EP0456789A4 - Convective acceleration flowmeter - Google Patents

Convective acceleration flowmeter

Info

Publication number
EP0456789A4
EP0456789A4 EP19900917488 EP90917488A EP0456789A4 EP 0456789 A4 EP0456789 A4 EP 0456789A4 EP 19900917488 EP19900917488 EP 19900917488 EP 90917488 A EP90917488 A EP 90917488A EP 0456789 A4 EP0456789 A4 EP 0456789A4
Authority
EP
European Patent Office
Prior art keywords
conduit
media
combination
flexural vibration
set forth
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
EP19900917488
Other languages
French (fr)
Other versions
EP0456789A1 (en
Inventor
Hyok Sang Lew
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Individual
Original Assignee
Individual
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from US07/440,693 external-priority patent/US5123287A/en
Priority claimed from US07/467,481 external-priority patent/US5060523A/en
Application filed by Individual filed Critical Individual
Publication of EP0456789A1 publication Critical patent/EP0456789A1/en
Publication of EP0456789A4 publication Critical patent/EP0456789A4/en
Ceased legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
    • G01F1/76—Devices for measuring mass flow of a fluid or a fluent solid material
    • G01F1/78—Direct mass flowmeters
    • G01F1/80—Direct mass flowmeters operating by measuring pressure, force, momentum, or frequency of a fluid flow to which a rotational movement has been imparted
    • G01F1/84—Coriolis or gyroscopic mass flowmeters
    • G01F1/845—Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits
    • G01F1/8468—Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits vibrating measuring conduits
    • G01F1/8481—Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits vibrating measuring conduits having loop-shaped measuring conduits, e.g. the measuring conduits form a loop with a crossing point
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
    • G01F1/76—Devices for measuring mass flow of a fluid or a fluent solid material
    • G01F1/78—Direct mass flowmeters
    • G01F1/80—Direct mass flowmeters operating by measuring pressure, force, momentum, or frequency of a fluid flow to which a rotational movement has been imparted
    • G01F1/84—Coriolis or gyroscopic mass flowmeters
    • G01F1/8409—Coriolis or gyroscopic mass flowmeters constructional details
    • G01F1/8427—Coriolis or gyroscopic mass flowmeters constructional details detectors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
    • G01F1/76—Devices for measuring mass flow of a fluid or a fluent solid material
    • G01F1/78—Direct mass flowmeters
    • G01F1/80—Direct mass flowmeters operating by measuring pressure, force, momentum, or frequency of a fluid flow to which a rotational movement has been imparted
    • G01F1/84—Coriolis or gyroscopic mass flowmeters
    • G01F1/845—Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits
    • G01F1/8468—Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits vibrating measuring conduits
    • G01F1/8472—Coriolis or gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits vibrating measuring conduits having curved measuring conduits, i.e. whereby the measuring conduits' curved center line lies within a plane

