EP1409968A1 - Device and method for measuring mass flow of a non-solid medium - Google Patents

Device and method for measuring mass flow of a non-solid medium

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Publication number
EP1409968A1
EP1409968A1 EP01272129A EP01272129A EP1409968A1 EP 1409968 A1 EP1409968 A1 EP 1409968A1 EP 01272129 A EP01272129 A EP 01272129A EP 01272129 A EP01272129 A EP 01272129A EP 1409968 A1 EP1409968 A1 EP 1409968A1
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EP
European Patent Office
Prior art keywords
sensing elements
sensors
sensing
frequency
mass flow
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EP01272129A
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German (de)
French (fr)
Inventor
Gabor Endroczi
Sandor Kun
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Individual
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Individual
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Publication of EP1409968A1 publication Critical patent/EP1409968A1/en
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Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01FMEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
    • G01F1/76Devices for measuring mass flow of a fluid or a fluent solid material
    • G01F1/78Direct mass flowmeters
    • G01F1/80Direct mass flowmeters operating by measuring pressure, force, momentum, or frequency of a fluid flow to which a rotational movement has been imparted
    • G01F1/84Coriolis or gyroscopic mass flowmeters
    • G01F1/8409Coriolis or gyroscopic mass flowmeters constructional details
    • G01F1/8413Coriolis or gyroscopic mass flowmeters constructional details means for influencing the flowmeter's motional or vibrational behaviour, e.g., conduit support or fixing means, or conduit attachments
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01FMEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
    • G01F1/76Devices for measuring mass flow of a fluid or a fluent solid material
    • G01F1/78Direct mass flowmeters
    • G01F1/80Direct mass flowmeters operating by measuring pressure, force, momentum, or frequency of a fluid flow to which a rotational movement has been imparted
    • G01F1/84Coriolis or gyroscopic mass flowmeters
    • G01F1/845Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits
    • G01F1/8468Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits vibrating measuring conduits
    • G01F1/849Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits vibrating measuring conduits having straight measuring conduits
    • G01F1/8495Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits vibrating measuring conduits having straight measuring conduits with multiple measuring conduits

Definitions

  • the present invention relates to a device, in particular to a combined device for measuring mass flow of a non-solid medium.
  • the nonzero angular velocity ⁇ of the flowing medium is provided, in particular, by exciting, i.e.
  • the apparatus comprises a pair of straight parallel sensing tubes equal in length provided with Y-shaped elements at the opposite ends thereof to assure the inflow and the outflow of the flowing medium to be studied, drive means for oscillating said sensing tubes towards and away from each other at a selected frequency in a transverse direction, wherein the drive means are arranged substantially at the midpoints of the sensing tubes, and further at least one sensor attached to the sensing tubes at a point spaced from both the opposite ends of sensing tubes and the location of the drive means.
  • phase shift is proportional to the rate of the mass flow under study according to the aforementioned.
  • U.S. Patent No. 4,823,614 issued to Dahlin et al. describes a further Coriolis-type mass flowmeter, wherein the sensing tube (for certain embodiments two sensing tubes) is (are) excited (oscillated) transversally in a higher anti-symmetric mode at a driving frequency equal to a natural frequency of the sensing tube, and by means of sensors arranged symmetrically on the sensing tube at equal distances from its midpoint, the actual values of one of the motion quantities characteristic to the vibration of the sensing tube are measured in the position of the sensors. Then the thus obtained two electronic signals are led into a processing unit, on the output of which an outgoing signal proportional to the mass flow rate is obtained as a result of operations applied to the incoming electronic signals.
  • time dependence of the driving signal is chosen to be sinusoidal, i.e. a harmonic excitation is used.
  • the frequency of the excitation i.e. the driving frequency
  • the frequency of the excitation is equal to a natural frequency of the sensing tube. Therefore, the mass flow rate is always measured at a natural frequency of the sensing tube for Coriolis-type methods and apparatuses known.
  • the reason behind this is, that the values of motion quantities are of maximum in this case; the effect of the Coriolis force appearing as a result of the oscillation is so small for an excitation at a driving frequency different from the natural frequency, that the measurement thereof would lead to an extremely low signal-to-noise ratio, which in turn would have a significant influence on the accuracy of the mass flow rate measured.
  • Coriolis-type mass flowmeters Another disadvantage of the Coriolis-type mass flowmeters is, besides the drawback of being reliably operable only at natural frequency, that the results they yield can be considered to be reliable only for relatively high current rates.
  • An increase in current rate can be reached eg. by decreasing the diameter of the tube containing the flowing medium.
  • the diameter of the tube cannot be reduced to an arbitrary extent, as the so far generally laminar flow of medium becomes turbulent if a critical current rate is reached.
  • a further drawback of the above mass flowmeters comprising straight sensing tube(s) is, that it/they suffers/suffer a longitudinal change of size due to the change in temperature of the medium flowing therethrough or of the surroundings, as a consequence of which the driving frequency shifts away from the natural frequency of the sensing tube(s).
  • the shift concerned should be always compensated.
  • the compensation is obtained by fabricating the sensing tube(s) from materials exhibiting a heat expansion coefficient negligible in value. This, however, leads to a significant increase in fabrication costs of the mass flowmeters of this type.
  • a mass flow also has, besides the Coriolis-force, further effects on the measuring elements, preferably in the form of sensing tubes arranged parallel in a flowing medium (i.e. in the mass flow) and excited (i.e. made to vibrate) transversally.
  • the third term represents the so-called Coriolis-term proportional to the mass flow pAv
  • the remaining second term gives the force required to displace the flowing medium. It can be seen from the expression of the second term, that the force represented thereby is also proportional to the mass flow pAv. Hence, the mass flow rate can be determined by measuring the second term.
  • literature see eg. Flow-Induced Vibration by R.D.
  • the second term relates to a damping occurring as a "structural damping" due to the mass flow, wherein the damping at issue can be easily determined via measuring the mechanical impedance.
  • a mass flowmeter is available that operates on a principle being different from the measurement of the effects of the Coriolis force.
  • the mechanical impedance is defined as a complex ratio of the external excitation (eg. driving force) and the response (eg. velocity measured at a given point) given thereto.
  • the phase difference between the external excitation and the response given thereto at the natural frequency is constant, independently on damping, and hence the effect of mass flow exerted on the structural damping cannot be determined in a measurement performed at the natural frequency.
