Abstrict An ultrasonic flow meter has two ring-shaped piezoelectric transducers
(1 2) comprising ring-shaped piezoelectric elements or being composed
of piezoelectric sections. Both the transducers (1 2) are arranged
in axial symmetry in a distance to each other. One of them is operated
as the ultrasonic transmitter and the other one as ultrasonic receiver.
The medium, the flow rate of which is to be measured, flows through
both the transducers (1 2) essentially parallel to the axis (L--L).
Claims I claim:
1. Ultrasonic flow meter, comprising two ring-shaped piezoelectric
transducers which have ring-shaped piezo elements, the transducers
being spaced to each other in axial symmetry and one of them being
operated as an ultrasonic transmitter and the other one as an ultrasonic
receiver, a medium, the flow rate of which is to be measured, flows
through both the transducers essentially parallel to the symmetry
axis of the transducer, wherein an output voltage of the transducer
operated as the ultrasonic receiver is fed back to the transducer
operated as the ultrasonic transmitter after amplification.
2. Ultrasonic flow meter according to claim 1 wherein each transducer
is surrounded by a separate transducer housing.
3. Ultrasonic flow meter according to claim 1 wherein both the
transducers are integrated into the wall of a cylindrical pipe,
the longitudinal axis of said cylindrical pipe coincides with the
common axis of the transducers and wherein the pipe cross section
at the positions of the transducers is the same as in the remainder
of the cylindrical pipe.
4. Ultrasonic flow meter according to claim 3 wherein both the
transducers are acoustically decoupled from the wall of the cylindrical
pipe by the transducer being embedded into soft material.
5. Ultrasonic flow meter according to claim 3 characterised in
that both the transducers are arranged inside said cylindrical pipe,
which is provided with connecting elements at its ends for the connection
to a pipe system.
6. Ultrasonic flow meter according to claim 1 wherein both the
transducers have substantially identical physical properties and
wherein for self-excitation of the system in a radially oscillating
mode of the transducers the relation
holds between the axial distance d between both the transducers
and the sound wavelength .lambda., where n is a natural number and
for .delta. the iteratively solvable equation
holds, where a is the inner radius of the transducers.
7. Ultrasonic flow meter according to claim 6 wherein the flow
velocity v of the medium results from the relation
wherein f.sub.0 is the ultrasonic frequency at self-excitation
with the medium being at rest, which has the velocity of sound c,
where .DELTA.f is the frequency tune shift at self-excitation in
the medium with the flow velocity v and where .lambda..sub.0 =c/f.sub.0
is the sound wavelength for which d is determined according to claim
6.
8. Ultrasonic flow meter according to claim 6 wherein both the
transducers are operated in self-excitation close to a resonant
frequency of a radially oscillating mode.
9. Ultrasonic flow meter according to claim 8 wherein the resonant
curve is broadened.
10. Ultrasonic flow meter according to claim 1 wherein each of
the transducers is selectively operable as an ultrasonic transmitter
or as an ultrasonic receiver.
11. Ultrasonic flow meter, comprising two ring-shaped piezoelectric
transducers which are composed of piezoelectric sections, both the
transducers being spaced to each other in axial symmetry and one
of them being operated as an ultrasonic transmitter and the other
one as an ultrasonic receiver, wherein a medium, the flow rate of
which is to be measured, flows through both the transducers essentially
parallel to the symmetry axis of the transducer, and an output voltage
of the transducer operated as the ultrasonic receiver is fed back
to the transducer operated as the ultrasonic transmitter after amplification.
12. Ultrasonic flow meter according to claim 11 wherein both the
transducers have essentially identical physical properties and wherein
for self-excitation of the system in a radially oscillating mode
of the transducers the relation
holds between the axial distance d between both the transducers
and the sound wavelength .lambda., where n is a natural number and
for .delta. the iteratively solvable equation
holds, where a is the inner radius of the transducers.
