the wire to bring its temperature
back up to the setpoint. The amount of current sent through the wire becomes a
representation of the mass air flow rate past the wire.
Most
mass air flow sensors used in automotive engine control applications employ
this principle. It is important for engine control computers to measure mass
air flow and not just volumetric air flow because it is important to maintain
proper air/fuel ratio even if the air density changes due to changes in
altitude. In other words, the computer needs to know how many air molecules are
entering the engine per second in order to properly meter the correct amount of
fuel into the engine for complete and efficient combustion. The “hot wire” mass
air flow sensor is simple and inexpensive to produce in quantity, which is why
it finds common use in automotive applications.
Industrial
thermal mass flowmeters usually consist of a specially designed “flow tube” with
two temperature sensors inside: one that is heated and one that is unheated.
The heated sensor acts as the mass flow sensor (cooling down as flow rate
increases) while the unheated sensor serves to compensate for the “ambient”
temperature of the process fluid.
A
typical thermal mass flow tube appears in the following diagrams (note the swirl
vanes in the close-up photograph, designed to introduce large-scale turbulence
into the flow stream to maximize the convective cooling effect of the fluid
against the heated sensor element):
The
simple construction of thermal mass flowmeters allows them to be manufactured
in very small sizes. The following photograph shows a small device that is not
only a mass flow meter but also a mass flow controller with its own built-in
throttling valve mechanism and control electronics. To give you a sense of
scale, the tube fittings have seen on the left- and right-hand sides of this device are
1/4 inch, making this photograph nearly full-size:
An
important factor in the calibration of a thermal mass flowmeter is the specific
heat of the process fluid. “Specific heat” is a measure of the amount of heat
energy needed to change the temperature of a standard quantity of a substance by
some specified amount. Some substances have much greater specific heat values
than others, meaning those substances have the ability to absorb (or release) a
lot of heat energy without experiencing a great temperature change. Fluids with
high specific heat values make good coolants because they are able to remove
much heat energy from hot objects without experiencing great increases in
temperature themselves. Since thermal mass flowmeters work on the principle of
convective cooling, this means a fluid having a high specific heat value will
elicit a greater response from a thermal mass flowmeter than the exact same
mass flow rate of a fluid having a lesser specific heat value (i.e. a fluid
that is not as good of a coolant).
This
means we must know the specific heat value of whatever fluid we plan to measure
with a thermal mass flowmeter, and we must be assured its specific heat value
will remain constant. For this reason, thermal mass flowmeters are not suitable
for measuring the flow rates of fluid streams whose chemical composition is
likely to change over time. This limitation is analogous to that of a pressure
sensor used to hydrostatically measure the level of liquid in a vessel: in
order for this level-measurement technique to be accurate, we must know the
density of the liquid and also be assured that density will be constant over time.
Thermal
mass flowmeters are simple and reliable instruments. While not as accurate or
tolerant of piping disturbances as Coriolis mass flowmeters, they are far less
expensive.
Perhaps
the greatest disadvantage of thermal mass flowmeters is their sensitivity to
changes in the specific heat of the process fluid. This makes the calibration
of any thermal mass flowmeter specific for one composition of fluid only. In
some applications such as automotive engine intake air flow, where the fluid
composition is constant, this limitation is not a factor. In many industrial applications,
however, this limitation is severe enough to prohibit the use of thermal mass
flowmeters. Industrial applications for thermal mass flowmeters include natural
gas flow measurement (non custody transfer), and the measurement of purified gas
flows (oxygen, hydrogen, nitrogen) where the composition is known to be very
stable.
Another
(potential) limitation of thermal mass flowmeters is the sensitivity of some
designs to changes in flow regime. Since the measurement principle is based on
heat transfer by fluid convection, any factor influencing the convective
heat-transfer efficiency will translate into a perceived difference in mass
flow rate. It is a well-known fact in fluid mechanics that turbulent flows are
more efficient at convecting heat than laminar flows because the “stratified”
nature of a laminar flow stream impedes heat transfer across the fluid width.
In some thermal flowmeter designs, the walls of a heated metal tube serve as
the “hot” element cooled by the fluid, and the difference between the rate of
heat transferred by a laminar flow stream from the walls of a heated tube versus
a turbulent flow stream can be great. Therefore, a change in flow regime (from
turbulent to laminar, and visa-versa) will cause a calibration shift for this
design of thermal mass flowmeter.
List
of Prominent Suppliers: ABB,
Bronkhorst,
Brooks,
Cameron,
Endress
+ Hauser, Flexim,
Holykell,
KEM,
Kobold, Krohne,
Omega, Oval, Q&T,
Rheonik, Siemens,
Sierra,
SKE, Technoton, Yokogawa
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