WO2025160537A1

WO2025160537A1 - Methods and apparatus to measure pressure variations within a conduit

Info

Publication number: WO2025160537A1
Application number: PCT/US2025/013171
Authority: WO
Inventors: Daniel Gysling
Original assignee: Corvera LLC
Current assignee: Corvera LLC
Priority date: 2024-01-26
Filing date: 2025-01-27
Publication date: 2025-07-31
Anticipated expiration: 2026-07-26

Abstract

Methods and systems for determining the speed at which sound propagates in a fluid within a conduit are disclosed that include positioning a first sensor and a second sensor on an external surface of the conduit, where the first and second sensors are spaced apart by a known distance along a length of the conduit. In addition, the methods and systems may include measuring a first signal generated by the first sensor in response to pressure variations within the conduit. The methods and systems may include measuring a second signal generated by the second sensor in response to pressure variations within the conduit. Moreover, the methods and systems may include calculating the speed at which sound propagates in the fluid within the conduit based on the first and second signals and the known distance between the first and second sensors.

Description

METHODS AND APPARATUS TO MEASURE PRESSURE VARIATIONS WITHIN A CONDUIT

CROSS REFERENCE TO RELATED APPLICATIONS

[0001]This Patent Application claims priority to U.S. Provisional Patent Application No. 63/625,460, filed on 26 January 2024. The disclosure of the prior Application is considered part of and are incorporated by reference into this Patent Application.

BACKGROUND

[0002] Embodiments of the disclosure generally relate to apparatus and methods for diagnose and control entrained air problems in hydraulic systems. As is known in the art, air is a significant contaminant in hydraulic systems.

[0003] What is needed are systems and methods to effectively measure strain associated with internal pressure variations within a conduit. What is further needed are systems and methods to effectively measure strain associated with internal pressure variations within a conduit where the conduit can be made of a composite of multiple types of materials such as hydraulic hoses which utilize steel and or other high strength fiber-like materials to reinforce one or more layers, or embedded within, elastomer-like materials, such as rubber.

[0004] What is needed are systems and methods which enable gas void fraction measurements to be made with a pair of sensors installed external to a conduit.

SUMMARY

[0005]A system of one or more computers can be configured to perform particular operations or actions by virtue of having software, firmware, hardware, or a combination of them installed on the system that in operation causes or cause the system to perform the actions. One or more computer programs can be configured to perform particular operations or actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions. [0006] In one general aspect, a method is disclosed that may include positioning a first sensor and a second sensor on an external surface of the conduit, where the first and second sensors are spaced apart by a known distance along a length of the conduit. The method may also include measuring a first signal generated by the first sensor in response to pressure variations within the conduit. The method may furthermore include measuring a second signal generated by the second sensor in response to pressure variations within the conduit. The method may in addition include calculating the speed at which sound propagates in the fluid within the conduit based on the first and second signals and the known distance between the first and second sensors. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

[0007] Implementations may include one or more of the following features. The method where the known distance defines an aperture. The method where the first sensor and the second sensor form an array and where the aperture is at least five times an effective diameter of the conduit within the aperture of the array. The method where the first sensor and the second sensor are electrically connected to a processing unit configured to interpret the first signal and the second signal as representative of internal pressure variations within the conduit. The method where the internal pressure variations are may include at least in part of one-dimensional acoustic waves propagating within the aperture. The method where the processing unit utilizes SONAR processing techniques to measure the speed at which one-dimensional acoustic waves propagate within the aperture utilizing the first signal and the second signal. The method where the first sensor and a second sensor each may include: a bending member configured to be positioned on the external surface of the conduit; one or more clamping elements releasably securing the bending member to the conduit; and a strain measuring device attached to the bending member, where the strain measuring device generates a strain signal proportional to a strain in the bending member caused by dimensional changes in the conduit. The method where the bending member may include a plurality of regions having different bending stiffnesses and where the strain measuring device spans at least two regions having different bending stiffness. The method may include creating the different bending stiffnesses using a subtractive process. The method may include creating the different bending stiffnesses using an additive process. The method where the bending member includes at least one strain amplification slot extending partially through a thickness of the bending member to increase the strain measured by the strain measuring device for a given dimensional change in the conduit. The method where the clamping elements may include U-bolts and associated fasteners, where tightening the associated fasteners preloads the bending member against the conduit. The method where the strain measuring device may include a piezoelectric strain gauge secured to the bending member. The method where the piezoelectric strain gauge includes a pair of feet in contact with the surface of the bending member and a mounting bolt configured to apply a normal force for maintaining contact between the pair of feet and the bending member. The method where the bending member is fabricated from a material having a lower bending stiffness compared to the clamping elements. The method where the bending member has a dog-bone configuration with a reduced width region at a location aligned with the strain measuring device. The method may include a base element positioned between the clamping elements and the conduit, where the base element is more rigid than the bending member. The method where the conduit is a composite hose having layers of elastomers and reinforcing fibers. The method where the reinforcing fibers are selected from the group of steel, fiberglass, and Dacron. The method where the composite hose has high material damping characteristics to reduce structural wave propagation. The method where the fluid within the conduit contains a gas void fraction (GVF), and the method further may include determining the GVF based on the speed at which sound propagates. The method may include filtering the first signal and the second signal to reduce noise caused by any of vortical and structural disturbances. Implementations of the described techniques may include hardware, the method or process, or a computer tangible medium.