Definitions

  • the mass flowmeter disclosed in the present patent applica- tion employs a single vibrating conduit, wherein the two opposite halves thereof are vibrated laterally in an antisymmetric mode, which contrasts the existing types employing a single or dual vibrating conduits wherein the two opposite halves thereof are vibrated in a symmetric mode.
  • the primary object of the present invention is to provide a mass flowmeter comprising a conduit with two extremities secured to a support, which conduit includes two end sections respectively extending from the two secured extremities thereof and a curved midsection connecting the two end sections, wherein the two oppo- site halves of the conduit are respectively disposed on two oppo- site sides of a hypothetical plane cutting across the midsection of the conduit in an angle generally perpendicular to the central axis of the conduit; wherein an electromagnetic vibrating means vibrates the two opposite halves of the conduit relative to one another in directions perpendicular to a plane generally includ- ing the curved midsection of the conduit, and vibratory motion sensing means measures the difference in the flexural vibration between the two opposite halves of the conduit as a measure of mass flow rate of media moving through the conduit.
  • Another object is to provide the mass flowmeter described in the above-described primary object, wherein the two end sections of the conduit extend from the respective secured extremities thereof towards a generally common direction; wherein the media moving through the conduit turns in a direction in the junction between the first end section and the curved midsection of the conduit, and in the junction between the second end section and the curved midsection of the conduit, which direction of turn is opposite to the direction of turn of the media in a middle portion of the curved midsection of the conduit.
  • a further object is to provide the mass flowmeter described in the above described primary object, wherein the two end sections of the conduit extend from the respective secured extremities thereof towards a generally common direction; wherein the media moving through the conduit turns in a direction in the junction between the first end section and the curved midsection of the con- duit, and in the junction between the second end section and the curved midsection of the conduit, which direction of turn is the same as the direction of turn of the media in a middle portion of the curved midsection of the conduit.
  • Yet another object is to provide the mass flowmeter described in the above-described primary object, wherein the two end sections of the conduit extend from the respective secured extremities there- of towards one another; wherein the media moving through the conduit turns in a direction in the junction between the first end section and the curved midsection of the conduit, and in the junction between the second end section and the curved midsection of the conduit, which direction of turn is opposite to the direc- tion of turn of the media in a middle portion of the curved mid- section of the conduit.
  • Yet a further object is to provide the mass flowmeter describ- ed in the above-described primary object, wherein the two end sections of the conduit extend from the respective secured extremi- ties thereof towards one another; wherein the media moving through the conduit turns in a direction in the junction between the first end section and the curved midsection of the conduit, and in the junction between the second end section and the curved midsection of the conduit, which direction of turn is the same as the direc- tion of turn of the media in a middle portion of the curved midsec- tion of the conduit.
  • Figure 1 illustrates a perspective view of an embodiment of the convective acceleration flowmeter of the present invention.
  • Figure 2 illustrates a perspective view of another embodiment of the convective acceleration flowmeter.
  • Figure 3 illustrates a perspective view of a further embodi- ment of the convective acceleration flowmeter.
  • Figure 4 illustrates a perspective view of yet another embodi- ment of the convective acceleration flowmeter.
  • Figure 5 illustrates a cross section of an embodiment of the accelero eter usable in the construction of the convective accel- ration flowmeter.
  • Figure 6 illustrates a cross section of another embodiment of the accelerometer usable in the construction of the convective acceleration flowmeter.
  • Figure 7 illustrates a cross section of an embodiment of the relative motion sensor usable in the construction of the convective acceleration flowmeter.
  • Figure 8 illustrates a cross section of another embodiment of the relative motion sensor usable in the construction of the convective acceleration flowmeter.
  • Figure 1 there is illustrated a perspective view of an embodiment of the convective acceleration flowmeter constructed in accordance with the principles of the present invention.
  • the conduit 1 with an inlet leg 2 and an outlet leg 3 is secured to a support 4 at two extremities 5 and 6 thereof respectively adjacent to the inlet and outlet legs 2 and 3.
  • the two end sections 7 and 8 of the conduit 1 disposed generally parallel to one another extend from the respective secured extremities 5 and 6 towards a common direction in a cantilever-like arrangement.
  • the curved mid- section 9 of the conduit 1 having an open-loop configuration generally disposed on a plane substantially perpendicular to a plane including the two end sections 7 and 8 connects the two end sections 7 and 8 to one another.
  • the two opposite halves of the conduit respectively including the two end sections 7 and 8 and the two opposite halves of the curved midsection 9 of the conduit 1 are respectively disposed on the two opposite sides of a plane generally coinciding with the x-y plane, which plane cuts through the middle section 10 of the conduit 1 in an angle generally perpendicular to the central axis of the conduit at the middle section 10 thereof.
  • the two opposite halves of the conduit 1 are vibrated relative to one another in lateral directions generally perpendicular to the plane including the curved midsection 9 by an electromagnetic vibrator 11 compris- ing an electromagnet affixed to the first end section 7 and energized by an alternating or pulsed elecLric current supplied by the vibrator power supply 12, and a ferromagnetic element reacting to the alternating magnetic force affixed to the second end section 8 of the conduit 1.
  • a pair of motion sensors 13 and 14 respective- ly included in the two opposite halves of the curved midsection of the conduit 1 respectively measures the flexural vibratory motions of the two opposite halves of the conduit.