  • at least two sensing tubes of different lengths and hence of different natural frequencies should be used in the measurement, wherein all the sensing tubes have to be subjected to an external excitation having a frequency equal to a natural frequency of one of the sensing tubes.
  • the mechanical impedance should be measured, in particular, on the sensing tube that is excited at a frequency different from its natural frequency.
  • Hungarian Patent No. 219,251 discloses a (temperature) compensated device for measuring the mass flow comprising sensing elements, preferably in the form of straight sensing tubes extending parallel both to the mass flow under study and to each other, vibration means and a sensor for measuring the mechanical impedance.
  • Sensing elements of the device at issue are of different lengths, the driving frequency of the vibration means is equal to the natural frequency of one of the sensing elements, and the mechanical impedance sensor is arranged on the sensing element that is characterized by a natural frequency different from the driving frequency.
  • 219,251 also describes a method for measuring mass flow, wherein the sensing elements are provided with different lengths and during the flow of the medium to be studied therethrough the sensing elements are excited transversally by means of vibration means at a driving frequency equal to the natural frequency of one of the sensing elements, and mechanical impedance is measured by means of a sensor arranged on the sensing element characterized by a natural frequency different from the driving frequency.
  • the mass flow rate is determined from the phase difference relative to the excitation of the mechanical impedance measured.
  • a non-solid medium flowing through a sensing element has an influence on the mode shape of the sensing element and hence on the measured value of the actual mass flow rate through a damping that occurs as the result of the viscosity of the medium.
  • the application of such a mass flowmeter of the mechanical impedance type is required, that has at least four sensing elements, preferably in the form of straight sensing tubes, of different lengths in pairs and hence having different natural frequencies in pairs.
  • Hungarian Patent Application No. P 9900544 describes a mass flowmeter accordant to the above requirements, and a method for a simultaneously temperature and viscosity compensated direct measurement of mass flow rate.
  • the aim of the present invention is to provide a combined mass flowmeter that enables to perform mass flow measurements with the highest precision possible for arbitrary mass flow rates, and is compensated with regard to the effects of the medium to be studied.
  • Another aim of the present invention is to develop a novel method for measuring the mass flow of a non-solid medium.
  • the phase difference between the excitation and the response given thereto has a constant value at the natural frequency independently of damping, therefore the measurement of the mass flow can be effected only at a frequency being apart from the natural frequency with a given constant relative distance. Accordingly, the problem of providing the excitation and the measurement of the phase simultaneously at a given frequency differing from the natural frequency is of great emphasis for the flowmeters aimed by the present invention. This can be reached with such sensing elements only that have different natural frequencies. This in turn means, that the natural frequencies of the pairs of sensing elements, realised preferably in the form of pairs of sensing tubes should be set to different values in this particular case.
  • the effect of the Coriolis force is maximal in those points of the sensing tubes, where the periodic change of the angular velocity of mass flow is the greatest, i.e. at the so-called nodal points.
  • nodal points For the person skilled in the art it is obvious, that in case of sensing elements of equal lengths, for keeping positions of nodal points in the same distance from each other, for ensuring different natural frequencies and for assuring energy input by excitation simultaneously extremely delicate technical solutions are required.
  • the mass flow alters, generally to a negligible extent only, the natural frequencies of the sensing elements made to vibrate, and the flowing medium (i.e. the mass flow) moreover influences the mode shape of the sensing elements and the damping being present in the system under excitation.
  • characteristic properties of the system excited first of all the natural frequency thereof, are modified up to a considerable extent by the temperature of the flowing medium and of the surroundings of the system concerned.
  • the present invention provides a novel device for measuring mass flow, wherein at least two sensing elements have a natural frequency equal to a first frequency value, at least two further sensing elements have a natural frequency equal to a second frequency value differing from the first frequency value, the frequency of excitation is equal to one of the natural frequencies mentioned, and the sensors are made in the form of response-sensors for measuring a motion quantity as a result of the Coriolis reaction force and mechanical impedance sensors.
  • the response-sensors for measuring a motion quantity are preferably displacement sensors and/or velocity sensors and/or accelerometers.
  • the sensing elements are connected to preferably at least one connecting element through at least one vibration damper.
  • a preferred embodiment of the device according to the present invention comprises preferably four sensing elements, wherein the sensing elements take the form of straight sensing tubes. It is also preferred, that the sensing tubes are arranged in pairs, one under the other, and are clamped together by at least one clamping element. Furthermore, the vibration means and the mechanical impedance sensors are arranged preferably between sensing tubes situated under each other, while the response-sensors are arranged preferably between sensing tubes situated side by side. It is preferred, that the difference between the first and second values of the natural frequency is provided by a difference in lengths of the sensing tubes in pairs. Furthermore, the response-sensors are arranged preferably at the nodal points of the mode shape of the sensing tubes.
  • the present invention provides a method for measuring mass flow, wherein the natural frequency of at least two sensing elements is equal to a first frequency value, the natural frequency of at least two further sensing elements is equal to a second frequency value differing from the first one; the frequency of excitation is equal to one of the natural frequencies mentioned; as a response to the excitation mechanical impedance and motion quantity due to the Coriolis reaction force are measured simultaneously with the sensors; and finally signals, each being proportional to the mass flow, are derived separately from the phase shifts of response signals of mechanical impedance and that of motion quantity measured relative to the excitation, and the signals obtained in this way are used to determine a mass flow rate.
  • the mechanical impedance is measured preferably on sensing elements having either equal or different natural frequencies.
  • the motion quantity is also measured preferably on sensing elements having either equal or different natural frequencies. Further- more, it is preferred that displacement and/or velocity and/or acceleration of the sensing elements is/are measured as motion quantity.
  • Figure 1 shows the mode shapes of straight sensing tubes of a possible embodiment of the device according to the invention made to vibrate transversally in an anti-symmetric mode
  • Figure 2a is an elevational, diagrammatic, sectional view of a preferred embodiment of the device according to the invention
  • Figure 2b is a diagrammatic cross-sectional view of the embodiment shown in Figure 2a with the vibration means and the sensors clearly indicated
  • Figures 3a and 3b are diagrammatic views of the embodiment shown in Figures 2a and 2b taken from two perpendicular directions, wherein the vibration means and the sensors are not illustrated.
