Abstrict Mass flow meter operating by the Coriolis principle, with a measuring
tube through which flows a medium, at least one exciter associated
with and exciting the measuring tube, and at least one sensor associated
with the measuring tube for capturing the Coriolis forces and/or
the Coriolis-force-induced oscillations. According to the invention
the measuring tube is designed as a thin shell. A thin shell is
understood to be characterized by a wall thickness h much smaller
than its radius R, and a length L of the same order of magnitude
of the radius R. The mass flow meter according to the invention
uses vibration modes with more than one circumferential wave. Thus,
a mass flow meter with high sensitivity and low pressure drop is
achieved.
Claims 1. Mass flow meter operating by the Coriolis principle, with a
measuring tube (1) through which flows a medium, at least one exciter
(2) associated with and exciting the measuring tube (1), and at
least one sensor (3) associated with the measuring tube (1) for
capturing the Coriolis forces and/or the Coriolis-force-induced
oscillations, characterized in that the measuring tube (1) is designed
as a thin shell.
2. Mass flow meter according to claim 1 characterized in that
the measuring tube (1) has a wall thickness which is much smaller
than the radius of the measuring tube (1), and a length of the same
order of magnitude of the radius.
3. Mass flow meter according to claim 1 or 2 characterized in
that the wall thickness of the measuring tube (1) is at least by
a factor of 50 smaller than the radius of the measuring tube (1).
4. Mass flow meter according to any of claims 1 to 3 characterized
in that the wall thickness of the measuring tube (1) is equal or
less than 0.5 mm, preferably equal or less than 0.25 mm.
5. Mass flow meter according to any of claims 1 to 4 characterized
in that the ratio of the length of the measuring tube (1) relative
to the radius of the measuring tube is equal or less than 6 preferably
equal or less than 4.
6. Mass flow meter according to any of claims 1 to 5 characterized
in that at least one added lumped mass (1) is placed on the measuring
tube (1).
7. Mass flow meter according to claim 6 characterized in that
the lumped mass (5) is provided on an anti-node of the driving mode.
8. Mass flow meter according to any of claims 1 to 7 characterized
in that at least two exciters (2) are used wherein the exciters
(2) are fixed to the measuring tube (1) at the same axial length
but spaced apart from each other by a predefined angle.
9. Mass flow meter according to claim 8 characterized in that
the angle is 90.degree. and the exciters (2) are operated in phase.
10. Mass flow meter according to claim 8 characterized in that
the angle is 45.degree. and the exciters (2) are operated in opposition
of phase.
11. Mass flow meter according to any of claims 1 to 10 characterized
in that an inner tube (6) is provided inside the measuring tube
(1) to make an annular flow.
12. Mass flow meter according to claim 11 characterized in that
the inner tube (6) is provided centrally in the measuring tube (1).
Description [0001] The invention concerns a mass flow meter operating by the
Coriolis principle, with a measuring tube through which flows a
medium, at least one exciter associated with and exciting the measuring
tube, and at least one sensor associated with the measuring tube
for capturing the Coriolis forces and/or the Coriolis-force-induced
oscillations.
[0002] Generally, the existing Coriolis flow meters are based on
vibrations of a measuring tube of length L much larger than the
radius R (L=20-100 R); this measuring tube has a mono-dimensional
dynamic behaviour, as a beam or a string. In fact, the vibration
mode used for the measurement comprises a movement of the axis of
the measuring tube itself. Such Coriolis flow meters according to
the prior art show a considerable pressure drop, wherein the pressure
drop is proportional to the length of the measuring tube. However,
Coriolis flow meters with shorter measuring tubes have the drawback
of an increased stiffness and thus, a higher natural frequency making
the excitation of the measuring tube more difficult and the measuring
process itself less sensitive.
[0003] Accordingly, it is the object of the invention to provide
a mass flow meter with high sensitivity and low pressure drop.
[0004] The mass flow meter according to the invention with which
the above mentioned object is achieved is characterized in that
the measuring tube is designed as a thin shell. A thin shell is
understood to be characterized by a wall thickness h much smaller
than its radius R, and a length L of the same order of magnitude
of the radius R. Such a mass flow meter according to the invention
will also be referred to as a vibrating shell flow meter in the
following.
