WO2024144404A1 - A non-invasive non-intrusive clamp-on transducer wedge and a method for arranging a transducer to a pipe or conduit for wave transmission along chordal paths in a fluid inside the pipe or conduit - Google Patents

A non-invasive non-intrusive clamp-on transducer wedge and a method for arranging a transducer to a pipe or conduit for wave transmission along chordal paths in a fluid inside the pipe or conduit Download PDF

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Publication number
WO2024144404A1
WO2024144404A1 PCT/NO2023/060139 NO2023060139W WO2024144404A1 WO 2024144404 A1 WO2024144404 A1 WO 2024144404A1 NO 2023060139 W NO2023060139 W NO 2023060139W WO 2024144404 A1 WO2024144404 A1 WO 2024144404A1
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Prior art keywords
transducer
conduit
pipe
wedge
clamp
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PCT/NO2023/060139
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French (fr)
Inventor
Remi Andre Kippersund
Tarjei Furnes ROMMETVEIT
Magne HUSEBØ
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Xsens As
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Publication of WO2024144404A1 publication Critical patent/WO2024144404A1/en

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    • 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
    • G01F1/66Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow by measuring frequency, phase shift or propagation time of electromagnetic or other waves, e.g. using ultrasonic flowmeters
    • G01F1/662Constructional details
    • 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
    • G01F1/66Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow by measuring frequency, phase shift or propagation time of electromagnetic or other waves, e.g. using ultrasonic flowmeters
    • G01F1/667Arrangements of transducers for ultrasonic flowmeters; Circuits for operating ultrasonic flowmeters
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/22Details, e.g. general constructional or apparatus details
    • G01N29/223Supports, positioning or alignment in fixed situation

Definitions

  • Ultrasound flow meters are frequently used for measurement of a flow rate of a fluid through a conduit/pipe due to their ability to provide a good turndown ratio. Precise and detailed measurements may be provided by in-line meters utilizing multi-path measurements to detect the fluid speed profiles. Clamp-on transducers are provided for center-path measurements.
  • the first side having an elongated recess adapted to the outside form of the surface of a pipe or conduit it is to be mounted to, wherein the elongated recess has a form such that its longitudinal axis running at the rotation angle relative the longitudinal z axis in the y-z plane of the pipe or conduit it is to be mounted to, and thus positioning the longitudinal orientation of the clamp-on transducer wedge at a predetermined known angle both in wedge angle and rotation angle.
  • the sending transducer is operable to stimulate waves in off-centre chordal paths within a fluid flow within the pipe or conduit the clamp-on transducer wedge is to be mounted to.
  • controllers controlling the first and second transducers are hosted by a single controller.
  • Acoustic waves and waves shall be understood to be acoustic waves of any mode, including but not limited to: lamb-wave, shear-wave or compressional-wave of any type.
  • Figure 3B and 3C shows the wedge angle and the and rotation angle of the transducer when arranged in the wedge.
  • Figure 4B shows a detailed study of the entry and exit point of the wave in a chordal path through the fluid, typically from a helical transmitted waves in the pipe stimulating waves in the off-centre chordal paths.
  • an attenuation measurement of radiation through the fluid in the conduit is used as a first measure of fluid density, based upon the attenuation of certain guided wave modes being substantially proportional to an acoustic impedance ratio between the fluid and the pipe or conduit.
  • Figure 2A and 2B illustrates one alternative embodiment of the wedge 1 according to present disclosure seen from different angles.
  • a clamp-on non-invasive non-intrusive transducer wedge 1 comprising: a first side 2 for being arranged on the outside surface of a pipe or conduit 50, a transducer connecting element 4' for connecting a transducer 21', 22', wherein the transducer connecting element 4' being arranged to position a transducer 21', 22' on a surface in in the y-z plane rotated in a longitudinal wedge angle 4> relative the vertical x axis in the z-x plane of the pipe or conduit 50, and a rotation angle 0 relative the longitudinal z axis in the y-z plane of the pipe or conduit 50.
  • first side 2 having an elongated recess adapted to the outside form of the surface of a pipe or conduit 50 it is to be mounted to, wherein the elongated recess has a form such that its longitudinal axis running at the rotation 0 relative the longitudinal z axis in the x-z plane of the pipe or conduit 10 it is to be mounted to.
  • the recess provides a fixed rotation angle predefined for the wedge. If a different rotation angle is desired, a wedge with a different recess provided with desired angle must be chosen.
  • the rotation angle 0 is positioning the longitudinal orientation 90 of the clamp-on transducer wedge at an angle between the longitudinal and perpendicular direction of a pipe or conduit it is to be mounted to.
  • a wedge angle 4> is chosen so that the transduces has a greater than 0° angle relative the vertical x axis, the pointing direction of the transducer will point more away from the center of the pipe or conduit the higher the rotation angle 0 is chosen.
  • the clamp-on transducer wedge 1 may thus operate in pairs, wherein a first clamp-on transducer wedge 1,21 is arranged to comprise a first transducer 21', and the second clamp-on transducer wedgel,22 is arranged to comprise a second transducer 22'.
  • the sending transducer 21', 22' is operable to stimulate waves in off-centre chordal paths 18 within a fluid flow 52 within the pipe or conduit 50 the clamp-on transducer wedge 1,21,22 is to be mounted to.
  • the angle that the clamp-on transducer wedge points the transducer at in the rotation angle 0 defines the construction circle 15, 15' that the off-centre chordal paths the waves will pass through a fluid 52 that fills the pipe or conduit 50.
  • the waves may excite into the fluid through a first refraction angle 13 between the transducer and the outer side of the pipe/conduit wall, and/or a second refraction angle 14 between the inner side of the pipe/conduit wall and the fluid inside the pipe/conduit.
  • the material of the pipe or conduit is plastic based
  • it is advantageously that the acoustic properties of the plastic is comparable or substantially equal to the fluid to be analysed.
  • the first refraction angle 13 is substantially close to or equal to 0.
  • the acoustic properties of the metal is comparable or substantially equal to the transducers.
  • the receiving transducer When operating in pairs the receiving transducer is operable to receive the waves in off-centre chordal paths 18 within the fluid flow 52 within the pipe or conduit 50 it is to be mounted to from the sending transducer 21', 22'.