  • sensing elements preferably in the form of straight sensing tubes 2a to 2d arranged parallel to the flow of medium 1 , vibration means 3 for providing a transverse vibration of the sensing tubes 2a to 2d and sensors in the form of Coriolis response-sensors 4a, 4b for measuring motion quantities due to the Coriolis reaction force acting at certain points of the sensing tubes 2a to 2d, and mechanical impedance sensors 5a, 5b being independent of the response-sensors 4a, 4b.
  • the sensing tubes 2a to 2d arranged in pairs side by side and under each other are held together at their ends by clamping elements 7 and are connected via vibration dampers 8 to connecting elements 9.
  • sensing tubes 2a to 2d concerned, the Coriolis response-sensors 4a, 4b, the mechanical impedance sensors 5a, 5b, the clamping elements 7 and the vibration dampers 8 are enclosed within a common house 6.
  • the mass flowmeter 10 of the present invention is further equipped with addi- tional electronics (not shown).
  • sensing tubes 2a to 2d are held together by means of a single clamping element 7 only at their one end. In such a case, preferably those ends of the sensing tubes 2a to 2d are clamped together that are reached by the medium first when flowing through.
  • the straight sensing tubes 2a to 2d are of different lengths in pairs: sensing tubes 2a and 2c are of a first length, while sensing tubes 2b and 2d are of a second length.
  • sensing tubes 2a and 2c are of a first length
  • sensing tubes 2b and 2d are of a second length.
  • the difference in lengths of sensing tubes 2a, 2c and 2b, 2d can be optional, nevertheless, it should be always greater than the inaccuracies possibly occurring during the fabrication and machining steps; it is preferred to be about a few centimetres.
  • the difference in the natural frequencies of pairs of sensing tubes can be realised in other ways too, one possibility for this is to affix masses of different weight to sensing tubes equal in length at the same location thereof.
  • the frequency of the external driving provided by the vibration means 3 is equal to one of the natural frequencies of either sensing tubes 2a, 2c or those of sensing tubes 2b, 2d. This means, that the members of one of the pairs of sensing tubes 2a, 2c or of sensing tubes 2b, 2d are made to oscillate, i.e. are excited, at a frequency different from the natural frequency thereof with the vibration means 3.
  • the sensors are preferred to be arranged on the sensing tubes 2a to 2d in the following way: the mechanical impedance sensors 5a, 5b are arranged on the sensing tubes 2a, 2c or 2b, 2d excited at a frequency differ- ent from the natural frequency chosen (but equal for the members of each pair), while the Coriolis response-sensors 4a, 4b are arranged at the nodal points, see Fig.
  • the pairs of measuring tubes comprising measuring tubes of different natural frequencies to be considered as pairs in view of the measurement are preferably excited, in accordance with mode shapes illustrated in Fig. 1 , antisymmetrically, i.e. in modes shifted by 180° in phase relative to each other (see the modes indicated by smooth and dashed lines in Fig. 1), in order that the full system, i.e. the mass flowmeter 10 according to the invention, be as balanced as it is possible as a result of symmetry.
  • the simultaneous measurement according to the invention is effected as it follows.
  • the combined mass flowmeter 10 according to the invention is connected in series or in parallel to the conduit containing the flowing medium in such a way, that a flow of medium 1 of the medium to be studied flows through each of the sensing tube 2a to 2d.
  • "connecting in series” means that the mass flowmeter 10 is arranged inside of the conduit containing the flowing medium
  • "connecting in parallel” means that it is arranged outside thereto.
  • the flow of medium 1 (or preferably a part of it) is led out from the conduit in a suitable way, led through each of the sensing tubes 2a to 2d, preferably in equal amounts, by the insertion of a manifold, eg. an Y-shaped pipe (not shown in the figures), and finally, is fed back into the conduit by means of a collector similar in shape to the manifold.
  • the sensing tubes 2a to 2d are excited for transversal oscillations at a frequency equal to the natural frequency of one of the sensing tube pairs (comprised of eg. sensing tubes 2a and 2c in Figs. 3a and 3b) of equal length by means of the vibration means 3, and the phase shift of the response to the excitation relative to the excitation is measured by a mechanical impedance measurement carried out with the mechanical impedance sensors 5a, 5b on that sensing tube pair (in this case comprised of eg. sensing tubes 2b and 2d) the members of which are excited at a frequency different from their natural frequency, and then the phase shift thus obtained is used to derive a mass flow rate.
  • the mechanical impedance sensors 5a, 5b on that sensing tube pair in this case comprised of eg. sensing tubes 2b and 2d
  • the thus obtained signals originating in two different effects are input into the common electronics, wherein two mass flow rates are derived by processing the signals, one from the structural damping (mechanical impedance type measuring of mass flow) and an other one from the phase shift relative to the excitation of the motion quantity chosen (Coriolis type measurement of mass flow, see eg. U.S. Patent No. 4,622,858).
  • the actual value of the mass flow rate accepted as the result of the measurement according to the present invention is obtained by the average of the above two mass flow rates. If a significant deviation is present between the two mass flow rates, then this deviation might indicate, on the one part, a failure of the mass flowmeter 10 or, on the other part, it might happen that the mass flow rate is actually either too small (i.e.
  • the mass flowmeter 10 works in its ideal measuring range, and hence, its data are extremely reliable.
  • the changes in lengths of the measuring tubes 2a to 2d due to the temperature are automatically compensated for the mass flowmeter 10 according to the invention.
  • the relative distance between the natural frequencies of pairs comprising the measuring tubes 2a, 2c and 2b, 2d is constant with respect to the change of temperature, therefore the phase difference based on measurement of the mechanical impedance and being proportional to the mass flow is detected every instant at a given relative frequency difference, which in turn means, that the response depends merely on the mass flow rate. All these facts mean, that the mass flowmeter 10 according to the invention can be manufactured from relatively cheap materials commercially available, which leads to a huge decrease in the costs of production of the mass flowmeter 10.
  • the combined mass flow meter of the present invention exhibits much more advantageous properties than the flowmeters being of purely either the Coriolis type or the mechanical impedance type of the art.
  • the most important benefit of such devices is, that the simultaneous and fully independent performance of the two measurements of different basis enables a possibility for the measurement to be done much more accurately compared to the traditional measurement of the mass flow.
  • the thus obtained two different types of measuring data can be compared and correlated with each other, as a result of which the reliability of the mass flow rate obtained as final result is enhanced.