  • the vibratory motion analyzer 15 analyzes the electrical signals supplied by the motion sensors 13 and 14, and the data processor 16 determines the mass flow rate and/or accumulated value thereof from a difference in the flexural vibration between the two opposite halves of the conduit 1. It is readily recognized that the electromagnetic vibrator 11 generates a flexural vibration of the conduit 1 that is antisym- metric about the middle section 10 of the conduit 1. In other words, the first half of the conduit intermediate the first secured extremity 5 and the middle section 10 is vibrated in directions always opposite to that of the second half of the conduit .inter- mediate the second secure extremity 6 and the middle section 10.
  • the flexural vibr.ition of velocity v produces a convective accele- dv ration U— -,— experienced by the media moving through the conduit 1, where U is the velocity of media moving through the conduit 1 and —j— is the space rate of change of the flexural vibration velo- city v in the direction following the central axis of the conduit 1.
  • the dynamic reaction force -yUA—— has a symmetric distribution about the middle section 10 of the conduit 1.
  • the amplitude of the dynamic reaction force is proportional to the mass flow rate of the media moving through the conduit 1
  • the amplitude of the secondary flexural vibration is proportional to the mass flow rate yUA. It is a well known fact that the amplitude of the secondary flexural vibration is proportional to the phase angle difference in the resultant flexural vibration between the two opposite halves of the conduit 1.
  • the mass flow rate of the media is determined from the phase angle difference between the two flexural vibratory motions respectively measured by the pair of motion sensors 13 and 14, wherein the proportionality relationship there- between is determined by calibrating the flowmeter.
  • the middle section 10 of the conduit is a nodal point in the flexural vibration, whereat the flexural vibration vanishes when the mass flow rate is equal to zero. Therefore, the mass flow rate may be determined from the amplitude of the flexural vibration of the conduit 1 measured at the nodal section by a motion sensor 17 disposed at the middle section 10 of the conduit 1.
  • the mass flow rate of the media should be determined from the amplitude of the flexural vibration measured at the nodal section minus the amplitude of the residual flexural vibration determined and recorded during the calibration of the flowmeter.
  • the density of media can be determined from the natural frequency of the flexural vibration of the conduit 1 and, consequently, the data processor may also determine the density of media from the natural frequency of the flexural vibration of the conduit induced by the electromagnetic vibrator 11.
  • Figure 2 there is illustrated a perspective view of another embodiment of the convective acceleration flowmeter, that is merely a structural modification of the embodiment shown in Figure 1 and operates on the same principles, which embodiment is obtained by bending the two end sections 7 and 8 included in the embodiment shown in Figure 1 over 90 degrees in two opposite directions on a plane generally parallel to the plane including the curved midsection 9 of the conduit 1.
  • the two end sections 18 and 19 of the conduit 20 extend towards one another from the respective secured extremities 21 and 22 thereof, which are connected to one another by a .&-shaped midsection 23.
  • the electromagnetic vibrator 24 induces flexural vibration of antisymmetric distribution.
  • the mass flow rate of the media is determined from the phase angle difference between the two flexu- ral vibrations respectively measured by the two vibratory motion sensors 25 and 26 respectively included in the two opposite halves of the curved midsection 23 of the conduit 20, or two vibra- tory motion sensors 27 and 28 respectively disposed in the two end sections 18 and 19 as an alternative design.
  • the mass flow rate may be determined from the amplitude of the flexu- ral vibration measured by the motion sensor 29 disposed at the middle section of the conduit.
  • the two motion sensors 13 and 14 shown in Figure 1 may be relocated to the two end sections 7 and 8 in an arrangement equivalent to the installation of the two motion sensors 27 and 28 shown in Figure 2.
  • the two opposite halves of the conduit 20 are respectively disposed on two opposite sides of a plane generally parallel to the x-y plane and cutting through the mid- die section of the conduit 20 at a generally perpendicular angle.
  • the media moving through the conduit in the junction between the first end section and the curved midsection, and in the junction between the second end section and the curved midsection turns in a direction oppo- site to the direction of turn of the media in a middle portion of the curved midsection of the conduit.
  • FIG 3 there is illustrated a perspective view of a further embodiment of the convective acceleration flowmeter, that is another structural modification of the embodiment shown in Figure 1, wherein the former results when the curved midsection of the latter is rotated over 180 degrees about an axis perpendicular to the plane including the two end sections.
  • the two end sections 30 and 31 of the conduit extending from respective secured extre- mities 32 and 33 towards a generally common direction are connected to one another by a curved midsection 34, wherein the middle section 35 of the conduit is disposed intermediate the secured extremities 23 and 33 and the over-hanging extremities of the two end sections, and between the two end sections 30 and 31.
  • the electromagnetic vibrator 36 induces flexural vibration of an antisymmetric dis- tribution, while the two vibratory motion sensors 37 and 38 res- pectively included in the two opposite halves of the curved mid- section 34 measures the flexural vibrations of the two opposite halves of the conduit, wherein the mass flow rate is determined from the phase angle difference therebetween.
  • the mass flow rate may be also determined from the amplitude of the flexural vibra- tion generated by the mass flow and measured by the motion sensor 39 disposed at a nodal section coinciding with the middle section 35 of the conduit.
  • the pair of motion sensors 37 and 38 may be relocated to the midsections of the two end sections 30 and 31 adjacent to the middle section 35 of the conduit.
  • the density of media can be determined from the natural frequency of the flexural vibration.
  • the two opposite halves of the conduit are- respectively disposed on two opposite sides of a plane general- ly perpendicular to the plane substantially including the curved midsection 34 of the conduit and cutting through the middle section 35 of the conduit at a generally perpendicular angle.
  • Figure 4 there is illustrated a perspective view of yet another embodiment of the convective acceleration flowmeter, that is a structural modification of the embodiment shown in Figure 3, wherein the former results when the two end sections 30 and 31 of the latter are bent over 90 degrees in two opposite directions on a plane generally including the curved midsection 34 of the conduit.