  • the equations may then be solved by setting p w to a known value and solve 0 O , or vice versa.
  • D is the inner diameter r 80 of the pipe or conduit 50
  • c/ is the sound speed of the fluid 52 in the pipe or conduit 50
  • c P his the horizontal phase speed in the pipe.
  • ⁇ po The angle of the helical path/rotation angle, 0o is assumed known (part of meter configuration)
  • v is the flow speed along the chordal path.
  • r cs is the shortest distance from origo in the x-y plane to the chord (or, equivalently, the radius of the construction circle).
  • a clamp-on attachment device advantageously comprising one or more attaching elements 26' for attaching clamp-on transducer wedge(s) to a pipe or conduit in a non-invasive non-intrusive manner.
  • the attaching elements 26' may provide for easy attachment and detachment of the wedges 1, such as using strips or the like for mounting the wedge to the pipe/conduit.
  • it may be advantageous to provide an easy to mount, but more permanent placement, such as welding/gluing or bolting the wedge 1 more or less permanently to the pipe/conduit.
  • FIG 3D it is shown one example of an embodiment of present disclosure wherein a frame 26' for easy attachment and detachment of a number of wedges and corresponding transducers to a pipe/conduit 50 is provided.
  • 2 wedge pairs according to present invention with corresponding wedge and transduces assembly 21, 22, 21' 22', and 3 traditional wedges with corresponding transducers 23, 23'.
  • the waves may be excited in off-centre chordal paths 18 between the wedge and transduces assemblies 21, 22, 21' 22' according to present disclosure, and that the waves may be excited through centre paths 23'' between the traditional wedge and transduces assemblies 23, 23'.
  • the second aspect of this disclosure shows a method for arranging a transducer to a pipe or conduit for wave transmission along chordal paths in the fluid 52 inside the pipe or conduit 50, the method comprising following steps: - arranging a first clamp-on transducer wedge 1,21 according to the first aspect to the pipe or conduit,

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Fluid Mechanics (AREA)
  • Chemical & Material Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • Analytical Chemistry (AREA)
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  • General Health & Medical Sciences (AREA)
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  • Measuring Volume Flow (AREA)

Abstract

The disclosure relates to a non-invasive non-intrusive clamp-on transducer wedge (1) comprising: a first side (2) for being arranged on the outside surface of a pipe or conduit (50), a transducer connecting element (4') for receiving a transducer (21', 22'), wherein the transducer conduit (3) being arranged to position a transducer (21', 22') in a wedge angle (4>) towards the pipe or conduit (50), and a rotation angle (6 ) relative the longitudinal direction of the pipe or conduit (50). The disclosure further relates to a method for arranging a transducer to a pipe or conduit for wave transmission along chordal paths in a fluid (52) inside the pipe or conduit (50).

Description

A NON-INVASIVE NON-INTRUSIVE CLAMP-ON TRANSDUCER WEDGE AND A METHOD FOR ARRANGING A
TRANSDUCER TO A PIPE OR CONDUIT FOR WAVE TRANSMISSION ALONG CHORDAL PATHS IN A FLUID INSIDE THE
PIPE OR CONDUIT
Technical field
The present disclosure relates to a non-invasive non-intrusive clamp-on transducer wedge and a method for arranging a transducer to a pipe or conduit for wave transmission along chordal paths in a fluid inside the pipe or conduit. More specifically, the disclosure relates to a non-invasive non-intrusive clamp-on transducer wedge and a method for arranging a transducer to a pipe or conduit for wave transmission along chordal paths inside the pipe or conduit as defined in the introductory parts of the independent claims.
Background art
Ultrasound flow meters are frequently used for measurement of a flow rate of a fluid through a conduit/pipe due to their ability to provide a good turndown ratio. Precise and detailed measurements may be provided by in-line meters utilizing multi-path measurements to detect the fluid speed profiles. Clamp-on transducers are provided for center-path measurements.
Other intrusive and/or invasive measurement techniques may be found in prior art.
In US 10317262 B2 it is shown a transducer waveguide and driver elements arranged around a curved surface of a pipe/conduit, exciting acoustic wave propagation within the wall of the pipe/conduit providing information indicative of properties of the material present in a vicinity of the wall which interacts with the acoustic wave propagation, being used to interrogate sampling points off-axis and on-axis in a cross-section of the region for determining characteristics of the region.
In US 11435211B2 is shown a transducer arrangement disposed at least partially around an external surface of a wall of the conduit and having one or more driver elements for exciting in operation a helical acoustic wave propagation within the wall of the conduit for leaking acoustical energy from the helical acoustic wave propagation over an extensive area of the wall of the conduit for stimulating waves in chordal paths within the flow, wherein the waves in the choral paths within the flow reenter the wall of the conduit to propagate further as a guided helical wave. The transducer arrangement includes one or more sensors for receiving a re-entered portion of the acoustic wave propagation along the paths within the flow which interacts with the flow and includes information characterizing properties of the flow.
However, it is not possible to use the above mentioned techniques for measuring fluid characteristics along chordal paths in embodiments where invasive and/or intrusive measurement techniques are prohibited and/or too resource demanding. If the sound speed in the wall is not "much greater" than in the fluid; it is difficult, or impossible, to use techniques based upon signals traveling as guided helical waves in the wall of the pipe/conduit for leaking waves in chordal paths within the fluid flow within the pipe or conduit.
There is a contemporary need for highly accurate non-intrusive non-invasive flow measuring apparatus for monitoring flows of fluids, also in the cases where the pipe/conduit have high attenuation where the energy is lost before chordal path signals are excited.
Specifically, in regards to the design of wedges holding the transducers in prior art, these tend to be formed to provide a wedge angle pointing the transducer direction into the pipe at an angle sending the waves through the center of the pipe towards a receiving wedge/transducer up- or down-stream the pipe.
A problem, specifically in flows having two phases, for example oil and water, oil and gas, water and gas, arise when the laminar flows are not divided by horizontal or vertical boundaries, but rather having an radial distribution pattern.
The present disclosure seeks to provide an improved wedge and method for measuring flow solving one or more of the above stated problems.