[0005] The vibrating shell flow meter uses vibration modes with
more than one circumferential wave. These mode-shapes are described
by a figure with lobes in a cross-section of the shell. The shell
vibration is generally provided with one or more exciters and the
vibration is measured by sensors placed at different axial locations.
The phase difference or time shift between (or among) the signals
coming from the sensors are proportional to the mass flow rate.
The oscillation frequency of the shell is univocally related to
the mass density of the flow and permits an independent measurement
of the mass flow rate and mass density of the flow at the same time.
[0006] According to a preferred embodiment of the invention the
wall thickness of the measuring tube is at least by a factor of
50 smaller than the radius of the measuring tube. Further, the wall
thickness of the measuring tube is preferably equal to or less than
0.5 mm, most preferably equal to or less than 0.25 mm. The ratio
of the length of the measuring tube relative to the radius of the
measuring tube is preferably equal to or less than 6 most preferably
equal to or less than 4.
[0007] According to a further preferred embodiment of the invention
at least one lumped mass is provided on the thin shell. Sensor(s)
or/and exciter(s) which are fixed to the thin shell can be used
as such lumped masses. In order to achieve best results, however,
it is preferred to use separate lumped masses, the mass of which
exactly fits the requirements.
[0008] The vibrating shell flow meter with one or more added masses
also uses vibration modes with more than one circumferential wave.
However, these are significantly modified by the added lumped masses
that are opportunely placed on the shell. These mode-shapes are
described by a figure with lobes in a cross-section of the shell
and present larger displacements at the locations of the lumped
masses. The lumped masses added to the shell, where constituted
by the sensor(s) or/and exciter(s), permit the frequency separation
of the vibration modes of the shell in order to assure that the
shell oscillation has exclusively the expected shape and permit
a significant increment of the sensitivity of the meter.
[0009] According to a further preferred embodiment of the invention
the exciter(s) is/are positioned on the anti-node(s) of the vibrating
thin shell and operate radially in- and outwardly. Preferably at
least two exciters are used wherein the exciters are fixed to the
thin shell at the same axial length of the shell but spaced apart
from each other by a predefined angle. Especially, it is preferred
that the angle is 90.degree. and the exciters are operated in phase
or that the angle is 45.degree. and the exciters are operated in
opposition of phase.
[0010] Further, it can be convenient in some applications to insert
an inner tube inside the measuring tube to make an annular flow.
Preferably the inner tube is provided centrally in the measuring
tube. With the use of an inner tube it is achieved that the effective
cross section of the measuring tube is decreased which in turn increases
the velocity of the flowing medium. Since the sensitivity of the
meter is proportional to the velocity of the flowing medium the
sensitivity is further increased.
[0011] There are numerous ways in which the mass flow meter according
to the invention can be configured and further enhanced. In this
context, reference is made to the dependent claims and to the following
description of preferred embodiments of the invention in conjunction
with the drawings, in which:
[0012] FIG. 1 is a schematic side view of a mass flow meter according
to a preferred embodiment of the invention,
[0013] FIG. 2 is a cross sectional view of the vibrating shell,
[0014] FIG. 3 is a graph showing the relationship between the receptance
and the frequency for the shell and the lumped masses, respectively,
[0015] FIG. 4 is a cross sectional view of a thin shell with an
added lumped mass,
[0016] FIG. 5a is a cross sectional view of a thin shell with two
exciters having an angle of 90.degree. relative to each other,
[0017] FIG. 5b is a cross sectional view of a thin shell with two
exciters having an angle of 45.degree. relative to each other,
[0018] FIG. 6a is a longitudinal section of a mass flow meter with
an inner tube inserted into the measuring tube, and
[0019] FIG. 6b is a cross sectional view of the mass flow meter
of FIG. 6a.
[0020] In FIG. 1 a mass flow meter according to a preferred embodiment
of the invention is shown. The mass flow meter comprises a measuring
tube 1 an exciter 2 and two sensors 3 fixed to the measuring tube
1. The measuring tube 1 is designed as a thin shell that is fixed
to the main tube 4 by welding. In some applications, conical tube
fittings can be used to connect the vibrating shell to the main
tube 4. The thin shell of the meter shown in FIG. 1 is made of titanium
and has a diameter of 25.4 mm, a wall thickness of 0.25 mm, and
a length of 90 mm. Thus, the length of the thin shell is in the
same order of magnitude as its diameter, and the ratio of the length
of the thin shell relative to its diameter is less than 4.