  • the two end sections 40 and 41 of the conduit extending from the respective secured extremities 42 and 43 thereof extending towards one another are connected to one another by a curved midsection 44 of the conduit of heart-shaped configuration.
  • the electromagnetic vibrator 45 generates flexural vibration of an antisymmetric distribution, while the two vibratory motion sensors 46 and 47 measure flexural vibrations of the two opposite halves of the conduit, wherein the mass flow rate of the media is determined from the phase angle difference therebetween.
  • the mass flow rate may be determined from the amplitude of the flexural vibration generated by the mass flow of the media and measured by the motion sensor 48 disposed at a nodal section coinciding with the middle section of the conduit.
  • the pair of motion sensors 46 and 47 may be relocated to the two end sections 40 and 41 in an alternative design as exemplified by the two motion sensors 27 and 28 included in the embodiment shown in Figure 2. It should be noticed that the two opposite halves of the conduit are respectively disposed on two opposite sides of a plane generally perpendicular to a plane generally including the curved midsection 44 of the conduit and cut- ting through the middle section of the conduit at a generally per- pendicular angle.
  • a transducer holder 49 is fixedly mounted on the conduit 50 provid- ing the flow passage, which transducer holder 49 includes a pair of piezo electric eleemnts 51 and 52 respectively disposed on two diametrically opposite sides of the conduit 50 across a plane subs- tantially perpendicular to the directions of the flexural vibration of the conduit.
  • Each of the two piezo electric elements sandwiched between two electrodes insulated from the surrounding elements are under compression as the two retainer caps 53 and 54 included in the retainer 55 are pulled towards one another by relatively thin side walls 56 and 57 under tensions created by the pins 58 and 59 driven between the retainer 55 and the holder 49.
  • One of the two electrodes respectively included in each of the two piezo electric elements is connected to one of the two amplifiers 60 and 61, which combination has a signal balancing means 62 therebetween.
  • the other electrodes of the piezo electric elements not connected to the amplifiers 60 or 61 are grounded.
  • the electrodes of the two piezo electric elements 51 and 52 connected to the amplifiers 60 and 61 are selected in such a way that they generate electro- motive forces of the same polarity under the flexural vibration of the conduit, whereby the two electromotive forces respectively generated by the two piezo electric elements 51 and 52 are combin- ed in such a way that the noises are cancelled between the two amplifiers 60 and 61 by adjusting the signal balancing means 62 and a resultant electrical signal 63 representing the flexural vibra- tion of the conduit is obtained.
  • the electrodes of the two piezo electric elements connected to the two amplifiers may be selected in such a way that they generate electromotive forces of two opposite polarities, which are now com- bined by a combination of a noninvertlng and an inverting amplifier with a signal balancing means therebetween. It should be mentioned that only one of the two piezo electric elements and only one of the two amplifiers without the signal balancing means may be retained in a simpler version of the vibratory motion sensor, that is an alternative to the embodiment shown in Figure 5. In Figure 6 there is illustrated a cross section of another embodiment of the vibratory motion sensor, that is a modification of the embodiment shown in Figure 5.
  • the pair of curved piezo electric elements 64 and 65 are disposed in a diametrically symmetric arrange- ment across the conduit 66 providing the flow passage and retained between an inner circular cylindrical retainer 67 fixedly mounted on the conduit 66 and an outer elliptical cylindrical retainer 68 in a squeezed arrangement therebetween, wherein the compressive forces compressing each of the two piezo electric elements 64 and 65 are created by the pins 69 and 70 driven between side walls of the inner and outer cylindrical retainers 67 and 68.
  • a simplified version of the embodiment shown in Figure 6 may include only one of the two piezo electric elements.
  • FIG. 7 there is illustrated a cross section of a further embodiment of the vibratory motion sensor usable in constructing the convective acceleration flowmeter, that measures relative vibra- tory motion between the conduit 71 and a rigid support 72 struc- turally integrated to the support securing the two extremities of the conduit 71.
  • An elongated flexible member 73 with one extremity anchored to the rigid support 72 and the other extremity connected to the conduit 71 is disposed in a direction generally perpendicu- lar to the directions of the flexural vibration of the conduit 71 and to the central axis of the conduit 71.
  • a pair of piezo elect- ric elements 74 and 75 are disposed on two opposite sides of the elongated flexible member 73, wherein each of the two piezo elect- ric elements is under squeezing action between the elongated flexi- ble member 73 and the one of the two halves of the rigid support 72.
  • the lead wires extending from the electrodes of the piezo electric elements may be connected to the amplifiers with noise cancelling means as shown and described in conjunction with Figure 5.
  • a simplified version of the motion sensor shown in Figure 7 may include only one of the two piezo electric elements shown in Figure 7.
  • a piezo electric force sensor commonly employed in the construction of the vortex shedding flowmeters that includes an elongated force transmitting member extending from a thin end wall of the cylindrical transducer con- tainer vessel anchored to the rigid support, may be used in place of the motion sensor shown in Figure 7.
  • Figure 8 there is illustrated a cross section of yet another embodiment of the vibratory motion sensor usable in the construction of the convective acceleration flowmeter, that measures relative vibratory motion between the conduit 76 and a rigid support 77 structurally integrated to the support anchoring the two secured extremities of the conduit.
  • a permanent magnet 78 affixed to the conduit 76 provides a magnetic field that induces an electromotive force in an induction coil 79 wound on a ferromagnetic core 80, when there is a relative motion between the permanent magnet 78 and the ferromagnetic core 80.
  • the combination of the induction coil 79 and the ferromagnetic coil 80 may be affixed to the conduit 76, while the permanent magnet 78 is anchored to the rigid support 77 in an alternative design.
  • other motion or displacement sensors such as those employing optical fiber, strain gauge, and capaci- tive disc element, etc. may be used in place of the embodiments shown in Figures 5 through 8.