Summary
In the following description of embodiments, reference will be made to the drawings, in which like reference numerals denote the same or corresponding elements. It should be noted that, unless otherwise stated, different features or elements may be combined with each other whether or not they have been described together as part of the same embodiment below. The combination of features or elements in the exemplary embodiments are done in order to facilitate understanding of the invention rather than limit its scope to a limited set of embodiments, and to the extent that alternative elements with substantially the same functionality are shown in respective embodiments, they are intended to be interchangeable, but for the sake of brevity, no attempt has been made to disclose a complete description of all possible permutations of features.
It is an object of the present disclosure to mitigate, alleviate or eliminate one or more of the above-identified deficiencies and disadvantages in the prior art and solve at least the above mentioned problem. According to a first aspect there is provided a clamp-on transducer wedge comprising: a first side for being arranged on the outside surface of a pipe or conduit, a transducer connecting element for connecting a transducer, wherein the transducer connecting element being arranged to position a transducer on a surface in the y-z plane rotated a longitudinal wedge angle relative the vertical x axis in the z-x plane of the pipe or conduit, and a rotation angle relative the longitudinal z axis in the y-z plane of the pipe or conduit.
The arrangement of the transducers in a rotation angle may provide for wave propagation along chordal paths in a pipe or conduit.
According to some embodiments, the first side having an elongated recess adapted to the outside form of the surface of a pipe or conduit it is to be mounted to, wherein the elongated recess has a form such that its longitudinal axis running at the rotation angle relative the longitudinal z axis in the y-z plane of the pipe or conduit it is to be mounted to, and thus positioning the longitudinal orientation of the clamp-on transducer wedge at a predetermined known angle both in wedge angle and rotation angle.
According to some embodiments, the clamp-on transducer wedge operates in pairs, wherein a first clamp-on transducer wedge is arranged to comprise a first transducer, and the second clamp-on transducer wedge is arranged to comprise a second transducer rotated 180 degrees relative to the first transducer.
According to some embodiments, the first the transducer is one of a sending and a receiving transducer, and the second transducer is the other of the sending and receiving transducer such that when one of the first or second transducer is sending the other of the first and second transducer is receiving.
Thereby by altering which transducer is sending and receiving, and fluid flows in the pipe/conduits one can estimate the fluid characteristics, composition, and flow rate. According to some embodiments, the sending transducer is operable to stimulate waves in off-centre chordal paths within a fluid flow within the pipe or conduit the clamp-on transducer wedge is to be mounted to.
When flow is non-uniform it is desirable to measure flow outside the center of the pipe/conduit.
According to some embodiments, the receiving transducer is operable to receive the waves in off-centre chordal paths within the fluid flow within the pipe or conduit it is to be mounted to from the sending transducer.
According to some embodiments, the sending transducer is operable to excite helically propagating acoustic waves within the wall of the pipe or conduit it is to be mounted to and stimulate the waves of the off-centre chordal paths within the fluid flow within the pipe or conduit by leaking acoustical energy from the helically propagating acoustic waves ; and the receiving transducer is operable to receive the waves of the off-centre chordal paths, helically re-entering the wall of the pipe or conduit it is to be mounted to, and further propagat-ing helically as guided acoustic waves into the receiving transducer.
In some embodiments when the material of the pipe/conduit allow propagating waves, it may be advantageous to provide for helically propagating waves in the wall of the pipe/conduit. This may be specifically advantageous when sending transducer excite Lamb waves.
According to some embodiments, the receiving transducer is operable to receive the waves in off-centre chordal paths within the fluid flow within the pipe or conduit it is to be mounted to from the sending transducer, and the off-centre chordal paths are defined by a construction circle.
According to some embodiments, the construction circle is determined by one or more of:
- the rotation angle,
- the wave mode and when conduit sound speed is higher than the fluid sound speed, and excited acoustic waves is of Lamb type : the frequency of the waves in off-centre chordal paths. It may be advantageous to be able to change the construction circle in-situ by changing the frequency of the waves only.
According to some embodiments, the arrangement of the second clamp-on transducer wedge relative the first clamp-on transducer wedge to calculate the flow speed along the chordal path, v, and the construction circle according to:
Figure imgf000007_0001
I I sin(acos(-^cos(0o) sin(<pw))) constrCirc = - sin atan - — rr -
2 I \ I \ tan I acos I cf W
\ \ \ \cp/t / /
Figure imgf000007_0002
Figure imgf000007_0003
The placement of the second and further wedge/transducers are specifically important to be able to receive the chordal path waves, to be able to analyze the flow in the chordal path segments of the flow.
According to some embodiments, the clamp-on comprises: one or more attaching elements for attaching the clamp-on transducer wedge to a pipe or conduit in a non-invasive non-intrusive manner.
According to a second aspect there is provided a method for arranging a non-invasive and non-intrusive transducer to a pipe or conduit for wave transmission along chordal paths in a fluid inside the pipe or conduit, the method comprising following steps:
- arranging a first clamp-on transducer wedge according to the first aspect to the pipe or conduit,
- arranging a first transducer in the transducer connecting element of the first clampon transducer wedge, - providing a controller for controlling the first transducer operation.
According to some embodiments, the method comprises:
- arranging a second clamp-on transducer wedge according to the first aspect to the pipe or conduit,
- positioning the second clamp-on transducer wedge in line with the chordal path to/from the first clamp-on transducer,
- arranging a second transducer in the transducer connecting element of the second clamp-on transducer wedge,
- providing a controller for controlling the second transducer operation.
According to some embodiments, the second clamp-on transducer wedge is arranged relative the first clamp-on transducer wedge and the construction circle according to:
Figure imgf000008_0001
According to some embodiments, wherein the controllers controlling the first and second transducers are hosted by a single controller.
According to some embodiments the pipe or conduit is made of metal.
According to some embodiments the pipe or conduit is of a non-metallic material.
According to some embodiments, the non-metallic material is a plastic based material. Effects and features of the second aspect are to a large extent analogous to those described above in connection with the first aspect. Embodiments mentioned in relation to the first aspect are largely compatible with the second aspect.
The present disclosure will become apparent from the detailed description given below. The detailed description and specific examples disclose preferred embodiments of the disclosure by way of illustration only. Those skilled in the art understand from guidance in the detailed description that changes and modifications may be made within the scope of the disclosure.