13. Ultrasonic flow meter according to claim 12 wherein the flow
velocity v of the medium results from the relation
where f.sub.0 is the ultrasonic frequency at self-excitation with
the medium being at rest, which has the velocity of sound c, where
.DELTA.f is the frequency tune shift at self-excitation in the medium
with the flow velocity v and where .lambda..sub.0 =c/f.sub.0 is
the sound wavelength for which d is determined according to claim
12.
14. Ultrasonic flow meter according to claim 12 wherein both the
transducers are operated in self-excitation close to a resonant
frequency of a radially oscillating mode.
15. Ultrasonic flow meter according to claim 14 wherein the resonant
curve is broadened.
16. Ultrasonic flow meter according to claim 11 wherein each transducer
is surrounded by a separate transducer housing.
17. Ultrasonic flow meter according to claim 11 wherein both the
transducers are integrated into the wall of a cylindrical pipe,
the longitudinal axis of said cylindrical pipe coincides with the
common axis of the transducers and wherein the pipe cross section
at the positions of the transducers is the same as in the remainder
of the cylindrical pipe.
18. Ultrasonic flow meter according to claim 17 wherein both transducers
are embedded in soft material to acoustically decouple the transducers
from the wall of the pipe.
19. Ultrasonic flow meter according to claim 17 wherein both transducers
are arranged inside said cylindrical pipe, which is provided with
connecting elements at its ends for connection to a pipe system.
20. Ultrasonic flow meter according to claim 11 wherein each of
the transducers is selectively operable as an ultrasonic transmitter
or as an ultrasonic receiver.
Description The invention relates to an ultrasonic flow meter for the measurement
of the flow rate of gaseous or liquid media.
BACKGROUND OF THE INVENTION
For industrial applications the measurement of the flow rate of
gases or liquids in tubing systems is of big importance. Most of
the existing measurement systems utilize the liquid or gas flow
to drive a wheel with its number of turns per unit time being proportional
to the flow rate. These systems however lack reliability over longer
time periods.
Other known measurement systems apply ultrasound. Here the phase
shift of an ultrasonic wave introduced by a flowing medium is a
measure of the flow velocity of the medium. Usually an ultrasonic
transmitter and an ultrasonic receiver are mounted in a tubing system
with a given angle with respect to the tube axis. A corresponding
example is described in EP 0 040 837 A1. Such systems have a rather
complex geometry and suffer from the additional disadvantage that
the measuring accuracy will be deteriorated because the phase shift
depends on the cosine of the given angle which is different from
0 degrees.
Principally the flow velocity of a medium may as well be determined
from the time delay of ultrasound from an ultrasonic transmitter
to an ultrasonic receiver where the transmitter is operated in the
pulsed mode.
BRIEF DESCRIPTION OF THE INVENTION
It is an object of the present invention to provide an ultrasonic
flow meter with a simple geometry which allows a high measurement
accuracy.
The ultrasonic flow meter according to the present invention has
two ring-shaped piezoelectric transducers, one of which is operated
as the ultrasonic transmitter and the other one as the ultrasonic
receiver. Both transducers are mounted with a spacing in between
and with their symmetry axes coinciding. Thus a complete axial symmetry
has been realized. The angle mentioned above is zero degrees so
that an optimum measurement accuracy is achieved.
Each of the transducers may be encapsulated into a separate transducer
housing. On the one hand this allows protection against influences
from the flow medium. On the other hand a transducer housing allows
the additional placement of material for acoustic decoupling and
the mounting of a damping ring surrounding the respective ring-shaped
piezoelectric transducer.
In a preferred layout both the transducers are integrated into
the wall of a cylindrical pipe (either directly or under application
of a separate transducer housing) with its longitudinal axis coinciding
with the common transducer axis. With this design the pipe cross
sectional area at the transducer positions is not reduced. The ultrasonic
flow meter therefore does not comprise an additional flow resistance
to the medium.