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

Abstract

A mass flowmeter comprises a conduit (1) with two extremities (5 and 6) secured to a support (4), which conduit includes a first and second end sections (7 and 8) extending from the respective secured extremities thereof in a cantilever-like arrangement and a curved midsection (9) connecting the first and second end sections (7 and 8) to one another, an electromagnetic vibrator (11) inducing a relative flexural vibration between the two opposite halves of the conduit, and a pair of vibration sensors (13 and 14) respectively measuring the flexural vibration of the conduit at two sections of the conduit respectively belonging to the two opposite halves of the conduit, wherein mass flow rate of media moving through the conduit (1) is determined from the phase angle difference between two vibrations respectively measured by the two vibration sensors (13 and 14).

Description

CONVECTIVE ACCELERATION FLOWMETER
The priority on the invention described and claimed in the present patent application is based on U.S.A. patent applica- tion S.N. 07/440,693 entitled "Vibrating Conduit Mass Flowmeter" filed on 11/24/89 and U.S.A. patent application S.N. 07/467,481 entitled "Vibrating Looped Conduit Mass Flowmeter" filed on 01/19/90 . The emergence of a type of flowmeter commonly known as the "Coriolis Force" flowmeter and wide-spread use thereof has revolu- tionized the mass flow measuring technology. In spite of the head- long progress in the design and operating principles of the "Coriolis Force" flowmeters, there remains many short-comings with the existing types of the Coriolis Force flowmeter. For example, simple designs employing vibrating conduits of simple geometry such as a straight tubing lacks the ability to measure low values of mass flow rate, while designs employing vibrating conduits of complex geometry such as curved or looped conduits are bulky and heavy. Without any exception, all existing versions of the Coriolis Force flowmeter are expensive and suffer from an inability to measure low values of mass flow rates of media. The mass flowmeter disclosed in the present patent applica- tion employs a single vibrating conduit, wherein the two opposite halves thereof are vibrated laterally in an antisymmetric mode, which contrasts the existing types employing a single or dual vibrating conduits wherein the two opposite halves thereof are vibrated in a symmetric mode. The primary object of the present invention is to provide a mass flowmeter comprising a conduit with two extremities secured to a support, which conduit includes two end sections respectively extending from the two secured extremities thereof and a curved midsection connecting the two end sections, wherein the two oppo- site halves of the conduit are respectively disposed on two oppo- site sides of a hypothetical plane cutting across the midsection of the conduit in an angle generally perpendicular to the central axis of the conduit; wherein an electromagnetic vibrating means vibrates the two opposite halves of the conduit relative to one another in directions perpendicular to a plane generally includ- ing the curved midsection of the conduit, and vibratory motion sensing means measures the difference in the flexural vibration between the two opposite halves of the conduit as a measure of mass flow rate of media moving through the conduit. Another object is to provide the mass flowmeter described in the above-described primary object, wherein the two end sections of the conduit extend from the respective secured extremities thereof towards a generally common direction; wherein the media moving through the conduit turns in a direction in the junction between the first end section and the curved midsection of the conduit, and in the junction between the second end section and the curved midsection of the conduit, which direction of turn is opposite to the direction of turn of the media in a middle portion of the curved midsection of the conduit. A further object is to provide the mass flowmeter described in the above described primary object, wherein the two end sections of the conduit extend from the respective secured extremities thereof towards a generally common direction; wherein the media moving through the conduit turns in a direction in the junction between the first end section and the curved midsection of the con- duit, and in the junction between the second end section and the curved midsection of the conduit, which direction of turn is the same as the direction of turn of the media in a middle portion of the curved midsection of the conduit. Yet another object is to provide the mass flowmeter described in the above-described primary object, wherein the two end sections of the conduit extend from the respective secured extremities there- of towards one another; wherein the media moving through the conduit turns in a direction in the junction between the first end section and the curved midsection of the conduit, and in the junction between the second end section and the curved midsection of the conduit, which direction of turn is opposite to the direc- tion of turn of the media in a middle portion of the curved mid- section of the conduit. Yet a further object is to provide the mass flowmeter describ- ed in the above-described primary object, wherein the two end sections of the conduit extend from the respective secured extremi- ties thereof towards one another; wherein the media moving through the conduit turns in a direction in the junction between the first end section and the curved midsection of the conduit, and in the junction between the second end section and the curved midsection of the conduit, which direction of turn is the same as the direc- tion of turn of the media in a middle portion of the curved midsec- tion of the conduit. Still another object is to provide the mass flowmeter describ- ed in the above-described primary object, wherein the vibratory motion sensing means includes a pair of accelerometers respectively measuring the flexural vibrations of the two opposite halves of the conduit, and the mass flow rate of the media is determined from the difference between two vibratory motions respectively measured by the pair of accelerometers. Still a further object is to provide the mass flowmeter des- cribed in the above-described primary object, wherein the vibratory motion sensing means includes a pair of relative motion sensors respectively measuring relative motions between a stationary support and the two opposite halves of the conduit, and the mass flow rate is determined from the difference between two vibratory motions respectively measured by the pair of relative motion sensors. These and other objects of the present invention will become clear as the description thereof progresses. The present invention may be described with a greater clarity and specificity by referring to the following figures : Figure 1 illustrates a perspective view of an embodiment of the convective acceleration flowmeter of the present invention. Figure 2 illustrates a perspective view of another embodiment of the convective acceleration flowmeter. Figure 3 illustrates a perspective view of a further embodi- ment of the convective acceleration flowmeter. Figure 4 illustrates a perspective view of yet another embodi- ment of the convective acceleration flowmeter. Figure 5 illustrates a cross section of an embodiment of the accelero eter usable in the construction of the convective accel- ration flowmeter. Figure 6 illustrates a cross section of another embodiment of the accelerometer usable in the construction of the convective acceleration flowmeter. Figure 7 illustrates a cross section of an embodiment of the relative motion sensor usable in the construction of the convective acceleration flowmeter. Figure 8 illustrates a cross section of another embodiment of the relative motion sensor usable in the construction of the convective acceleration flowmeter. In Figure 1 there is illustrated a perspective view of an embodiment of the convective acceleration flowmeter constructed in accordance with the principles of the present invention. The conduit 1 with an inlet leg 2 and an outlet leg 3 is secured to a support 4 at two extremities 5 and 6 thereof respectively adjacent to the inlet and outlet legs 2 and 3. The two end sections 7 and 8 of the conduit 1 disposed generally parallel to one another extend from the respective secured extremities 5 and 6 towards a common direction in a cantilever-like arrangement. The curved mid- section 9 of the conduit 1 having an open-loop configuration generally disposed on a plane substantially perpendicular to a plane including the two end sections 7 and 8 connects the two end sections 7 and 8 to one another. It should be noticed that the two opposite halves of the conduit respectively including the two end sections 7 and 8 and the two opposite halves of the curved midsection 9 of the conduit 1 are respectively disposed on the two opposite sides of a plane generally