Abstrict 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. 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 What is claimed is:
1. 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 wherein the
measuring tube is designed as a thin shell, and an inner tube is
provided inside the measuring tube to make an annular flow.
2. The mass flow meter according to claim 1 wherein the measuring
tube has a wall thickness which is much smaller than the radius
of the measuring tube, and a length of the same order of magnitude
as the radius.
3. The mass flow meter according to claim 1 or 2 wherein the wall
thickness of the measuring tube is smaller than the radius of the
measuring tube at least by a factor of 50.
4. The mass flow meter according to claim 1 or 2 wherein the wall
thickness of the measuring tube is equal or less than 0.5 mm, preferably
equal to or less than 0.25 mm.
5. The mass flow meter according to claim 1 or 2 wherein the ratio
of the length of the measuring tube relative to the radius of the
measuring tube is equal to or less than 6 preferably equal to or
less than 4.
6. The mass flow meter according to claim 1 or 2 wherein the inner
tube is provided centrally in the measuring tube.
7. 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 wherein the
measuring tube is designed as a thin shell, the measuring tube has
a length of the same order of magnitude of the radius, and the wall
thickness of the measuring tube is smaller than the radius of the
measuring tube at least by a factor of 50.
8. The mass flow meter according to the claim 7 wherein the wall
thickness of the measuring tube is equal or less than 0.5 mm, preferably
equal to or less than 0.25 mm.
9. The mass flow meter according to claim 7 or 8 wherein the ration
of the length of the measuring tube relative to the radius of the
measuring tube is equal to or less than 6 preferably equal to or
less than 4.
10. The mass flow meter according to claim 7 or 8 wherein at least
one added lumped mass is placed on the measuring tube.
11. The mass flow meter according to claim 10 wherein the lumped
mass is provided on an anti-node of the driving mode.
12. 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 wherein the
measuring tube is designed as a thin shell, the wall thickness of
the measuring tube is smaller than the radius of the measuring tube
at least by a factor of 50 the wall thickness of the measuring
tube is equal to or less than the 0.5 mm, and the ratio of the length
of the measuring tube relative to the radius of the measuring tube
is equal to or less than 6.
13. The mass flow meter according to claim 12 wherein at least
one added lumped mass is placed on the measuring tube.
14. The mass flow meter according to claim 13 wherein the lumped
mass is provided on an anti-mode of the driving mode.
Description BACKGROUND OF THE INVENTION
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.
Generally, the existing Coriolis flow meters are based on vibrations
of a to 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.
SUMMARY OF THE INVENTION
Accordingly, it is the object of the invention to provide a mass
flow meter with high sensitivity and low pressure drop.
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.
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.
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.
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.
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.
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.
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.
BRIEF DESCRIPTION OF THE DRAWINGS
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:
FIG. 1 is a schematic side view of a mass flow meter according
to a preferred embodiment of the invention,
FIG. 2 is a cross sectional view of the vibrating shell,
FIG. 3 is a graph showing the relationship between the receptance
and the frequency for the shell and the lumped masses, respectively,
FIG. 4 is a cross sectional view of a thin shell with an added
lumped mass,
FIG. 5a is a cross sectional view of a thin shell with two exciters
having an angle of 90.degree. relative to each other,
FIG. 5b is a cross sectional view of a thin shell with two exciters
having an angle of 45.degree. relative to each other,
FIG. 6a is a longitudinal section of a mass flow meter with an
inner tube inserted into the measuring tube, and
FIG. 6b is a cross sectional view of the mass flow meter of FIG.
6a.
DESCRIPTION OF THE PREFERRED EMBODIMENT
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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. |