Preferably both the transducers are mounted in a short pipe section
which is supplied with connecting elements at its ends for the connection
to the pipe system. These connecting elements may be e.g. flanges
or sleeves of the kind provided for the given tubing system. Thus
a compact component is available which may be mounted into a given
tubing system without great effort.
The ultrasonic flow meter according to the present invention is
preferably operated in self-excitation where the output voltage
of the ultrasonic transducer operated as the receiver--after having
been amplified --is fed back to the ultrasonic transducer operated
as the transmitter. Details result from the following description.
Alternatively the ultrasonic transducer operated as the receiver
is switched to measure the delay time of the ultrasound after pulsed
excitation of the ultrasonic transducer operated as the transmitter.
The delay time measurement is advantageous in the case of distortions
of the system due to external sound coupled into the tubing system
and into the housing. In this case the short run time through the
tubing system or housing can be separated from the longer run time
through the medium by means of an electronic gate.
DESCRIPTION OF THE DRAWINGS
In the following the invention will be further explained by way
of example with reference to the accompanying drawings, wherein:
FIG. 1 shows an axial section through a piece of pipe, into which
two piezoelectric transducers are integrated,
FIG. 2 shows an axial section through a piezoelectric transducer
which is surrounded by a separate transducer housing, and
FIG. 3 shows a sketch for the illustration of the symbols applied
within the formulae.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
As shown in FIG. 1 a ring-shaped piezoelectric transducer 1 and
a ring-shaped piezoelectric transducer 2 are arranged, at a distance
to each other with their axes of symmetry coinciding. The transducers
1 and 2 may each have ring-shaped piezoelectric elements or may
consist of piezoelectric sections. Both the transducers 1 2 are
located in a pipe section 3 through which the liquid or gaseous
medium, the flow rate of which is to be determined, flows in the
direction of the longitudinal axis L--L. The flow cross section
is circular. The common axis of rotational symmetry of the transducers
1 2 coincides with the longitudinal axis L--L.
Both the transducers 1 2 are embedded into the wall 4 of the pipe
section 3 in the same manner. A soft material 5 e.g. foam, serves
as acoustical decoupling material between the transducers 1 2 and
the wall 4. The electrical connections 6 of the transducers 1 2
are led through the wall 4 to the outside in a sealed manner. They
may be simple wire conductors or thin copper sheets.
An alternative layout consists in the transducers 1 2 not directly
being integrated into the wall 4 of the pipe section 3 but rather
each of the transducers 1 2 being surrounded by a separate transducer
housing. FIG. 2 shows how the transducer 1 is arranged in such a
ring-shaped transducer housing 10. A preferably soft decoupling
material 11 serves as acoustic decoupling and directly on its outer
periphery the transducer 1 is surrounded by a damping ring 12. The
electrical connections 6 are led to the outside in a sealed manner.
The transducer housing 10 may consist of e.g. a stainless metal,
ceramic or plastic material. Also a metal-ceramic design is possible.
Preferably the arrangements for the transducer 1 and for the transducer
2 are identical.
In the layout with separate transducer housings the transducers
1 and 2 with their transducer housings are preferrably inserted
into the pipe section 3 in such a way that no parts jut out into
the inner pipe. In addition to the decoupling material 11 in the
inner of the transducer housing further decoupling measures may
be provided for between the outer side of the transducer housing
and the pipe section 3 e.g. soft material 5 which is arranged
in a way similarly to FIG. 1 in order to avoid that the pipe section
3 takes part in the propagation of the ultrasonic sound field. A
proper decoupling may for example also be achieved by damping the
pipe section 3 itself between the transducers 1 and 2 with known
methods.
The pipe section 3 is provided with a flange 7 and a flange 8 at
its ends. The flow sensor consisting of the pipe section 3 and both
the transducers 1 2 may therefore without great effort be integrated
into an existing pipe system, in which flanges are customary.