  • a further major benefit of such devices is that they can be used in a much broader measuring range than that of the traditional flowmeters; as regard to the current rate of the medium, the flowmeters of the present invention extends the measuring range of flowmeters known in the art both to small and large values while keeping measuring accuracy and reliability.
  • Our studies suggest, that the mass flow can be measured also for small current rates, i.e. for current rates greater than at least about 0.1 m/s, relatively accurately with devices enabling a combined measurement of mass flow according to the present invention. As a result of this, measurement of mass flow rates of a magnitude smaller than the measuring limit of the traditional Coriolis type mass flowmeters becomes possible.
  • a further advantage of the combined mass flowmeters of to the present invention is that they can be used for conduits of arbitrary diameter. In this way, problems emerging especially in connection with the measurement of a mass flow of a medium flowing in wide conduits (eg. for transporting crude oil), greater than about 0.25 meter in diameter, can be eliminated successfully by the application of the flowmeters according to the invention.

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  • Physics & Mathematics (AREA)
  • Fluid Mechanics (AREA)
  • General Physics & Mathematics (AREA)
  • Measuring Volume Flow (AREA)

Abstract

The present invention relates to a device and a method for measuring mass flow of a nonsolid medium. The device comprises sensing elements arranged parallel to current rate of the medium and to each other and ensuring the flow of medium through the sensing elements, vibrators located on the sensing elements and exciting those at a given frequency in a transverse direction, and sensors detecting response of sensing elements due to excitation, wherein at least two sensing elements have a self-frequency equal to a first frequency value, at least two further sensing elements have a self-frequency equal to a second frequency value different from the first frequency value, the frequency of excitation is equal to one of the self-frequencies mentioned, and the sensors are response sensors for measuring motion quantity emerging as a result of the Coriolis reaction force and sensors for measuring mechanical impedance.

Description

DEVICE AND METHOD FOR MEASURING MASS FLOW OF A NON-SOLID MEDIUM
The present invention relates to a device, in particular to a combined device for measuring mass flow of a non-solid medium.
To measure mass flow rate, numerous methods and apparatuses are known in literature. One class of these comprises the so-called Coriolis-type devices and measuring techniques, while another class of these is constituted by presently being developed devices and measuring methods based on mechanical impedance measurement.
The basic principle underlying a Coriolis-type measurement is that a so- called Coriolis force of Fc = 2 m- ώ* v acts upon a medium of mass m translating with velocity vector v and rotating simultaneously with angular velocity ώ around a fixed axis. If the path of the medium at issue is defined by a geometrical constraint, for example by the inner wall of a conduit, the medium performing simultaneous translation and rotation exerts a reaction force equal in magnitude, but opposite in direction to the Coriolis force Fc on the element representing the constraint. For Coriolis-type mass flowmeters the nonzero angular velocity ώ of the flowing medium is provided, in particular, by exciting, i.e. by oscillating, the sensing element(s) representing the main portion of the device in a transverse direction. In such circumstances motion of any point of the sensing element takes place as a result of superposition of the Coriolis reaction force and the excitation. As according to the above expression the magnitude of the Coriolis force Fc is proportional to the mass flow rate m| v |, the motion of the points of the sensing element due to the excitation, i.e. the mode shape thereof, will depend on the mass flow rate. In particular the dependence arises from the fact that the mode shape is distorted, which in turn means, that depending on the mass flow rate, the motion of the various points of the sensing element is apparently shifted in phase. U.S. Patent No. 4,622,858 issued to The Babcock & Wilcox Company discloses a Coriolis-type apparatus and a method based on the same principle to measure mass flow. According to the specification concerned the apparatus comprises a pair of straight parallel sensing tubes equal in length provided with Y-shaped elements at the opposite ends thereof to assure the inflow and the outflow of the flowing medium to be studied, drive means for oscillating said sensing tubes towards and away from each other at a selected frequency in a transverse direction, wherein the drive means are arranged substantially at the midpoints of the sensing tubes, and further at least one sensor attached to the sensing tubes at a point spaced from both the opposite ends of sensing tubes and the location of the drive means. The main point behind the method introduced is, that an apparent shift of the phase of one of the motion quantities, eg. displacement, velocity or acceleration, of the sensing tubes is measured relative to the phase of the same motion quantity, eg. displacement, velocity or acceleration, of the excitation, wherein the phase shift is proportional to the rate of the mass flow under study according to the aforementioned.
U.S. Patent No. 4,823,614 issued to Dahlin et al. describes a further Coriolis-type mass flowmeter, wherein the sensing tube (for certain embodiments two sensing tubes) is (are) excited (oscillated) transversally in a higher anti-symmetric mode at a driving frequency equal to a natural frequency of the sensing tube, and by means of sensors arranged symmetrically on the sensing tube at equal distances from its midpoint, the actual values of one of the motion quantities characteristic to the vibration of the sensing tube are measured in the position of the sensors. Then the thus obtained two electronic signals are led into a processing unit, on the output of which an outgoing signal proportional to the mass flow rate is obtained as a result of operations applied to the incoming electronic signals.
For the measuring devices/techniques introduced above, time dependence of the driving signal is chosen to be sinusoidal, i.e. a harmonic excitation is used. The frequency of the excitation, i.e. the driving frequency, is equal to a natural frequency of the sensing tube. Therefore, the mass flow rate is always measured at a natural frequency of the sensing tube for Coriolis-type methods and apparatuses known. The reason behind this is, that the values of motion quantities are of maximum in this case; the effect of the Coriolis force appearing as a result of the oscillation is so small for an excitation at a driving frequency different from the natural frequency, that the measurement thereof would lead to an extremely low signal-to-noise ratio, which in turn would have a significant influence on the accuracy of the mass flow rate measured.
Another disadvantage of the Coriolis-type mass flowmeters is, besides the drawback of being reliably operable only at natural frequency, that the results they yield can be considered to be reliable only for relatively high current rates. An increase in current rate can be reached eg. by decreasing the diameter of the tube containing the flowing medium. Nevertheless, for a given tube profile and for a certain medium (having a definite viscosity) the diameter of the tube cannot be reduced to an arbitrary extent, as the so far generally laminar flow of medium becomes turbulent if a critical current rate is reached. This feature is highly disadvantageous from the aspect of transportation of the medium, since in case of a turbulent flow, for transporting a unit mass of the given medium substantially a greater amount of energy has to be invested relative to the amount of energy that needs in case of a laminar flow. Furthermore, in such a case the pressure drop through the flowmeter also rises extremely. It is noted, that reliable operation of Coriolis-type mass flowmeters requires a mass flow rate of the flowing medium to be at least about 1 m/s.