It should be noted that, as used in the specification and the appended claim, the articles "a", "an", "the", and "said" are intended to mean that there are one or more of the elements unless the context explicitly dictates otherwise. Thus, for example, reference to "a unit" or "the unit" may include several devices, and the like. Furthermore, the words "comprising", "including", "containing" and similar wordings does not exclude other elements or steps.
Terminology -
The term "Wedge" is to be interpreted as a coupling device for providing acoustic coupling between a transducer and a component to be inspected.
The 3-dimentional orientation of the x-, y- and z- axis is in present disclosure defined to be as follows: the z-axis is parallel to the longitudinal direction of a horizontal pipe or conduit, the y-axis is horizontal and perpendicular to the z-axis, whist the x-axis is vertical and perpendicular to the y-, and z- axis.
Acoustic waves and waves, shall be understood to be acoustic waves of any mode, including but not limited to: lamb-wave, shear-wave or compressional-wave of any type.
When the material plastic is used it shall be understood to comprise any plastic or plastic composite materials used for piping/conduits having non-metallic properties, including but not limited to PE and PVC based plastic materials.
Brief descriptions of the drawings
The above objects, as well as additional objects, features, and advantages of the present disclosure, will be more fully appreciated by reference to the following illustrative and non-limiting detailed description of example embodiments of the present disclosure, when taken in conjunction with the accompanying drawings.
Figure 1 shows a setup according to prior art of intrusive transducers measuring flows under different flow regimes.
Figure 2A shows a side view of the wedge according to present disclosure
Figure 2B shows a side view from below of the wedge according to present disclosure
Figure 3A shows an embodiment wherein the wedge with a mounted transducer is arranged to explore the internal volume of a pipe or conduit
Figure 3B and 3C shows the wedge angle and the and rotation angle of the transducer when arranged in the wedge.
Figure 3D shows an embodiment of present disclosure of a frame for easy attachment and detachment of a number of wedges and corresponding transducers according to present disclosure to a pipe or conduit, in combination with wedges and corresponding transducers according to prior art.
Figure 4A shows a cross section of a pipe or conduit and the construction circle according to present disclosure
Figure 4B shows a detailed study of the entry and exit point of the wave in a chordal path through the fluid, typically from a helical transmitted waves in the pipe stimulating waves in the off-centre chordal paths.
Figure 5 shows a cross section of a pipe or conduit and the chordal paths of the waves according to present disclosure
Figure 6 shows a pipe or conduit and the effect of helically propagating acoustic waves, the chordal paths, and potential optimal location of sending and receiving wedges/transducers
Detailed description
The present disclosure will now be described with reference to the accompanying drawings, in which preferred example embodiments of the disclosure are shown. The disclosure may, however, be embodied in other forms and should not be construed as limited to the herein disclosed embodiments. The disclosed embodiments are provided to fully convey the scope of the disclosure to the skilled person. In figure 1 it is shown an example of prior art where it is demonstrated an invasive transducer setup, where a) shows the system setup, b) shows the parallel wave paths through a cross section of the pipe, and c) shows the setup from above of one transducer pair and the wedges setting up a wave path through the center of the flow. The example show that transducers are set up in pairs or quadruples defining parallel horizontal planes in which the flow is measured.
The problem of such prior art transducer setups for lamina flow measurements are that they are intrusive systems and thus not usable in embodiments where manipulation of the pipe/conduit is prohibited.
Present disclosure provides a non-invasive non-intrusive wedge and transducer assembly as defined in appended claim 1: there is provided a wedge for connecting a transducer relative a pipe or conduit for measuring properties of a flow of a fluid within a pipe or conduit.
The wedge and transduces assembly provides transducer connecting elements for connecting transducers enabled to stimulate waves in off-centre chordal paths within a fluid flow within the pipe or conduit for emitting and receiving ultrasonic radiation in upstream and downstream directions in respect of the flow of fluid, and a signal processing arrangement/controller for generating signals to excite the transducer arrangement and for processing received signals provided by the wedge and transduces assembly for generating output signals from the signal processing arrangement/controller indicative of properties of the flow, characterized in that for upstream and downstream directions respectively, the apparatus is operable to perform measurements along first and/or second wave paths in off- centre chordal paths within a fluid flow within the pipe or conduit associated with each of the directions;
There is further provided a set of equations for defining the best position for arranging a receiving wedge and transduces assembly relative the sending wedge and transduces assembly and the excited off-centre chordal paths.
The set of equations has been developed to calculate the chordal beams set up by helical guided wave propagation in the pipe at a predefined helical angle/the wedge angles. The calculations assume knowledge of the beam incidence angle for the axial configuration. Time Of Flight calculations further assume a uniform flow profile. Time of flight in fluid is considered to be variable (propagation to a fixed point) for the chordal measurements (like for wetted flow meters). This is in contrast to the axial non- invasive signal propagation, where pipe propagation distance is considered variable.
A possibility to decrease path length along with frequency has been identified. This may be a way to increase robustness with respect to attenuating fluids.
Optionally for the first path, the wedge and transduces assembly in cooperation with the conduit is operable to provide the first path solely via the one or more walls for Lambwave ultrasonic radiation coupling directly from a transducer for emitting ultrasonic radiation to a transducer for receiving ultrasonic radiation to generate a first received signal; for the second path, the wedge and transduces assembly in cooperation with the conduit is operable to provide the second path for propagation of ultrasonic radiation within the one or more walls via Lamb waves coupling to at least a portion of the fluid to propagate through the fluid in off-centre chordal paths within the fluid flow within the pipe or conduit from a transducer for emitting ultrasonic radiation to a transducer for receiving ultrasonic radiation to generate a second received signal; and the signal processing arrangement/controller may be operable to determine from the first and second signals ultrasonic radiation propagation time periods through the first path and through the second path in each of the upstream and downstream flow directions, and to perform computational operations on the propagation time periods to determine the properties of the flow in respect of at least one of: a flow velocity (v) of the fluid in the conduit, a velocity of sound (c) through the fluid.