[0021] The vibrating shell flow meter shown in FIG. 1 uses vibration
modes of the shell with more than one circumferential wave; these
mode-shapes are described by a figure with lobes in a cross-section
of the shell, as shown in FIG. 2. Modes with more than one circumferential
wave present no movement of the shell axis. These vibration modes
are the lowest frequency modes for a shell that is not too long
and can be used to make shorter meters with respect to existing
Coriolis flow meters. The fact that the vibrating shell has a length
of the same order of magnitude of the shell radius permits the application
to measuring tubes 1 with large diameter, avoiding the problem of
very long (and expensive) Coriolis flow meters based on measuring
tube vibration. Keeping the same radius, the shorter is the length
of the shell, the larger is the number of circumferential waves
associated with the fundamental mode (which is the mode with the
lowest natural frequency) of the shell. The sensitivity of the meter,
i.e. the phase difference between signals measured by two vibration
sensors 3 placed at different axial locations, increases with the
number of circumferential waves.
[0022] The meter shown in FIG. 1 is composed by a circular cylindrical
shell, which is connected to the measuring tube 1 containing the
flow that has to be measured. It must be observed that the circular
cylindrical shell can be substituted by shells with a non-circular
cross-section or with a non-straight axis without changing the basic
mechanical behaviour of the meter.
[0023] The shell can be driven in vibrations by one or more exciters
2 even if flow-induced vibrations of the shell due to the flow
itself could be used in some meters. It seems that it is possible
to have a better behaviour of the shell flow meter if the vibration
of the fundamental mode (which is the mode with the lowest natural
frequency) of the shell is driven into vibration. However, different
modes with higher frequency can be driven into vibration, by changing
the excitation frequency, without changing the basic mechanical
behaviour of the meter.
[0024] It seems convenient that the measurement of the shell vibration
is made by two sensors 3 placed on the same generating line (parallel
to the axial flow) of the shell where is placed one of the exciters
2 (or the single exciter 2), at two different axial locations sufficiently
distant from each other. A possible configuration is shown in FIG.
1 where the sensors 3 are placed at the same distance from the
middle of the shell. It must be clarified that a different number
of sensors 3 can be used to measure the shell vibration without
changing the general working of the meter; similar results are obtained
with different positions of the sensors 3; all these solutions must
be considered as variants of the same meter. The sensors 3 can be
accelerometers, capacitive proximity sensors, optical sensors (e.g.
laser interferometers or triangulation telemeters) or any other
type of sensor that is capable of measuring the local shell displacement,
velocity or acceleration.
[0025] The vibrating shell flow meter according to the invention
is based on the fact that vibration mode-shapes of a circular cylindrical
shell (or a shell with a different form, as previously explained)
are modified by an internal (or external) flow. For an axisymmetric
shell without added masses, the fundamental mode has a symmetric
shape with respect to a middle cross-section of the shell and it
is a natural mode, that is all the points of the shell surface have
in-phase oscillation. The presence of axial flow changes the shape
of the fundamental mode, which loses the symmetry with respect to
the middle of the shell and presents a phase difference among the
oscillation of points with different axial position on the shell.
This phase difference among points with different axial position
gives a complex mode and is characteristic of gyroscopic systems.
The phase difference or the time shift necessary to reach a certain
configuration (for example the maximum amplitude of oscillation)
at a fixed axial position can be used to measure the mass flow rate.
Both phase difference and time shift increase practically linearly
with the flow rate if the measurement is made for flow velocities
far enough from the critical velocity of the shell.
[0026] The phase difference is computed between (or among) the
signals coming from the sensors 3 that measure the shell vibration.
The time shift is computed between (or among) the signals coming
from the sensors 3 for example by using a cross-correlation between
the signals. The measurement of the time shift is linear with the
mass flow rate and is independent of the fluid mass density; therefore
it is suitable to measure directly the mass flow rate.