A further drawback of the above mass flowmeters comprising straight sensing tube(s) is, that it/they suffers/suffer a longitudinal change of size due to the change in temperature of the medium flowing therethrough or of the surroundings, as a consequence of which the driving frequency shifts away from the natural frequency of the sensing tube(s). For an accurate operation, however, the shift concerned should be always compensated. For currently used mass flowmeters, the compensation is obtained by fabricating the sensing tube(s) from materials exhibiting a heat expansion coefficient negligible in value. This, however, leads to a significant increase in fabrication costs of the mass flowmeters of this type.
The basic principle behind a flow rate measurement based on the mechanical impedance is that a mass flow also has, besides the Coriolis-force, further effects on the measuring elements, preferably in the form of sensing tubes arranged parallel in a flowing medium (i.e. in the mass flow) and excited (i.e. made to vibrate) transversally. The effects can be given precisely by the equation of motion of a sensing tube filled with a medium performing a laminar flow, that is t E-.l 34y + ρA Λv 2^ 52y ~ + 2ρA Λv ø2y '— + ^ — d2y = _ F-t(x, «t) , ax4 dxz y ax st at2 wherein E represents the Young modulus of the material used for the sensing tube, I stands for the second order moment of inertia of the sensing tube, while A is the cross-section thereof; v is the current rate and p is the (volume) density of the flowing medium; M stands for the mass (of the sensing tube and of the flowing medium contained therein) of unit length, y represents the transverse deflection of the sensing tube (at a given point and in a certain moment), while F(x,t) represents the external (generally harmonic) driving force as a function of the position x and time t.
The first and the forth terms on the left-hand side of the above equation are the well-known stiffness and mass terms, respectively, the third term represents the so-called Coriolis-term proportional to the mass flow pAv, while the remaining second term gives the force required to displace the flowing medium. It can be seen from the expression of the second term, that the force represented thereby is also proportional to the mass flow pAv. Hence, the mass flow rate can be determined by measuring the second term. As it is known from literature (see eg. Flow-Induced Vibration by R.D. Blevins [published by Van Nostrand Reinhold, New York, US, 1977]), the second term relates to a damping occurring as a "structural damping" due to the mass flow, wherein the damping at issue can be easily determined via measuring the mechanical impedance. Hence, a mass flowmeter is available that operates on a principle being different from the measurement of the effects of the Coriolis force. As it is also known for the person skilled in the art, that the mechanical impedance is defined as a complex ratio of the external excitation (eg. driving force) and the response (eg. velocity measured at a given point) given thereto.
As it is also well-known, the phase difference between the external excitation and the response given thereto at the natural frequency is constant, independently on damping, and hence the effect of mass flow exerted on the structural damping cannot be determined in a measurement performed at the natural frequency. Keeping this in mind, at least two sensing tubes of different lengths and hence of different natural frequencies should be used in the measurement, wherein all the sensing tubes have to be subjected to an external excitation having a frequency equal to a natural frequency of one of the sensing tubes. Furthermore, the mechanical impedance should be measured, in particular, on the sensing tube that is excited at a frequency different from its natural frequency.
To eliminate problems of Coriolis-type mass flowmeters, Hungarian Patent No. 219,251 discloses a (temperature) compensated device for measuring the mass flow comprising sensing elements, preferably in the form of straight sensing tubes extending parallel both to the mass flow under study and to each other, vibration means and a sensor for measuring the mechanical impedance. Sensing elements of the device at issue are of different lengths, the driving frequency of the vibration means is equal to the natural frequency of one of the sensing elements, and the mechanical impedance sensor is arranged on the sensing element that is characterized by a natural frequency different from the driving frequency. Besides the above flowmeter, Hungarian Patent No. 219,251 also describes a method for measuring mass flow, wherein the sensing elements are provided with different lengths and during the flow of the medium to be studied therethrough the sensing elements are excited transversally by means of vibration means at a driving frequency equal to the natural frequency of one of the sensing elements, and mechanical impedance is measured by means of a sensor arranged on the sensing element characterized by a natural frequency different from the driving frequency. According to this method, the mass flow rate is determined from the phase difference relative to the excitation of the mechanical impedance measured.
According to our theoretical and experimental knowledge, a non-solid medium flowing through a sensing element has an influence on the mode shape of the sensing element and hence on the measured value of the actual mass flow rate through a damping that occurs as the result of the viscosity of the medium. To compensate the measuring error due to the viscosity of the medium, the application of such a mass flowmeter of the mechanical impedance type is required, that has at least four sensing elements, preferably in the form of straight sensing tubes, of different lengths in pairs and hence having different natural frequencies in pairs. Hungarian Patent Application No. P 9900544 describes a mass flowmeter accordant to the above requirements, and a method for a simultaneously temperature and viscosity compensated direct measurement of mass flow rate.
Unfortunately, the measuring error of mass flowmeters of the mechanical impedance type increases under certain circumstances in such an extent, that the traditional Coriolis-type devices result in much more reliable measuring data. This is the case eg. when the mass flow rate, for any reason, increases to a great extent. For large mass flow rates the sensitivity of flowmeters of the mechanical impedance type decreases considerably as a result of the non-linear behaviour of the response; in principle there is a current rate, the crossing of which results, that the sensitivity of the system for measuring becomes smaller than that of a Coriolis-type flowmeter. This feature takes place when the Reynolds number characteristic to the flowing concerned exceeds the value of about 9000-10000. The origin of the feature is not cleared up yet in its full depth, how- ever, the experiments done suggest, that burbling of vortices from the sensing elements plays an essential role in its occurrence.
In view of the aforementioned, the aim of the present invention is to provide a combined mass flowmeter that enables to perform mass flow measurements with the highest precision possible for arbitrary mass flow rates, and is compensated with regard to the effects of the medium to be studied. Another aim of the present invention is to develop a novel method for measuring the mass flow of a non-solid medium.