coinciding with the x-y plane, which plane cuts through the middle section 10 of the conduit 1 in an angle generally perpendicular to the central axis of the conduit at the middle section 10 thereof. The two opposite halves of the conduit 1 are vibrated relative to one another in lateral directions generally perpendicular to the plane including the curved midsection 9 by an electromagnetic vibrator 11 compris- ing an electromagnet affixed to the first end section 7 and energized by an alternating or pulsed elecLric current supplied by the vibrator power supply 12, and a ferromagnetic element reacting to the alternating magnetic force affixed to the second end section 8 of the conduit 1. A pair of motion sensors 13 and 14 respective- ly included in the two opposite halves of the curved midsection of the conduit 1 respectively measures the flexural vibratory motions of the two opposite halves of the conduit. The vibratory motion analyzer 15 analyzes the electrical signals supplied by the motion sensors 13 and 14, and the data processor 16 determines the mass flow rate and/or accumulated value thereof from a difference in the flexural vibration between the two opposite halves of the conduit 1. It is readily recognized that the electromagnetic vibrator 11 generates a flexural vibration of the conduit 1 that is antisym- metric about the middle section 10 of the conduit 1. In other words, the first half of the conduit intermediate the first secured extremity 5 and the middle section 10 is vibrated in directions always opposite to that of the second half of the conduit .inter- mediate the second secure extremity 6 and the middle section 10. The flexural vibr.ition of velocity v produces a convective accele- dv ration U— -,— experienced by the media moving through the conduit 1, where U is the velocity of media moving through the conduit 1 and —j— is the space rate of change of the flexural vibration velo- city v in the direction following the central axis of the conduit 1. The convective acceleration U—:— experienced by the media moving through the conduit 1 produces a dynamic reaction force -yUA~— exerted on the conduit 1 by the media moving therethrough, where 9 is the density of the media in the conduit 1 and A is the cross section area of the flow passage provided by the conduit 1. It is readily recognized that the dynamic reaction force -yUA—— has a symmetric distribution about the middle section 10 of the conduit 1. In summary, the primary flexural vibration having an antisym- metric distribution, that is induced by the electromagnetic vibra- tor 11, produces a secondary flexural vibration having a symmetric distribution, that is generated by the dynamic reaction force of the media moving through the conduit. As the amplitude of the dynamic reaction force is proportional to the mass flow rate of the media moving through the conduit 1, the amplitude of the secondary flexural vibration is proportional to the mass flow rate yUA. It is a well known fact that the amplitude of the secondary flexural vibration is proportional to the phase angle difference in the resultant flexural vibration between the two opposite halves of the conduit 1. Consequently, the mass flow rate of the media is determined from the phase angle difference between the two flexural vibratory motions respectively measured by the pair of motion sensors 13 and 14, wherein the proportionality relationship there- between is determined by calibrating the flowmeter. It should be mentioned that the middle section 10 of the conduit is a nodal point in the flexural vibration, whereat the flexural vibration vanishes when the mass flow rate is equal to zero. Therefore, the mass flow rate may be determined from the amplitude of the flexural vibration of the conduit 1 measured at the nodal section by a motion sensor 17 disposed at the middle section 10 of the conduit 1. In actual practice, there may be a residual flexural vibration at the nodal point and, consequently, the mass flow rate of the media should be determined from the amplitude of the flexural vibration measured at the nodal section minus the amplitude of the residual flexural vibration determined and recorded during the calibration of the flowmeter. In general, it is desirable to vibrate the conduit at its natural frequency, which natural frequency of the flexural vibration can be determined by energizing the electro- magnetic vibrator in a frequency sweep mode, wherein the natural frequency is equal to the frequency producing the maximum ampli- tude of the flexural frequency, which information is fed back from the vibratory motion analyzer 15 to the vibratory power supply 12. It is well known that the density of media can be determined from the natural frequency of the flexural vibration of the conduit 1 and, consequently, the data processor may also determine the density of media from the natural frequency of the flexural vibration of the conduit induced by the electromagnetic vibrator 11. In Figure 2 there is illustrated a perspective view of another embodiment of the convective acceleration flowmeter, that is merely a structural modification of the embodiment shown in Figure 1 and operates on the same principles, which embodiment is obtained by bending the two end sections 7 and 8 included in the embodiment shown in Figure 1 over 90 degrees in two opposite directions on a plane generally parallel to the plane including the curved midsection 9 of the conduit 1. As a consequence, the two end sections 18 and 19 of the conduit 20 extend towards one another from the respective secured extremities 21 and 22 thereof, which are connected to one another by a .&-shaped midsection 23. The electromagnetic vibrator 24 induces flexural vibration of antisymmetric distribution. The mass flow rate of the media is determined from the phase angle difference between the two flexu- ral vibrations respectively measured by the two vibratory motion sensors 25 and 26 respectively included in the two opposite halves of the curved midsection 23 of the conduit 20, or two vibra- tory motion sensors 27 and 28 respectively disposed in the two end sections 18 and 19 as an alternative design. Of course, the mass flow rate may be determined from the amplitude of the flexu- ral vibration measured by the motion sensor 29 disposed at the middle section of the conduit. It should be mentioned that the two motion sensors 13 and 14 shown in Figure 1 may be relocated to the two end sections 7 and 8 in an arrangement equivalent to the installation of the two motion sensors 27 and 28 shown in Figure 2. It should be noticed that the two opposite halves of the conduit 20 are respectively disposed on two opposite sides of a plane generally parallel to the x-y plane and cutting through the mid- die section of the conduit 20 at a generally perpendicular angle. In the embodiments shown in Figures 1 and 2, the media moving through the conduit in the junction between the first end section and the curved midsection, and in the junction between the second end section and the curved midsection turns in a direction oppo- site to the direction of turn of the media in a middle portion of the curved midsection of the conduit. In Figure 3 there is illustrated a perspective view of a further embodiment of the convective acceleration flowmeter, that is another structural modification of the embodiment shown in Figure 1, wherein the former results when the curved midsection of the latter is rotated over 180 degrees about an axis perpendicular to the plane including the two end sections. The two end sections 30 and 31 of the conduit extending from respective secured extre- mities 32 and 33 towards a generally common direction are connected to one another by a curved midsection 34, wherein the middle section 35 of the conduit is disposed intermediate the secured extremities 23 and 33 and the over-hanging extremities of the two end sections, and between the two end sections 30 and 31. The electromagnetic vibrator 36 induces flexural vibration of an antisymmetric dis- tribution, while the two vibratory motion sensors 37 and 38 res- pectively included in the two opposite halves of the curved mid- section 34 measures the flexural vibrations of the two opposite halves of the conduit, wherein the mass flow rate is determined from the phase angle difference therebetween. The mass flow rate may be also determined from the amplitude of the flexural vibra- tion generated by the mass flow and measured by the motion sensor 39 disposed at a nodal section coinciding with the middle section 35 of the conduit. Of course, the pair of motion sensors 37 and 38 may be relocated to the midsections of the two end sections 30 and 31 adjacent to the middle section 35 of the conduit. As men- tioned in conjunction with Figure 1, the density of media can be determined from the natural frequency of the flexural vibration. It should be noticed that the two opposite halves of the conduit are- respectively disposed on two opposite sides of a plane general- ly perpendicular to the plane substantially including