Different manufacturing possibilities are envisioned. So the transducers
1 2 may be moulded into the pipe, section 3 may consist of plastic
material. Alternatively the system could be glued from prefabricated
ring-shaped sections. Such prefabricated ring-shaped sections may
be manufactured from various metallic or nonmetallic materials.
Ceramic material with a metal ceramic sealing is envisioned. In
order that the transducers 1 2 which preferably consist of piezoceramic
material should not come into contact with the flow medium, they
may be covered with a protectional layer. Besides that the separate
transducer housings mentioned already allow protection against contact
with the flow medium.
Since the transducers 1 2 do not jut out into the inner space
of the pipe section 3 they do not present an obstacle for the flow
medium so that its flow velocity will practically not be changed
by the transducers 1 2.
The ultrasonic flow meter has a high sensitivity if the transducers
1 2 are operated in self-excitation (especially if this occurs
close to a resonant frequency, see below), which will be explained
in more detail in the following.
FIG. 3 illustrates the ring-shaped geometry of the system with
both the transducers 1 2 in a perspective view. The transducer
1 is operated as an ultrasonic transmitter and the transducer 2
as an ultrasonic receiver. The distance r between a source point
Q at the inner surface of the transducer 1 which has the inner
radius a (as has the transducer 2), and a field point P at the inner
surface of transducer 2 may be derived from FIG. 3 as ##EQU1## d
is the distance between the transducers 1 2. Application of trigonometric
relations leads to a transformation of eq. (1) into ##EQU2##
Now transducer 1 operated as the ultrasonic transmitter will be
assumed to oscillate in a pure radial mode with the complex velocity
amplitude v.sub.0 above a given cutoff frequency which depends on
the diameter of the pipe section 3. (Below the cutoff frequency
no transverse but rather longitudinal waves exist propagating as
plane waves along the pipe section 3. ) Then the sound field inside
the medium with the density .rho. may be described by the complex
pressure amplitude p as ##EQU3##
see Cremer, L. Hubert, M., "Vorlesungen uber Technische Akustik",
4. Auflage Springer, Berlin 1990 eq. 2-217 p. 178. Here the wave
number k is the quotient of the angular frequency .omega. of the
transmitter and the sound velocity c in the medium under consideration:
##EQU4##
The integration has to be extended across the surface S of the
total sound field area under consideration. Assuming rigid walls
with v.sub.0 =0 everywhere on this surface except on the inner surface
of the piezoelectric ring operated as the ultrasonic transmitter,
the integration has to be extended across the inner ring surface
of transducer 1 only.
To a first approximation the radius a may be assumed to be small
compared to the distance d between the transducers 1 and 2 (see
FIG. 3):
The integrand of eq. (3) may then be expanded into a Taylor's series
which with eq. (2) under consideration of first order terms leads
to: ##EQU5##
For the pressure field it follows from eq. (3): ##EQU6##
After having performed the integration one receives: ##EQU7##
This result may easily be interpreted: A sound wave propagating
in the axial direction from the ultrasonic transmitter 1 to the
ultrasonic receiver 2 placed at a distance d undergoes a phase delay
being composed of the expected phase delay kd plus the correction
term ##EQU8## which under the assumption according to eq. (5) may
approximately be expressed as ##EQU9##
This correction terms summarizes the path length differences between
all the source points on the ultrasonic transmitter ring 1 and a
field point on the ultrasonic receiver ring 2. The correction is
smaller the larger the distance d between the transducers 1 and
2 is compared to the inner radius a of the ring-shaped transducers
1 and 2.
The pressure field observed at the ultrasonic receiver 2 will be
transformed into a corresponding output voltage since the ultrasonic
receiver is a piezoelectric transducer. This signal as a feed back
signal will now be amplified and fed back to the piezoelectric transducer
1 operated as the ultrasonic transmitter. This may lead to a self-excitation
of the system under the condition that the phase difference between
the input voltage of the ultrasonic transmitter and the output voltage
of the ultrasonic receiver is zero or an integer multiple of 2.pi..