According to our studies, the above aims could be reached if the Coriolis- type measurement and the mechanical impedance type measurement of the mass flow were carried out simultaneously using the same device. A further advantage of a device of the above type would be that, as a result of the comparison and the suitable averaging of the mass flow rates measured on the basis of two different phenomena, on the one hand, more reliable data could be achieved and, on the other hand, a possible failure of the flowmeter could be automatically indicated if the deviation of the two values was greater than a pre-set threshold value. Taking into consideration that mass flowmeters have wide range of application in the field of economy (eg. accurate measuring of the amount of substance having flowed through over the gas or oil conduits), there is a considerable demand for the development of a combined mass flow meter of enhanced measuring accuracy and of relatively small fabrication costs, as no such device and method are known up to this day.
Nevertheless, the implementation of a mass flowmeter that enables exploitation of the advantageous features provided by a simultaneous performance of two mass flow measurements of different origin requires huge amount of technical problems to be solved.
As it was mentioned earlier, the phase difference between the excitation and the response given thereto has a constant value at the natural frequency independently of damping, therefore the measurement of the mass flow can be effected only at a frequency being apart from the natural frequency with a given constant relative distance. Accordingly, the problem of providing the excitation and the measurement of the phase simultaneously at a given frequency differing from the natural frequency is of great emphasis for the flowmeters aimed by the present invention. This can be reached with such sensing elements only that have different natural frequencies. This in turn means, that the natural frequencies of the pairs of sensing elements, realised preferably in the form of pairs of sensing tubes should be set to different values in this particular case. Furthermore, the effect of the Coriolis force is maximal in those points of the sensing tubes, where the periodic change of the angular velocity of mass flow is the greatest, i.e. at the so-called nodal points. For the person skilled in the art it is obvious, that in case of sensing elements of equal lengths, for keeping positions of nodal points in the same distance from each other, for ensuring different natural frequencies and for assuring energy input by excitation simultaneously extremely delicate technical solutions are required. Furthermore, the mass flow alters, generally to a negligible extent only, the natural frequencies of the sensing elements made to vibrate, and the flowing medium (i.e. the mass flow) moreover influences the mode shape of the sensing elements and the damping being present in the system under excitation. As it was mentioned earlier, characteristic properties of the system excited, first of all the natural frequency thereof, are modified up to a considerable extent by the temperature of the flowing medium and of the surroundings of the system concerned.
In view of the above, in a first aspect, the present invention provides a novel device for measuring mass flow, wherein at least two sensing elements have a natural frequency equal to a first frequency value, at least two further sensing elements have a natural frequency equal to a second frequency value differing from the first frequency value, the frequency of excitation is equal to one of the natural frequencies mentioned, and the sensors are made in the form of response-sensors for measuring a motion quantity as a result of the Coriolis reaction force and mechanical impedance sensors. The response-sensors for measuring a motion quantity are preferably displacement sensors and/or velocity sensors and/or accelerometers. Furthermore, the sensing elements are connected to preferably at least one connecting element through at least one vibration damper.
A preferred embodiment of the device according to the present invention comprises preferably four sensing elements, wherein the sensing elements take the form of straight sensing tubes. It is also preferred, that the sensing tubes are arranged in pairs, one under the other, and are clamped together by at least one clamping element. Furthermore, the vibration means and the mechanical impedance sensors are arranged preferably between sensing tubes situated under each other, while the response-sensors are arranged preferably between sensing tubes situated side by side. It is preferred, that the difference between the first and second values of the natural frequency is provided by a difference in lengths of the sensing tubes in pairs. Furthermore, the response-sensors are arranged preferably at the nodal points of the mode shape of the sensing tubes.
In a second aspect, the present invention provides a method for measuring mass flow, wherein the natural frequency of at least two sensing elements is equal to a first frequency value, the natural frequency of at least two further sensing elements is equal to a second frequency value differing from the first one; the frequency of excitation is equal to one of the natural frequencies mentioned; as a response to the excitation mechanical impedance and motion quantity due to the Coriolis reaction force are measured simultaneously with the sensors; and finally signals, each being proportional to the mass flow, are derived separately from the phase shifts of response signals of mechanical impedance and that of motion quantity measured relative to the excitation, and the signals obtained in this way are used to determine a mass flow rate.
According to the method of the present invention, the mechanical impedance is measured preferably on sensing elements having either equal or different natural frequencies. The motion quantity is also measured preferably on sensing elements having either equal or different natural frequencies. Further- more, it is preferred that displacement and/or velocity and/or acceleration of the sensing elements is/are measured as motion quantity.
The device and the method for measuring the mass flow of a non-solid medium according to the present invention will be explained in detail with reference to the accompanied drawings, wherein
Figure 1 shows the mode shapes of straight sensing tubes of a possible embodiment of the device according to the invention made to vibrate transversally in an anti-symmetric mode; Figure 2a is an elevational, diagrammatic, sectional view of a preferred embodiment of the device according to the invention; Figure 2b is a diagrammatic cross-sectional view of the embodiment shown in Figure 2a with the vibration means and the sensors clearly indicated; and Figures 3a and 3b are diagrammatic views of the embodiment shown in Figures 2a and 2b taken from two perpendicular directions, wherein the vibration means and the sensors are not illustrated. The preferred embodiment of the combined mass flowmeter 10 shown in Figs. 2 and 3 according to the invention comprises sensing elements, preferably in the form of straight sensing tubes 2a to 2d arranged parallel to the flow of medium 1 , vibration means 3 for providing a transverse vibration of the sensing tubes 2a to 2d and sensors in the form of Coriolis response-sensors 4a, 4b for measuring motion quantities due to the Coriolis reaction force acting at certain points of the sensing tubes 2a to 2d, and mechanical impedance sensors 5a, 5b being independent of the response-sensors 4a, 4b. The sensing tubes 2a to 2d arranged in pairs side by side and under each other are held together at their ends by clamping elements 7 and are connected via vibration dampers 8 to connecting elements 9. The sensing tubes 2a to 2d concerned, the Coriolis response-sensors 4a, 4b, the mechanical impedance sensors 5a, 5b, the clamping elements 7 and the vibration dampers 8 are enclosed within a common house 6. The mass flowmeter 10 of the present invention is further equipped with addi- tional electronics (not shown). However, for a possible further embodiment of the device, sensing tubes 2a to 2d are held together by means of a single clamping element 7 only at their one end. In such a case, preferably those ends of the sensing tubes 2a to 2d are clamped together that are reached by the medium first when flowing through.