[0027] The measurement of the mass density of the fluid can be
made by using the vibrating shell. In fact, the natural frequencies
of the shell are functions of the mass density of the still fluid;
the fluid velocity, in the range of application of the present flow
meter, practically does not change this frequency. Therefore the
measurement is independent of the flow velocity. A linear relationship
is obtained between the mass density and the reciprocal of the squared
frequency of the mode excited. Therefore an independent measurement
of the mass flow rate and mass density are obtained with the same
vibrating shell.
[0028] The proper working of the vibrating shell meter is obtained
when the vibration mode of the shell is exactly known. The exciters
can be useful in order to obtain the vibration with the expected
mode-shape. The exciters 2 (or the single exciter 2) can be controlled
in frequency in order to drive the vibration of the expected mode
for any mass density of the flowing fluid; in fact, different densities
give different natural frequencies of the shell, as previously discussed.
[0029] In order to avoid that different modes, and not only the
one expected, participate to the shell vibration it is important
to have a sufficient frequency separation between the expected mode
and the modes with closer natural frequency. A good frequency separation
between the fundamental mode and the following modes is obtained
with a good design of the shell. This operation is significantly
improved by adding appropriate lumped masses 5 to the shell as can
be seen from FIG. 4. In FIG. 4 a separate added lumped mass 5 is
shown. However, these lumped masses 5 can also be given by the sensors
3 and exciters 2 if contact sensors 3 and exciters 2 are applied
to the vibrating shell.
[0030] Favourable positions of these lumped masses 5 are on antinodes
of the driving mode, in case on the same generating line of the
shell where the sensors 3 are placed. The effect of an added lumped
mass 5 is that of moving the natural frequencies of the shell to
smaller values; this decrement of the natural frequency is much
larger for the fundamental mode with respect to the following modes;
this phenomenon can also be seen from FIG. 3 where the receptances
(vibration amplitude/force) of the shell (s) and a lumped mass (m)
are shown. The intersections between the receptances of the shell
and the lumped mass 5 give the natural frequencies of the shell
with added lumped mass 5; the original natural frequencies of the
shell are the vertical asymptotes in the shell receptance.
[0031] Another advantage given by lumped masses 5 added to the
vibrating shell is the possibility to have an increment of the sensitivity
of the meter. For example, added masses on the same generating line
(of a circular cylindrical shell) of the sensors 3 that measure
the shell vibration can give a significant increment to the phase
difference (i.e. to the sensitivity). Also the axial position of
the lumped masses 5 is important. For example, lumped masses 5 placed
in correspondence of the points where the shell vibration is measured
can increase significantly the sensitivity of the meter.
[0032] As already stated above, in FIG. 4 a cross sectional view
of a thin shell with a lumped mass 5 is shown. It can be seen that
the vibration mechanics of a shell with added lumped masses 5 is
very different with respect to the one of the shell without added
masses (compare FIGS. 2 and 4). In fact, the mode-shapes of the
shell are significantly modified by connection with lumped masses
5 so they become different with respect to mode-shapes of the shell
without masses. Moreover, the symmetry is lost if only one or an
odd number of lumped masses 5 is used.
[0033] FIGS. 5a and b show cross sectional views of a thin shell
with two exciters 2 which are fixed to the shell at the same axial
length but with a predefined angle relative to each other. In both
cases the exciters 2 are fixed on antinodes of the driving mode.
However, according to the embodiment shown in FIG. 5a, the exciters
2 are fixed to the thin shell with an angle of 90.degree. relative
to each other, and according to the embodiment shown in FIG. 5b
the exciters 2 are fixed to the thin shell with an angle of 45.degree.
relative to each other. Thus, according to the first arrangement,
the exciters 2 are operated in phase, wherein according to the second
arrangement, the exciters 2 are operated in anti-phase.
[0034] From FIGS. 6a and b a mass flow meter according to a preferred
embodiment of the invention in a longitudinal and a cross sectional
view, respectively, can be seen that comprises an inner tube 6 inserted
into the measuring tube 1. Thus, the effective cross section for
the flowing medium (indicated by arrows from the left) is decreased,
increasing the sensitivity of the meter as explained further above.
[0035] The meters with vibrating shell, object of the present invention,
can also be inserted in an annular or unbounded flow, and are not
only suitable to contain an internal flow. The behaviour of the
meter is substantially unchanged. In application with the meter
immersed in the flow, the sensors and exciters will be placed at
the opposite side of the shell skin with respect to the surface
in contact with the flow. |