It is further provided a wedge and transduces assembly including one or more of pairs of transducers for measuring spatially differential fluid flows within the conduit, for example, for increased robustness for, and/or corrections for, measuring radially laminar fluid flow velocity profiles in the conduit or spatial phase distributions in the conduit if more than one fluid phase is present in the conduit. Optionally, the wedge and transduces assembly is implemented such that the attenuation of the ultrasonic signal following the first path can be monitored to provide input to a frequency tuning arrangement for tuning operation of the apparatus for providing in operation optimal energy transfer between the wedge and transduces assembly and the fluid. Optionally, an attenuation measurement of radiation through the fluid in the conduit is used as a first measure of fluid density, based upon the attenuation of certain guided wave modes being substantially proportional to an acoustic impedance ratio between the fluid and the pipe or conduit. Figure 2A and 2B illustrates one alternative embodiment of the wedge 1 according to present disclosure seen from different angles.
The wedge 1 is used as a coupling device for providing coupling between a transducer 21', 22' and a fluid 52 to be inspected flowing in a pipe or conduit 50. The wedge may according to present disclosure be comprised of an attenuating portion 3 produced of an attenuating material and a non-attenuating portion 4, wherein the non-attenuating portion 4 is produced of a non-attenuating material is arranged as a conduit in the attenuating portion and provides for a first contact surface 4' for being in contact with an attached transducer element 21', 22', and a second surface 4'' providing contact with the component 50 to be inspected. Thus the waves are directed in the direction of the conduit of non-attenuating material for stimulating waves in off-centre chordal paths within the fluid 52 inside the pipe or conduit 50, and waves are dampened in other directions by the attenuating portions of the wedge 1.
In a further embodiment of the wedge 1, the attenuating portion 3 may be minimized and even eliminated completely, and the wedge may be formed as an elongated waveguide to enhance waves propagating along the component 50 to be inspected and to stimulate waves in off-centre chordal paths 18 within the fluid 52 inside the pipe or conduit 50.
In figure 3A it is demonstrated the first aspect of this disclosure showing a clamp-on non-invasive non-intrusive transducer wedge 1 comprising: a first side 2 for being arranged on the outside surface of a pipe or conduit 50, a transducer connecting element 4' for connecting a transducer 21', 22', wherein the transducer connecting element 4' being arranged to position a transducer 21', 22' on a surface in in the y-z plane rotated in a longitudinal wedge angle 4> relative the vertical x axis in the z-x plane of the pipe or conduit 50, and a rotation angle 0 relative the longitudinal z axis in the y-z plane of the pipe or conduit 50.
It is the ability to preset the angle not only relative the vertical x axis in the z-x plane but also relative the longitudinal z axis in the y-z plane direction that provides the flexibility and unique characteristics of the wedge according to the present disclosure.
The features are provided by the first side 2 having an elongated recess adapted to the outside form of the surface of a pipe or conduit 50 it is to be mounted to, wherein the elongated recess has a form such that its longitudinal axis running at the rotation 0 relative the longitudinal z axis in the x-z plane of the pipe or conduit 10 it is to be mounted to. The recess provides a fixed rotation angle predefined for the wedge. If a different rotation angle is desired, a wedge with a different recess provided with desired angle must be chosen.
The rotation angle 0 is positioning the longitudinal orientation 90 of the clamp-on transducer wedge at an angle between the longitudinal and perpendicular direction of a pipe or conduit it is to be mounted to. Thus, when a wedge angle 4> is chosen so that the transduces has a greater than 0° angle relative the vertical x axis, the pointing direction of the transducer will point more away from the center of the pipe or conduit the higher the rotation angle 0 is chosen.
It is then possible to select a path for the acoustic waves excited by a sending transducer and set up a receiving transducer at a suitable location for receiving the signal excited by the sending transducer. The clamp-on transducer wedge 1 may thus operate in pairs, wherein a first clamp-on transducer wedge 1,21 is arranged to comprise a first transducer 21', and the second clamp-on transducer wedgel,22 is arranged to comprise a second transducer 22'.
When more than one transducer is deployed, it may be possible at any time to configure each transducer to be one of a sending and receiving transducer. Thus, when operating in pairs, the first transducer 21' is one of a sending and a receiving transducer, and the second transducer 22' is the other of the sending and receiving transducer such that when one of the first or second transducer is sending the other of the first and second transducer is receiving. It is within the scope of present disclosure to use more than two transducers/wedges operating in cooperation. Such that for example one or more sending transducers are paired with one or more receiving transducers. In one example when measuring a flow of a pipe one sending transducer may be arranged upstream of a receiving transducer, and a second sending transducer is arranged downstream of the same receiving transducer. The position of the wedge and its wedge angle 4> relative the vertical x axis in the perpendicular z-x plane of the pipe 50, and rotation angle 0 relative the longitudinal z axis in the y-z plane of the pipe 50 of each of the sending transducers must be chosen/calculated such that excited signal can be detected and read by the receiving transducer/wedge.
The sending transducer 21', 22' is operable to stimulate waves in off-centre chordal paths 18 within a fluid flow 52 within the pipe or conduit 50 the clamp-on transducer wedge 1,21,22 is to be mounted to. The angle that the clamp-on transducer wedge points the transducer at in the rotation angle 0 defines the construction circle 15, 15' that the off-centre chordal paths the waves will pass through a fluid 52 that fills the pipe or conduit 50. Depending on the material of the pipe or conduit, the waves may excite into the fluid through a first refraction angle 13 between the transducer and the outer side of the pipe/conduit wall, and/or a second refraction angle 14 between the inner side of the pipe/conduit wall and the fluid inside the pipe/conduit.
When the material of the pipe or conduit is plastic based, it is advantageously that the acoustic properties of the plastic is comparable or substantially equal to the fluid to be analysed. In a plastic based embodiment it has been surprisingly found that the first refraction angle 13 is substantially close to or equal to 0.
When the material of the pipe or conduit is metal based, it is advantageously that the acoustic properties of the metal is comparable or substantially equal to the transducers.
Larger construction circle 15, 15' result in shorter chordal paths 18 lengths. This may be a way to get a signal through attenuating fluids.
Two ways to increase the construction circle; by decreasing frequency (for example valid for AO mode) and/or by increasing the helical angle. In figure 4A frequency is as an example decreased while the helical angle is constant at 45^, wherein the smallest construction circle 15 is provided by a 215 kHz AO mode wave signal, and the larger construction circle 15' is provided by a 120 kHz A0 mode wave signal.