For the embodiment of the mass flowmeter 10 according to the invention to be described here in detail, the straight sensing tubes 2a to 2d are of different lengths in pairs: sensing tubes 2a and 2c are of a first length, while sensing tubes 2b and 2d are of a second length. As a result of this, the natural frequencies measured without a flow of medium 1 present, i.e. in an empty state, of each pair of tubes differ in value. The difference in lengths of sensing tubes 2a, 2c and 2b, 2d can be optional, nevertheless, it should be always greater than the inaccuracies possibly occurring during the fabrication and machining steps; it is preferred to be about a few centimetres. It is noted, that the difference in the natural frequencies of pairs of sensing tubes can be realised in other ways too, one possibility for this is to affix masses of different weight to sensing tubes equal in length at the same location thereof.
The frequency of the external driving provided by the vibration means 3 is equal to one of the natural frequencies of either sensing tubes 2a, 2c or those of sensing tubes 2b, 2d. This means, that the members of one of the pairs of sensing tubes 2a, 2c or of sensing tubes 2b, 2d are made to oscillate, i.e. are excited, at a frequency different from the natural frequency thereof with the vibration means 3.
As the mass flow rate is aimed to be determined on the one hand by performing a measurement of mechanical impedance from the effect of the mass flow on the structural damping, and on the other hand simultaneously from the phase shift relative to the excitation of a certain motion quantity due to the Coriolis reaction force, the sensors are preferred to be arranged on the sensing tubes 2a to 2d in the following way: the mechanical impedance sensors 5a, 5b are arranged on the sensing tubes 2a, 2c or 2b, 2d excited at a frequency differ- ent from the natural frequency chosen (but equal for the members of each pair), while the Coriolis response-sensors 4a, 4b are arranged at the nodal points, see Fig. 1 , of the sensing tubes 2a to 2d showing a maximal Coriolis-effect. The construction and the operation of the vibration means 3, of the Coriolis response- sensors 4a, 4b and of the mechanical impedance sensors 5a, 5b can be known from literature (see eg. the Bruel-Kjaer Master Catalog, 1980). Furthermore it is noted, that the pairs of measuring tubes comprising measuring tubes of different natural frequencies to be considered as pairs in view of the measurement are preferably excited, in accordance with mode shapes illustrated in Fig. 1 , antisymmetrically, i.e. in modes shifted by 180° in phase relative to each other (see the modes indicated by smooth and dashed lines in Fig. 1), in order that the full system, i.e. the mass flowmeter 10 according to the invention, be as balanced as it is possible as a result of symmetry.
The simultaneous measurement according to the invention is effected as it follows. At start, the combined mass flowmeter 10 according to the invention is connected in series or in parallel to the conduit containing the flowing medium in such a way, that a flow of medium 1 of the medium to be studied flows through each of the sensing tube 2a to 2d. For purposes of the present description "connecting in series" means that the mass flowmeter 10 is arranged inside of the conduit containing the flowing medium, while "connecting in parallel" means that it is arranged outside thereto. In this latter case the flow of medium 1 (or preferably a part of it) is led out from the conduit in a suitable way, led through each of the sensing tubes 2a to 2d, preferably in equal amounts, by the insertion of a manifold, eg. an Y-shaped pipe (not shown in the figures), and finally, is fed back into the conduit by means of a collector similar in shape to the manifold.
Assuming identical geometry and flow conditions, natural frequencies of the sensing tubes 2a to 2d measurable in the empty states thereof are modified in pairs by the mass flow through each of the sensing tubes 2a to 2d. The change is proportional to the mass added, hence to the density of the mass flow 1. If the differences between the natural frequencies of the sensing tubes 2a to 2d in pairs with and without the flow of medium 1 are measured in a suitable way for each member of the pairs, the density of the flow of medium 1 can also be determined from the measuring data. As it was already mentioned, the mass flow also modifies, generally only to a negligible extent, the natural frequency of the vibrating system, i.e. that of a system being excited. Furthermore, the mass flow alters the mode shape, and the damping of the system excited, too.
Taken all the above facts into consideration, the sensing tubes 2a to 2d are excited for transversal oscillations at a frequency equal to the natural frequency of one of the sensing tube pairs (comprised of eg. sensing tubes 2a and 2c in Figs. 3a and 3b) of equal length by means of the vibration means 3, and the phase shift of the response to the excitation relative to the excitation is measured by a mechanical impedance measurement carried out with the mechanical impedance sensors 5a, 5b on that sensing tube pair (in this case comprised of eg. sensing tubes 2b and 2d) the members of which are excited at a frequency different from their natural frequency, and then the phase shift thus obtained is used to derive a mass flow rate. Simultaneously with this measurement, during the transversal vibration of the sensing tubes 2a to 2d excited with the vibration means 3 a detection of one of the motion quantities, i.e. one of displacement and/or velocity and/or acceleration of the sensing tubes 2a and/or 2b and/or 2c and/or 2d due to the Coriolis reaction force is performed by means of the response-sensors 4a, 4b arranged at the nodal points illustrated in Fig. 1. The thus obtained signals originating in two different effects are input into the common electronics, wherein two mass flow rates are derived by processing the signals, one from the structural damping (mechanical impedance type measuring of mass flow) and an other one from the phase shift relative to the excitation of the motion quantity chosen (Coriolis type measurement of mass flow, see eg. U.S. Patent No. 4,622,858). The actual value of the mass flow rate accepted as the result of the measurement according to the present invention is obtained by the average of the above two mass flow rates. If a significant deviation is present between the two mass flow rates, then this deviation might indicate, on the one part, a failure of the mass flowmeter 10 or, on the other part, it might happen that the mass flow rate is actually either too small (i.e. so small that the Coriolis type measurement is not reliable any longer) or too large (i.e. the mechanical impedance type measurement becomes unreliable, as the mass flowmeter 10 operates in the non-linear measuring range as a consequence of the actual value of the current rate). As a consequence, if the relative difference between the two rates is smaller than a certain threshold value, then the mass flowmeter 10 works in its ideal measuring range, and hence, its data are extremely reliable. Thus, by the simultaneous and joint implementation of the two measuring principles within a single flowmeter, the measurement of the mass flow can be performed much more reliably compared to the traditional measurements.
As the measurements are carried out at a frequency different from the natural frequency, the changes in lengths of the measuring tubes 2a to 2d due to the temperature are automatically compensated for the mass flowmeter 10 according to the invention. The relative distance between the natural frequencies of pairs comprising the measuring tubes 2a, 2c and 2b, 2d is constant with respect to the change of temperature, therefore the phase difference based on measurement of the mechanical impedance and being proportional to the mass flow is detected every instant at a given relative frequency difference, which in turn means, that the response depends merely on the mass flow rate. All these facts mean, that the mass flowmeter 10 according to the invention can be manufactured from relatively cheap materials commercially available, which leads to a huge decrease in the costs of production of the mass flowmeter 10.