This total phase difference consists of two contributions, the one
due to the sound propagation and the other one from the sum of the
internal phase shifts of the ultrasonic transmitter and receiver,
respectively. The latter vanishes if both the transducers 1 and
2 have the same physical properties. This may be achieved, e.g.,
by selecting them as pairs manufactured under the same conditions.
A further embodiment uses a pair of an ultrasonic transmitter and
an ultrasonic receiver with the same properties by cutting a piezoelectric
ring into two half rings. Then one of these half rings may be operated
as the ultrasonic transmitter and the other one as the ultrasonic
receiver.
To achieve self-excitation of the system therefore the phase shift
due to the sound propagation has to be an integer multiple of 2.pi..
Taking into account eqs. (8), (9) and (10) the following condition
for the axial distance d between the ultrasonic transmitter and
the ultrasonic receiver, for which at a given angular frequency
.omega.=c k self-excitation occurs, may be derived: ##EQU10##
With the addition theorem for the tangent function it follows ##EQU11##
Eq. (13) may be solved for d iteratively. For this purpose the
correction term .delta. will be defined by
where .lambda.=2 .pi./k is the wavelength of the ultrasound and
n is a natural number. From eqs. (13) and (14) the iteration condition
##EQU12## follows.
In the following a numerical example of the iteration process will
be presented for two different values of n.
The ultrasonic frequency f=.omega./(2.pi.) is assumed to be 150
kHz in each case and the velocity of sound c 1400 m/s leading to
a sound wave length .lambda. of 9.330.degree.10.sup.-3 m; for a
value of 0.01 m has been assumed. The starting value for .delta.
in both cases is assumed to be -2.degree.10.sup.-3 m. The following
table shows four iterational steps to be sufficient: ##EQU13##
The derivation given above is valid for any ultrasonic frequency.
However the system works especially efficiently if both the transducers
1 and 2 are operated close to a resonant frequency. Namely at the
resonant frequency the electrical power will be optimally transformed
into sound field power and vice versa. This will once more be illustrated:
The self-excitation of the closed loop system consisting of transmitter,
sound propagation path, receiver and electrical feed back including
the amplifier has to be distinguished from the resonant frequency
of the transducers. Principally self-excitation is possible at any
ultrasonic frequency if additionally the phase condition in the
sound field is fulfilled and a sufficient amplification is guaranteed.
However especially preferable is the selection of a self-excitation
frequency which coincides with the transducer resonant frequency.
Namely in this case a small amount only of amplification in the
electrical signal feed back path is required.
In practice the parameters for an ultrasonic transmitter-receiver
pair may be determined according to the following scheme:
Selection of a proper eigenmode (radial oscillation) of the piezoelectric
system, where both the transducers 1 and 2 have the same properties.
From this the operating frequency at self-excitation results as
the eigenfrequency; the sum of the internal phase delays vanishes.
Selection of the natural number n, i.e. the number of wavelengths
between ultrasonic transmitter and receiver.
Determination of the correct distance d by application of eq. (14).
Until now the medium in which the sound waves propagate between
ultrasonic transmitter and ultrasonic receiver has been assumed
to be at rest. Now a constant flow velocity v will be considered
which is a measure of the flow rate.
In the case of a moving medium the propagation velocity of the
ultrasound increases or decreases depending on whether the direction
of the sound field propagation is in the direction of the flow velocity
or opposite to it. If operating with a fixed sound field frequency,
the wavelength changes, resulting in a phase shift. Assuming the
system to be tuned to self-excitation with the medium at rest, where
f.sub.0 is the ultrasonic frequency of an eigenmode as explained
before, the system would be detuned at a nonvanishing flow velocity,
since the phase condition according to eq. (14) is no longer fulfilled.