When operating in pairs the receiving transducer is operable to receive the waves in off-centre chordal paths 18 within the fluid flow 52 within the pipe or conduit 50 it is to be mounted to from the sending transducer 21', 22'.
For some waves modes such as Lamb waves when the pipe/conduit is a steel or metal, or metal alloy material, the sending transducer 21', 22' may be operable to excite helically propagating acoustic waves 16 within the wall of the pipe or conduit 50 it is to be mounted to and stimulate the waves of the off-centre chordal paths 18 within the fluid flow 52 within the pipe or conduit 50 by leaking acoustical energy from the helically propagating acoustic waves 16; and the receiving transducer 21', 22' is operable to receive the waves of the off-centre chordal paths 18, helically re-entering the wall of the pipe or conduit 50 it is to be mounted to, and further propagating helically as guided acoustic waves 17 into the receiving transducer 21', 22'. The latter scenario may also be valid for some wave modes for which the phase velocity of the propagating Lamb wave mode is higher than the sound speed in the fluid, and the pipe/conduit is a plastic based material.
Helically propagating waves is exemplified in figure 6A, and a corresponding unwrapped 2D view of the wave propagation in the pipe or conduit wall and its stimulated waves in the off-centre chordal paths is illustrated in figure 6B. It can be assumed that received waves from the off-center chordal paths of the helically propagating waves will be summed along its path. To plan the positioning of the helically oriented wedge transducers, it is useful to plot the signal propagation in the unwrapped view. Note that this illustrates sound propagation in the pipe. The lines indicating where the sound beam is in the fluid is indicated by the chordal path lines 18 between the helical propagating path pair 16, 17 of lines. Note also that the chord paths combine to set up a new helical wave 17 in the pipe. This wave propagates in the same helical angle as the original one 16, but at a different "height".
More than one receiving transducer may be deployed along the propagation path at different locations to provide for sector-wise analysis. For example, a received signal of a first receiving transducer arranged upstream may be subtracted from a received signal of a second transducer arranged downstream resulting in a received signal from the segment between the first and second receiving transducer.
The size of the sending and/or receiving transducer defines the room of maneuvering for positioning the receiving transducer relative the helically propagating acoustic waves and/or the off-centre chordal paths. Larger transduced element gives larger room of maneuvering.
It is thus possible to achieve the operating wave pattern that is exemplified in figure 6, where the chordal paths 18 of the propagating waves are excited into the fluid along the helically propagating path 17 of the acoustic waves. When arranging the receiving wedges/transducers along the receiving path 16 of the propagating waves and the corresponding chordal paths, is possible to estimate an improved understanding of the fluid passing along the chordal volumes outside the construction circle of the pipe/conduit.
Thus, the receiving transducer 21', 22' is operable to receive the waves in off-centre chordal paths within the fluid flow 52 the pipe or conduit 50 from the sending transducer 21', 22', wherein the off-centre chordal paths are defined by a construction circle 15,15'.
It can be said that the construction circle 15,15' is determined by one or more of: - the rotation angle 0,
- the wave mode, and when conduit sound speed is higher than the fluid sound speed, and excited acoustic waves is of Lamb type : the frequency of the waves in off-centre chordal paths.
It has been discussed how the rotation angle changes the construction circle, but also the frequency may be used to alter the construction circle, as varying the frequency may vary one or both of the first and second refraction angle 13, 14. The refraction angles will alter the wave angle from what is defined by the rotation angle 0 and the wedge angle 4>-
The 'effective' wedge helix angle for the AO-wave is given by:
Z X
Qhelix = acos(upipe z) = acos(
Figure imgf000017_0001
It has further been found that the arrangement of the second clamp-on transducer wedge 1,22 may be arranged relative the first clamp-on transducer wedgel,21, wherein the second clamp-on transducer wedge is arranged to comprise a second transducer rotated 180 degrees relative to the first transducer, and the construction circle 15,15' according to the following two equations, which is shown for AO mode wave signal and helical acoustic wave propagation within the wall of the conduit for leaking acoustical energy from the helical acoustic wave propagation over an extensive area of the wall of the conduit for stimulating waves in chordal paths within the flow:
Figure imgf000017_0002
One pre-requisite for being able to use the above (1) and (2), is to further assume that cPipe = cPh, where cPh is a function of frequency*pipe_wall_thickness, and (pr l = The calculations
Figure imgf000018_0001
are valid for the centerpoint of the transducer/wedge/beam, where the curvature of the pipe can be ignored.
The equations may then be solved by setting pw to a known value and solve 0O, or vice versa.
We define the following:
• R: outer radius of pipe 81
• D or r: inner radius of pipe 80
• z: pipe-axis 51
• wh: wedge height from pipe to center of transducer/wedge interface 82
• x0 = [xOx, 0, 0] = [R + wh, 0, 0]: center-point of transducer-wedge interface/center of transmitted beam from transducer into wedge 83. Without loss of generality, we position the wedge so that the y- and z- component of this point is zero. This is the starting point of our ray-tracing.
• Xi: Intersection point of center of beam between wedge and pipe 13
• X2: Intersection point of center of beam between pipe and fluid 14
• X3: Intersection point of center of beam between fluid and pipe 14'
• X4: Intersection point of center of beam between pipe and wedge 13'
• X5: Center point of received beam on receiving transducer on wedge-transducer interface 83' (similar to x0, but on the receiving end)
• 0o: Wedge rotation angle (for axial wedge, 0o = 0. For a modeline waveguide, this is equivalent to the helix angle)
• pw'. wedge angle
::: 7 — (PW : complementary wedge angle
• <p; i: Incident beam angle from wedge into pipe
• (pr j Refracted beam angle from wedge into pipe
• cw Speed of sound in wedge (compressional)
• cph phase velocity in pipe
• cp p-wave/compressional wave velocity in pipe
• cs s-wave/shear wave velocity in pipe
The equations outlined in this document can be condensed into two expressions relevant to the chordal path calculationsdt = tgA ~ IAB .