It can be concluded, that the combined mass flow meter of the present invention exhibits much more advantageous properties than the flowmeters being of purely either the Coriolis type or the mechanical impedance type of the art. The most important benefit of such devices is, that the simultaneous and fully independent performance of the two measurements of different basis enables a possibility for the measurement to be done much more accurately compared to the traditional measurement of the mass flow. Furthermore, the thus obtained two different types of measuring data can be compared and correlated with each other, as a result of which the reliability of the mass flow rate obtained as final result is enhanced. A further major benefit of such devices is that they can be used in a much broader measuring range than that of the traditional flowmeters; as regard to the current rate of the medium, the flowmeters of the present invention extends the measuring range of flowmeters known in the art both to small and large values while keeping measuring accuracy and reliability. Our studies suggest, that the mass flow can be measured also for small current rates, i.e. for current rates greater than at least about 0.1 m/s, relatively accurately with devices enabling a combined measurement of mass flow according to the present invention. As a result of this, measurement of mass flow rates of a magnitude smaller than the measuring limit of the traditional Coriolis type mass flowmeters becomes possible. Besides the above features, a further advantage of the combined mass flowmeters of to the present invention is that they can be used for conduits of arbitrary diameter. In this way, problems emerging especially in connection with the measurement of a mass flow of a medium flowing in wide conduits (eg. for transporting crude oil), greater than about 0.25 meter in diameter, can be eliminated successfully by the application of the flowmeters according to the invention.

Claims

CLAI S
1. A device for measuring mass flow of a non-solid medium, comprising sensing elements ensuring the flow of medium therethrough and arranged parallel both to current rate of the medium and to each other, vibration means (3) located on the sensing elements and exciting those at a given frequency in a transverse direction, and sensors detecting response of sensing elements due to the excitation, characterized in that at least two sensing elements have a natural frequency equal to a first frequency value, at least two further sensing elements have a natural frequency equal to a second frequency value differing from the first frequency value, that the frequency of excitation is equal to one of the natural frequencies mentioned, and that the sensors are made in the form of response-sensors (4a, 4b) for measuring a motion quantity as a result of the Coriolis reaction force and mechanical impedance sensors (5a, 5b).
2. The device according to Claim 1 , characterized in that the response- sensors (4a, 4b) for measuring a motion quantity are displacement sensors and/or velocity sensors and/or accelerometers.
3. The device according to Claim 1 or 2, characterized in that the sensing elements are connected to at least one connecting element (9) through at least one vibration damper (8).
4. The device according to any of the preceding Claims, characterized in that it comprises four sensing elements, wherein the sensing elements take the form of straight sensing tubes (2a to 2d).
5. The device according to Claim 4, characterized in that the sensing tubes (2a to 2d) are arranged in pairs, one under the other, and are clamped together by at least one clamping element (7).
6. The device according to Claim 5, characterized in that the vibration means (3) and the mechanical impedance sensors (5a, 5b) are arranged between sensing tubes (2a to 2d) situated under each other, and the response- sensors (4a, 4b) are arranged between sensing tubes (2a to 2d) situated side by side.
7. The device according to any of Claims 4 to 6, characterized in that the difference between the first and second values of the natural frequency is provided by a difference in lengths of the sensing tubes (2a to 2d) in pairs.
8. The device according to any of Claims 4 to 7, characterized in that the response-sensors (4a, 4b) are arranged at the nodal points of the mode shape of the sensing tubes (2a to 2d).
9. A method for measuring mass flow of a non-solid medium wherein sensing elements are arranged parallel both to current rate of the medium and to each other, the medium is passed through the sensing elements which in the meantime are excited at a given frequency in a transverse direction with vibration means (3) arranged thereon, and further the response of sensing elements due to the excitation is detected by means of sensors, characterized in that the natural frequency of at least two sensing elements is equal to a first frequency value, the natural frequency of at least two further sensing elements is equal to a second frequency value differing from the first one; the frequency of excitation is equal to one of the natural frequencies mentioned; as a response to the excitation mechanical impedance and motion quantity due to the Coriolis reaction force are measured simultaneously with the sensors; finally signals, each being proportional to the mass flow, are derived separately from the phase shifts of response signals of mechanical impedance and that of motion quantity measured relative to the excitation, and the signals obtained in this way are used to determine a mass flow rate.
10. The method according to Claim 9, characterized in that the mechanical impedance is measured on sensing elements having equal natural frequencies.
11. The method according to Claim 9, characterized in that the mechanical impedance is measured on sensing elements having different natural frequencies.
12. The method according to any of Claims 9 to 11 , characterized in that the motion quantity is measured on sensing elements having equal natural frequencies.
13. The method according to any of Claims 9 to 11 , characterized in that the motion quantity is measured on sensing elements having different natural frequencies.
14. The method according to any of Claims 9 to 13, characterized in that displacement and/or velocity and/or acceleration of the sensing elements is/are measured as motion quantity.
15. The method according to any of Claims 9 to 14, characterized in that it is carried out by using the device according to Claims 1 to 8.
EP01272129A 2000-12-21 2001-12-21 Device and method for measuring mass flow of a non-solid medium Withdrawn EP1409968A1 (en)

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DE102008039867B4 (en) 2008-08-27 2015-09-10 Krohne Ag mass flowmeter
EP2406593A1 (en) 2009-03-11 2012-01-18 Martin Anklin-Imhof Vibration sensor and in-line measuring device comprising said sensor
AU2010357211B2 (en) 2010-07-09 2013-09-19 Micro Motion, Inc. A vibrating meter including an improved meter case
RU2533332C2 (en) * 2010-07-09 2014-11-20 Майкро Моушн, Инк. Vibration meter including improved damped part of meter
CN103180695B (en) 2010-09-02 2016-01-20 恩德斯+豪斯流量技术股份有限公司 There is the measuring system of the measurement translator of oscillatory type
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DE102021113642A1 (en) * 2020-05-29 2021-12-02 Drägerwerk AG & Co. KGaA Connection arrangement with a volume flow sensor and a homogenization unit for artificial ventilation of a patient and a manufacturing method
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