If however another sound field frequency will be selected as to
keep the wavelength .lambda. fixed at the value .lambda..sub.0 under
consideration of eq. (14), the system may be held in the state of
self-excitation even for nonvanishing flow velocity. The corresponding
condition may be expressed as ##EQU14## where .DELTA.f is the frequency
shift. From eq. (16) it follows ##EQU15##
For a narrow resonant curve of the transducers 1 and 2 i.e. for
a pronounced maximum, the frequency shift leads to an operating
point off the maximum so that the oscillation amplitude of the transducers
1 2 would rapidly decrease for a flow measurement. For a stable
operation under self-excitation conditions this is problematic,
also if an amplifier will be applied. A proper countermeasure exists
in an enhanced bandwidth of the system, i.e. a broadening of the
resonant curve which is e.g; achievable if transducer housing and
attached mechanical components (see e.g. FIG. 2) have resonances
close to the selected resonance of the piezoelectric components.
In this case the resonant curve behaves as that of coupled resonators.
For a flat resonant curve sufficient damping is required.
The proper tune shift .DELTA.f will be automatically established
by the system since the closed transmitter-sound path-receiver system
tends to keep the state of self-excitation in order to fulfill the
phase condition. This is the case if the system operates at the
tune shift corresponding to the flow velocity v.
Until here the velocity of sound has been assumed to be constant
or to depend on the flow velocity of the medium, respectively.
In practice, however, this will be correct for a constant temperature
only. Deviations from this temperature cause changes in the velocity
of sound resulting in additional phase changes. To compensate for
this effect, the frequency has to be further tuned in order to keep
the state of self-excitation. In practice, the tune shift due to
temperature effects often exceeds that due to the flow velocity.
However the temperature effect may be compensated for by measuring
in both directions of sound propagation, i.e. parallel and antiparallel
to the direction of flow and then taking into account the difference
of the tune shifts. The bandwidth has to cover the sum of the tune
shifts according to the temperature and the flow velocity.
In order to measure in both directions, each of the transducers
1 2 has to be operated selectively as ultrasonic transmitter and
as ultrasonic receiver. Whereas--as assumed until now--the transducer
1 operates as the ultrasonic transmitter and transducer 2 as the
ultrasonic receiver, their roles will be interchanged for the measurement
in the opposite direction. This may be achieved by proper circuit
means known to the skilled person.
The flow velocity v of the medium is a measure of the flow rate.
To deduce the mass of the medium passing the region of the transducers
1 2 per unit time, the flow velocity has to be multiplied by the
density of the medium and the cross sectional area. If the flow
velocity is not constant across the cross section the dependence
of the flow rate on the measured tune shift may be determined by
calibration measurements.
A further possibility for determining the flow velocity of the
flowing medium exists in measuring the delay time an ultrasonic
pulse needs to travel from the ring-shaped piezoelectric transducer
operated as the ultrasonic transmitter to the ring-shaped piezoelectric
transducer operated as the ultrasonic receiver. For a known distance
between the transducers the delay time is a measure of the propagation
velocity of the ultrasound depending on the flow velocity and the
flow direction.
In contrast to the method of self-excitation, which requires a
quasistationary operation periodic in time, the delay time measurement
operates in the pulsed mode. This offers the advantage to discriminate
between the sound propagation inside the walls of the pipe section
and the sound propagation through the flowing medium to be measured
by electronic means with the help of a gate. Further advantages
are due to the clear separation possibilities against distortions,
e.g. by sound radiation from outside or from reflexions of ultrasonic
waves. A delay time measurement is also advantageous in the case
of nonsufficient acoustic decoupling between transducers and pipe
section or housing.
Temperature effects may--similarly to what has already been described
for the self-excitation method--be eliminated by parallel and antiparallel
measurements with respect to the flow direction of the medium to
determine the time delay difference where the roles of ultrasonic
transmitter and receiver have to be interchanged. |