the curved midsection 34 of the conduit and cutting through the middle section 35 of the conduit at a generally perpendicular angle. In Figure 4 there is illustrated a perspective view of yet another embodiment of the convective acceleration flowmeter, that is a structural modification of the embodiment shown in Figure 3, wherein the former results when the two end sections 30 and 31 of the latter are bent over 90 degrees in two opposite directions on a plane generally including the curved midsection 34 of the conduit. The two end sections 40 and 41 of the conduit extending from the respective secured extremities 42 and 43 thereof extending towards one another are connected to one another by a curved midsection 44 of the conduit of heart-shaped configuration. The electromagnetic vibrator 45 generates flexural vibration of an antisymmetric distribution, while the two vibratory motion sensors 46 and 47 measure flexural vibrations of the two opposite halves of the conduit, wherein the mass flow rate of the media is determined from the phase angle difference therebetween. The mass flow rate may be determined from the amplitude of the flexural vibration generated by the mass flow of the media and measured by the motion sensor 48 disposed at a nodal section coinciding with the middle section of the conduit. The pair of motion sensors 46 and 47 may be relocated to the two end sections 40 and 41 in an alternative design as exemplified by the two motion sensors 27 and 28 included in the embodiment shown in Figure 2. It should be noticed that the two opposite halves of the conduit are respectively disposed on two opposite sides of a plane generally perpendicular to a plane generally including the curved midsection 44 of the conduit and cut- ting through the middle section of the conduit at a generally per- pendicular angle. It should be mentioned that the media moving through the conduit employed in the embodiments shown in Figures 3 and 4 turns in the same direction in the junction between the first end section and the curved midsection of the conduit and in the junction between the second end section and the curved mid- section of the conduit as the direction of turn of the media in a middle portion of the curved midsection of the conduit. It should be understood that the middle section of the conduit coinciding with the nodal section may be secured to a support structure. In Figure 5 there is illustrated-a cross section of an embodi- ment of the motion sensor employed in the construction of the con- vective acceleration flowmeter shown in Figures 1 through 4. A transducer holder 49 is fixedly mounted on the conduit 50 provid- ing the flow passage, which transducer holder 49 includes a pair of piezo electric eleemnts 51 and 52 respectively disposed on two diametrically opposite sides of the conduit 50 across a plane subs- tantially perpendicular to the directions of the flexural vibration of the conduit. Each of the two piezo electric elements sandwiched between two electrodes insulated from the surrounding elements are under compression as the two retainer caps 53 and 54 included in the retainer 55 are pulled towards one another by relatively thin side walls 56 and 57 under tensions created by the pins 58 and 59 driven between the retainer 55 and the holder 49. One of the two electrodes respectively included in each of the two piezo electric elements is connected to one of the two amplifiers 60 and 61, which combination has a signal balancing means 62 therebetween. The other electrodes of the piezo electric elements not connected to the amplifiers 60 or 61 are grounded. The electrodes of the two piezo electric elements 51 and 52 connected to the amplifiers 60 and 61 are selected in such a way that they generate electro- motive forces of the same polarity under the flexural vibration of the conduit, whereby the two electromotive forces respectively generated by the two piezo electric elements 51 and 52 are combin- ed in such a way that the noises are cancelled between the two amplifiers 60 and 61 by adjusting the signal balancing means 62 and a resultant electrical signal 63 representing the flexural vibra- tion of the conduit is obtained. In an alternative arrangement, the electrodes of the two piezo electric elements connected to the two amplifiers may be selected in such a way that they generate electromotive forces of two opposite polarities, which are now com- bined by a combination of a noninvertlng and an inverting amplifier with a signal balancing means therebetween. It should be mentioned that only one of the two piezo electric elements and only one of the two amplifiers without the signal balancing means may be retained in a simpler version of the vibratory motion sensor, that is an alternative to the embodiment shown in Figure 5. In Figure 6 there is illustrated a cross section of another embodiment of the vibratory motion sensor, that is a modification of the embodiment shown in Figure 5. The pair of curved piezo electric elements 64 and 65, each of which includes a pair of electrodes with matched surface geometry sandwiching the piezo electric element, are disposed in a diametrically symmetric arrange- ment across the conduit 66 providing the flow passage and retained between an inner circular cylindrical retainer 67 fixedly mounted on the conduit 66 and an outer elliptical cylindrical retainer 68 in a squeezed arrangement therebetween, wherein the compressive forces compressing each of the two piezo electric elements 64 and 65 are created by the pins 69 and 70 driven between side walls of the inner and outer cylindrical retainers 67 and 68. A simplified version of the embodiment shown in Figure 6 may include only one of the two piezo electric elements. In Figure 7 there is illustrated a cross section of a further embodiment of the vibratory motion sensor usable in constructing the convective acceleration flowmeter, that measures relative vibra- tory motion between the conduit 71 and a rigid support 72 struc- turally integrated to the support securing the two extremities of the conduit 71. An elongated flexible member 73 with one extremity anchored to the rigid support 72 and the other extremity connected to the conduit 71 is disposed in a direction generally perpendicu- lar to the directions of the flexural vibration of the conduit 71 and to the central axis of the conduit 71. A pair of piezo elect- ric elements 74 and 75 are disposed on two opposite sides of the elongated flexible member 73, wherein each of the two piezo elect- ric elements is under squeezing action between the elongated flexi- ble member 73 and the one of the two halves of the rigid support 72. The lead wires extending from the electrodes of the piezo electric elements may be connected to the amplifiers with noise cancelling means as shown and described in conjunction with Figure 5. A simplified version of the motion sensor shown in Figure 7 may include only one of the two piezo electric elements shown in Figure 7. It should be mentioned that a piezo electric force sensor commonly employed in the construction of the vortex shedding flowmeters, that includes an elongated force transmitting member extending from a thin end wall of the cylindrical transducer con- tainer vessel anchored to the rigid support, may be used in place of the motion sensor shown in Figure 7. In Figure 8, there is illustrated a cross section of yet another embodiment of the vibratory motion sensor usable in the construction of the convective acceleration flowmeter, that measures relative vibratory motion between the conduit 76 and a rigid support 77 structurally integrated to the support anchoring the two secured extremities of the conduit. A permanent magnet 78 affixed to the conduit 76 provides a magnetic field that induces an electromotive force in an induction coil 79 wound on a ferromagnetic core 80, when there is a relative motion between the permanent magnet 78 and the ferromagnetic core 80. Of course, the combination of the induction coil 79 and the ferromagnetic coil 80 may be affixed to the conduit 76, while the permanent magnet 78 is anchored to the rigid support 77 in an alternative design. It should be understood that other motion or displacement sensors such as those employing optical fiber, strain gauge, and capaci- tive disc element, etc. may be used in place of the embodiments shown in Figures 5 through 8. While the principles of the invention have now become clear by the illustrative embodiments shown and described, there will be many modifications of the structures, arrangements, proportions, elements and materials, which are obvious to those skilled in the art and particularly adapted to the specific working environments and operating conditions in the practice of the invention without departing from those principles. It is not desired to limit the invention to the illustrative embodiments shown and described and accordingly, all suitable modifications and equivalents may be regarded as falling within the scope of the invention as defined by the claims which follow.