In the equations: D is the inner diameter r 80 of the pipe or conduit 50, c/is the sound speed of the fluid 52 in the pipe or conduit 50, cPhis the horizontal phase speed in the pipe. Along with known fluid sound speed and horizontal phase speed, comes the axial angle of transmission into the fluid/wedge angle, <po. The angle of the helical path/rotation angle, 0o is assumed known (part of meter configuration), v is the flow speed along the chordal path.
Furthermore, a uniform flow profile is assumed. The reasoning for making this assumption (when actually targeting cases of non-uniform flow), is that flow profile analysis will be based on deviations from expected measurement results. Furthermore it is provided for providing «clockwise» and «counter clockwise" transducer pairs to facilitate for measuring asymmetries such as swirl.
The intersection point of center of beam between wedge and pipe, Xi, can be found before the incident angle of beam from wedge into pipe. When the refracted angle/ray from wedge into pipe in AO mode is found the beam propagation in pipe may be found.
Finding the refracted angle/ray from pipe into fluid the refracted angle may then be found using the standard form of Snell's law:
Figure imgf000019_0001
>
The beam unit vector in the direction of the refracted ray, Ufiuld, can be found using the vector form of Snell's law:
Figure imgf000019_0002
Considering the chordal path/construction circle it is now possible to find the projected chordal path, which also corresponds to the concentric ring in the derivation for the helical guided wave. First Uftuld is projected onto the x-y plane and the projection is scaled to a normal vector. This is denoted as UfiuldXy. Next, the angle, a, can be calculated defining the chord, using the following equation:
Figure imgf000019_0003
This is further illustrated in 4B, where rcs is the shortest distance from origo in the x-y plane to the chord (or, equivalently, the radius of the construction circle). The ratio between rcs = rcos(a) (where the subscript 'cs' denotes construction circle) and the inner pipe-radius, r, gives the equivalent to the construction circle, i.e.: constrCirc = -^ = cos(a) = cos (— asin( n2 • Ufiuld,xy ) = cos (asin( n2
Figure imgf000020_0001
The above functions is developed for calculating the construction circle for guided waves and helical paths as shown in figure 6A and 6B. It has been found that similar functions may be developed for the arrangement of the wedge and sending/receiving transducers when wave path follows a direct path from the transducer through the pipe wall and in a chordal path to the receiving transducer as set up in figure 4A and figure 4B.
Typically the complete flow picture of the entire cross section of the conduit may be estimated by adding weighted flow estimates from chordal path measurements and direct or reflected diameter path measurements using traditional wedge and transduces assemblies 23, 23' according to well-known methods of flow integration from in-line multipath ultrasonic transit-time flowmeters.
There is further provided a clamp-on attachment device, advantageously comprising one or more attaching elements 26' for attaching clamp-on transducer wedge(s) to a pipe or conduit in a non-invasive non-intrusive manner. The attaching elements 26' may provide for easy attachment and detachment of the wedges 1, such as using strips or the like for mounting the wedge to the pipe/conduit. In other embodiments it may be advantageous to provide an easy to mount, but more permanent placement, such as welding/gluing or bolting the wedge 1 more or less permanently to the pipe/conduit.
In figure 3D it is shown one example of an embodiment of present disclosure wherein a frame 26' for easy attachment and detachment of a number of wedges and corresponding transducers to a pipe/conduit 50 is provided. In the figure it is shown 2 wedge pairs according to present invention with corresponding wedge and transduces assembly 21, 22, 21' 22', and 3 traditional wedges with corresponding transducers 23, 23'. It is also indicated how the waves may be excited in off-centre chordal paths 18 between the wedge and transduces assemblies 21, 22, 21' 22' according to present disclosure, and that the waves may be excited through centre paths 23'' between the traditional wedge and transduces assemblies 23, 23'.
The second aspect of this disclosure shows a method for arranging a transducer to a pipe or conduit for wave transmission along chordal paths in the fluid 52 inside the pipe or conduit 50, the method comprising following steps: - arranging a first clamp-on transducer wedge 1,21 according to the first aspect to the pipe or conduit,
- arranging a first transducer 21' to the transducer connecting element 4' of the first clamp-on transducer wedge 1,21,
- providing a controller for controlling the first transducer operation.
The method may further comprise the steps:
- arranging a second clamp-on transducer wedge 1,22 according to the first aspect to the pipe or conduit,
- positioning the second clamp-on transducer wedge 1,22 in line with the chordal path to/from the first clamp-on transducer 21' ,
- arranging a second transducer 22' to the transducer connecting element 4'of the second clamp-on transducer wedge 1,22, and
- providing a controller for controlling the second transducer operation.
The method further comprise the step to calculate the position at which the second clamp-on transducer wedge 1,22 is arranged relative the first clamp-on transducer wedgel,21 and the construction circle 15,15' . It has advantageously been found that the position along the pipe/conduit can be calculated using the equations:
Figure imgf000021_0001
The controllers controlling the first and second transducers may be hosted by a single controller.
It has been found that the device and method is suitable for arranging a transducer system for investigating fluids inside a pipe wherein the pipe is made of metal. It has been found that the device and method is suitable for arranging a transducer system for investigating fluids inside a pipe wherein the pipe is of a non-metallic material.
The non-metallic material may be a PE based material.
The person skilled in the art realizes that the present disclosure is not limited to the preferred embodiments described above. The person skilled in the art further realizes that modifications and variations are possible within the scope of the appended claims. Additionally, variations to the disclosed embodiments can be understood and effected by the skilled person in practicing the claimed disclosure, from a study of the drawings, the disclosure, and the appended claims.

Claims

1. A non-invasive non-intrusive clamp-on transducer wedge (1) comprising: a first side (2) for being arranged on the outside surface of a pipe or conduit (50), a transducer connecting element (4') for connecting an acoustic transducer (21', 22'), wherein the transducer connecting element (4') being arranged to position an acoustic transducer
(21', 22') on a surface in the y-z plane rotated a longitudinal wedge angle ( ) higher than 0° relative the vertical x axis in the z-x plane of the pipe or conduit (50), and a rotation angle (0) higher than 0° and lower than 90° relative the longitudinal z axis in the y-z plane of the pipe or conduit (50), wherein the pipe or conduit (50) being arranged with its longitudinal direction parallel with the z-axis.
2. The clamp-on transducer wedge (1) according to claim 1, wherein the first side (2, 4") having an elongated recess 51 adapted to the outside form of the surface of a pipe or conduit (50) it is to be mounted to, wherein the elongated recess 51 has a form such that its longitudinal axis 51' is running at the rotation angle (0 ) relative the longitudinal z axis in the y-z plane of the pipe or conduit (10) it is to be mounted to.
3. The clamp-on transducer wedge (1) according to any of the previous claims, wherein the clamp-on transducer wedge (1) operates in pairs, wherein a first clamp-on transducer wedge (1, 21) is arranged to comprise a first acoustic transducer (21'), and the second clamp-on transducer wedge (1, 22) is arranged to comprise a second acoustic transducer (22'), such that the second acoustic transducer (22') isrotated 180 degrees relative to the first acoustic transducer (21').
4. The clamp-on transducer wedge (1) according to claim 3, wherein the first transducer (21') is one of a sending and a receiving transducer, and the second transducer (22') is the other of a sending and receiving transducer such that when one of the first or second transducer is sending the other of the first and second transducer is receiving.
5. The clamp-on transducer wedge (1) according to claim 3 or 4, wherein the sending acoustic transducer (21', 22') is operable to stimulate waves in off-centre chordal paths (18) within a fluid flow (52) within the pipe or conduit (50) the clamp-on transducer wedge (1, 21, 22) is to be mounted to.
6. The clamp-on transducer wedge (1) according to claim 5, wherein the receiving acoustic transducer is operable to receive the waves in off-centre chordal paths
(18) within the fluid flow (52) within the pipe or conduit (50) it is to be mounted to from the sending transducer (21', 22').
7. The clamp-on transducer wedge (1) according to claim 6, wherein the sending acoustic transducer (21', 22') is operable to excite helically propagating acoustic waves (16) within the wall of the pipe or conduit (50) the clamp-on transducer wedge (1) is to be mounted to and stimulate the waves of the off-centre chordal paths (18) within the fluid flow (52) within the pipe or conduit (50) by leaking acoustical energy from the helically propagating acoustic waves (16); and the receiving acoustic transducer (21', 22') is operable to receive the waves of the off-centre chordal paths (18), helically re-entering the wall of the pipe or conduit (50) and further propagat-ing helically as guided acoustic waves (17) into the clamp-on transducer wedge (1) and the receiving acoustic transducer (21', 22').
8. The clamp-on transducer wedge (1) according to claim 6 or 7, wherein the receiving acoustic transducer is operable to receive the waves in off-centre chordal paths (18) within the fluid flow (52) within the pipe or conduit (50) the clamp-on transducer wedge (1) is to be mounted to from the sending acoustic transducer (21', 22'), and the off-centre chordal paths (18) are defined by a construction circle (15, 15') having its center in origo of the cross section of the pipe or conduit (50) a radius describing the shortest distance from origo in the x-y plane to the chord.
9. The clamp-on transducer wedge (1) according to claim 8, wherein the construction circle (15, 15') is determinated by one or more of: the rotation angle (0), the wave mode, and when conduit sound speed is higher than the fluid sound speed, and excited acoustic waves is of Lambe type : the frequency of the waves in off-centre chordal paths.
10.The clamp-on transducer wedge (1) according to any of the previous claims 3 to 9, wherein for A0 mode wave signal and helical acoustic wave propagation within the wall of the conduit for leaking acoustical energy from the helical acoustic wave propagation over an extensive area of the wall of the conduit for stimulating waves in chordal paths within the flow: the second clamp-on transducer wedge(l, 22) is arranged relative the first clamp-on transducer wedge(l, 21) to calculate the flow speed along the chordal path, v, and the construction circle (15,
15') according to:
Figure imgf000025_0001
wherein
<pw: wedge angle
0o: Wedge rotation angle cw Speed of sound in wedge
Cf sound speed of the fluid in the pipe or conduit
Cph : horizontal phase speed in the pipe.
11. The clamp-on transducer wedge according to any of the previous claims, further comprising: one or more attaching elements (26') for attaching the clamp-on transducer wedges to a pipe or conduit in an non-intrusive manner.
12. A method for arranging a non-intrusive acoustic transducer to a pipe or conduit for wave transmission along chordal paths inside the pipe or conduit, the method comprising following steps:
- arranging a first clamp-on transducer wedge (1, 21) according to any of claim 1 to 11 to the pipe or conduit,
- arranging a first acoustic transducer (21') to the transducer connecting element (3) of the first clamp-on transducer wedge (1, 21),
- providing a controller for controlling the first acoustic transducer operation.
13.The method according to claim 12, further comprising:
- arranging a second clamp-on transducer wedge (1, 22) according to any of claim 1 to 11 to the pipe or conduit,
- positioning the second clamp-on transducer wedge (1, 22) in line with the chordal path to/from the first clamp-on acoustic transducer (21') ,
- arranging a second acoustic transducer (22') to the transducer connecting element (3) of the second clamp-on transducer wedge (1, 22),
- providing a controller for controlling the second acoustic transducer operation.
14.The method according to claim 13, wherein for AO mode wave signal and helical acoustic wave propagation within the wall of the conduit for leaking acoustical energy from the helical acoustic wave propagation over an extensive area of the wall of the conduit for stimulating waves in chordal paths within the flow: the second clamp-on transducer wedge(l, 22) is arranged relative the first clamp-on transducer wedge(l, 21) and a construction circle (15, 15') according to:
Figure imgf000026_0001
wherein cpw wedge angle
0o: Wedge rotation angle cw Speed of sound in wedge
Cf sound speed of the fluid in the pipe or conduit cPh : horizontal phase speed in the pipe.
15. The method according to any of the previous claims 12 to 14, wherein the controllers controlling the first and second acoustic transducers are hosted by a single controller.
16.The method according to any of the previous claims 12 to 15, wherein the pipe or conduit is made of metal.
17.The method according to any of the previous claims 12 to 15, wherein the pipe or conduit is of a non-metallic material. 18.The method according to claim 17, wherein the non-metallic material is a plastic based material.
PCT/NO2023/060139 2022-12-29 2023-12-28 A non-invasive non-intrusive clamp-on transducer wedge and a method for arranging a transducer to a pipe or conduit for wave transmission along chordal paths in a fluid inside the pipe or conduit WO2024144404A1 (en)

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