Claims

The embodiments of the invention, in which an exclusive property or priviledge is claimed, are defined as follows : 1. An apparatus for measuring flow rate of media compris- ing in combination : a) a conduit with two extremities secured to a support including a first end section extending from one of said two secured extremities in a cantilever-like arrangement, a second end section extending from the other of said two secured extremities in a cantilever- like arrangement, and a curved midsection connecting the first and second end sections to one another ,in a configuration wherein two opposite halves of the conduit are respectively disposed substantially on two opposite sides of a hypothetical plane cutting across a middle section of the curved midsection of the conduit at generally perpendicular relationship therebetween; b) means for exerting a vibratory force to two sections of the conduit respectively adjacent to over-hanging extre- mities of the first and second end sections for generat- ing a relative flexural vibration between two opposite halves of the conduit; and c) means for determining difference in flexural vibration of the conduit between the two opposite halves of the conduit as a measure of mass flow rate of media moving through the conduit. 2. A combination as set forth in Claim 1 wherein said means for determining difference in flexural vibration comprises a pair of vibration sensors respectively measuring the flexural vibration of the conduit at two sections of the conduit respectively belong- ing to the two opposite halves of the conduit. 3. A combination as set forth in Claim 2 wherein said combi- nation includes means for determining mass flow rate of the media from phase angle difference between the two flexural vibrations respectively measured by the two vibration sensors. 4. A combination as set forth in Claim 3 wherein said combi- nation includes means for determining the density of media from a 1 natural frequency of the flexural vibration of the conduit.
2 5. A combination as set forth in Claim 1 wherein said means
3 for determining difference in flexural vibration comprises a pair
4 of accelerometers respectively secured to two sections of the con-
5 duit respectively belonging to the two opposite halves of the
7 conduit.
8 6. A combination as set forth in Claim 5 wherein said combi-
9 nation includes means for determining mass flow rate of the media
10 from phase angle difference between two electrical signals res-
11 pectively generated by the two accelerometers.
12 7. A combination as set forth in Claim 6 wherein said combi-
13 nation includes means for determining the density of media from a
14 natural frequency of the flexural vibration of the conduit.
15 8. A combination as set forth in Claim 1 wherein said means
16 for determining difference in flexural vibration comprises a
17 vibration sensor measuring the flexural vibration of the conduit
18 at a middle section of the conduit whereat the flexural vibration
19 substantially vanishes when the media contained in the conduit is
20 stationary; wherein said combination includes means for determin-
21 ing mass flow rate of the media from amplitude of the flexural
22 vibration measured by said vibration sensor ,
23 9. A combination as set forth in Claim 8 wherein said combi-
24 nation includes means for determining the density of media from a
25 natural frequency of the flexural vibration of the conduit.
26 10. A combination as set forth in Claim 1, wherein said
27 means for determining difference in flexural vibration comprises
28 an accelerometer secured to the middle section of the conduit
29 whereat the flexural vibration substantially vanishes when the
30 media contained in the conduit is stationary; wherein said
31 combination includes means for. determining mass flow rate of the
32 media from amplitude of electrical signal generated by said
33 accelerometer.
34 11. A combination as set forth in Claim 10 wherein said
35 combination includes means for determining the density of media
36 from a natural frequency of the flexural vibration of the conduit. 12. A combination as set forth in Claim 1 wherein the first and second end sections of the conduit extend towards a generally c.mmon direction, arid the direction of turn of the media in junc- tion between the first end section and the curved midsection and in junction between the second end section and the curved mid- section is opposite to the direction of turn of the media in a middle portion of the curved midsection of the conduit. 13. A combination as set forth in Claim 12 wherein said means for determining difference in flexural vibration comprises a pair of vibration sensors respectively measuring the flexural vibration of the conduit at two sections respectively belonging to the two opposite halves of the conduit; wherein said combina- tion includes means for determining mass flow rate of the media from phase angle difference between two vibrations respectively measured by the two vibration sensors. 14. A combination as set forth in Claim 1 wherein the first and second end sections of the conduit extend generally towards one another, and the direction of turn of the media in junction between the first end section and the curved midsection and in junction between the second end section and the curved midsection is opposite to the direction of turn of the media in a middle portion of the curved midsection of the conduit. 15. A combination as set forth in Claim 14 wherein said means for determining difference in flexural vibration comprises a pair of vibration sensors respectively measuring the flexural vibration of the conduit at two sections respectively belonging to the two opposite halves of the conduit,wherein said combina- tion includes means for determining mass flow rate of the media from phase angle difference between two vibrations respectively measured by the two vibration sensors. 16. A combination as set forth in Claim 1 wherein the first and second end sections of the conduit extend towards a generally common direction, and the direction of turn of the media in junction between the first end section and the curved midsection and in junction between the second end section and the curved mid- section is the same as the direction of turn of media in a middle portion of the curved midsection of the conduit. 17. A combination as set forth in Claim 16 wherein said means for determining difference in flexural vibration comprises a pair of vibration sensors respectively measuring the flexural vibration of the conduit at two sections respectively belonging to the two opposite halves of the conduit; wherein said combina- tion includes means for determining mass flow rate of the media from phase angle difference between two vibrations respectively measured by the two vibration sensors. 18. A combination as set forth in Claim 1 wherein the first and second sections of the conduit extend generally towards one another, and the direction of turn of the media in junction between the first end section and the curved midsection and in junction between the second end section and the curved midsection is the same as the direction of turn of the media in a middle portion of the curved midsection of the conduit. 19. A combination as set forth in Claim 18 wherein said means for determining difference in flexural vibration comprises a pair of vibration sensors respectively measuring the flexural vibration of the conduit at two sections respectively belonging to the two opposite halves of the conduit; wherein said combi- nation includes means for determining mass flow rate of the media from phase angle difference between two vibrations respectively measured by the two vibration sensors.
EP19900917488 1989-11-24 1990-11-17 Convective acceleration flowmeter Ceased EP0456789A4 (en)

Applications Claiming Priority (4)

Application Number Priority Date Filing Date Title
US440693 1989-11-24
US07/440,693 US5123287A (en) 1989-11-24 1989-11-24 Vibrating conduit mass flowmeter
US467481 1990-01-19
US07/467,481 US5060523A (en) 1990-01-19 1990-01-19 Vibrating looped conduit mass flowmeter

Publications (2)

Publication Number Publication Date
EP0456789A1 EP0456789A1 (en) 1991-11-21
EP0456789A4 true EP0456789A4 (en) 1992-03-11

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US6606573B2 (en) * 2001-08-29 2003-08-12 Micro Motion, Inc. Sensor apparatus, methods and computer program products employing vibrational shape control
KR101206377B1 (en) 2005-09-20 2012-11-29 마이크로 모우션, 인코포레이티드 Meter electronics and methods for generating a drive signal for a vibratory flowmeter

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WO1986000699A1 (en) * 1984-07-11 1986-01-30 Exac Corporation Improved apparatus for mass flow rate and density measurement
FR2617962A1 (en) * 1987-07-06 1989-01-13 Fischer & Porter Co MASS FLOWMETER OF THE CORIOLIS TYPE WITH DOUBLE LOOP
WO1989001134A1 (en) * 1987-07-27 1989-02-09 Lew Hyok S Convective inertia force flowmeter

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CN1022646C (en) * 1987-04-20 1993-11-03 东机工株式会社 Mass flowmeter

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WO1986000699A1 (en) * 1984-07-11 1986-01-30 Exac Corporation Improved apparatus for mass flow rate and density measurement
FR2617962A1 (en) * 1987-07-06 1989-01-13 Fischer & Porter Co MASS FLOWMETER OF THE CORIOLIS TYPE WITH DOUBLE LOOP
WO1989001134A1 (en) * 1987-07-27 1989-02-09 Lew Hyok S Convective inertia force flowmeter

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JPH04503256A (en) 1992-06-11
EP0456789A1 (en) 1991-11-21
CA2030298A1 (en) 1991-05-25

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