[0008] In one general aspect, a system is disclosed which may include a first sensor and a second sensor positioned on an external surface of the conduit, where the first and second sensors are spaced apart by a known distance along a length of the conduit. The system may also include the first sensor is configured to generate a first signal in response to pressure variations within the conduit. The system may furthermore include the second sensor is configured to generate a second signal in response to pressure variations within the conduit. The system may in addition include a processing unit configured to determine the speed at which sound propagates in the fluid within the conduit based on the first and second signals and the known distance between the first and second sensors. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

[0009] Implementations may include one or more of the following features. The system where the known distance defines an aperture, the first sensor and the second sensor form an array and where the aperture is at least five times an effective diameter of the conduit within the aperture of the array. The system where the first sensor and the second sensor are electrically connected to the processing unit and where the processing unit is further configured to interpret the first signal and the second signal as representative of internal pressure variations within the conduit. The system where the internal pressure variations may include at least in part of one-dimensional acoustic waves propagating within the aperture. The system where the processing unit utilizes SONAR processing techniques to measure the speed at which one-dimensional acoustic waves propagate within the aperture utilizing the first signal and the second signal. The system where the first sensor and a second sensor each may include: a bending member configured to be positioned on the external surface of the conduit; one or more clamping elements releasably securing the bending member to the conduit; and a strain measuring device attached to the bending member, where the strain measuring device generates a strain signal proportional to a strain in the bending member caused by dimensional changes in the conduit. The system where the bending member may include a plurality of regions having different bending stiffnesses and where the strain measuring device spans at least two regions having different bending stiffness. The system may include creating the different bending stiffnesses using a subtractive process. The system may include creating the different bending stiffnesses using an additive process. The system where the bending member includes at least one strain amplification slot extending partially through a thickness of the bending member to increase the strain measured by the strain measuring device for a given dimensional change in the conduit. The system where the clamping elements may include U-bolts and associated fasteners, where tightening the associated fasteners preloads the bending member against the external surface of the conduit. The system where the strain measuring device may include a piezoelectric strain gauge secured to the bending member. The system where the piezoelectric strain gauge includes a pair of feet in contact with the surface of the bending member and a mounting bolt configured to apply a normal force for maintaining contact between the pair of feet and the bending member. The system where the bending member is fabricated from a material having a lower bending stiffness compared to the clamping elements. The system where the bending member has a dog-bone configuration with a reduced width region at a location aligned with the strain measuring device. The system may include a base element positioned between the clamping elements and the conduit, where the base element has a higher bending stiffness than the bending member. The system where the conduit is a composite hose having layers of elastomers and reinforcing fibers. The system where the reinforcing fibers are selected from the group having of steel, fiberglass, and Dacron. The system where the composite hose has high material damping characteristics to reduce structural wave propagation. The system where the fluid within the conduit contains a gas void fraction (GVF), and where the processing unit is further configured to determine the GVF based on the speed at which sound propagates. The system where the processing unit is further configured to filter the first signal and the second signal to reduce noise caused by any of vortical and structural disturbances. Implementations of the described techniques may include hardware, a method or process, or a computer tangible medium.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] So that the manner in which the above-recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this disclosure and are therefore not to be considered limiting of its scope, for the disclosure may admit to other equally effective embodiments. [0011] Figure 1 is a top view of a diameter strain translator in accordance with the present disclosure;

[0012] Figure 2 is a side view of a diameter strain translator in accordance with the present disclosure;

[0013] Figure 3 is a schematic view of a diameter strain translator in accordance with the present disclosure;

[0014] Figure 4 is a graphical representation of the hinge deflection of a diameter strain translator versus pressure for various pipes in accordance with the present disclosure;

[0015] Figure 5 is a top view of a diameter strain translator in accordance with the present disclosure;

[0016] Figure 6 is a side view of a diameter strain translator in accordance with the present disclosure;

[0017] Figure 7 is a side view of a diameter strain translator in accordance with the present disclosure;

[0018] Figure 8 is a schematic view of GVF measurement system in accordance with the present disclosure;

[0019] Figure 9 is an isometric view of a diameter strain translator positioned on a conduit in accordance with the present disclosure;

[0020] Figure 10 is an isometric view of GVF measurement system including a pair of diameter strain translators in accordance with the present disclosure;

[0021] Figure 11 is a graphical representation of a ported GVF measurement system the versus a diameter strain translator GVF measurement system in accordance with the present disclosure;

[0022] Figure 12 is a side view of a composite hose of the prior art; and [0023] Figure 13 is a side view of a composite hose of the prior art.

DETAILED DESCRIPTION

[0024] In the following detailed description of the embodiments, reference is made to the accompanying drawings, which form a part hereof, and within which are shown by way of illustration specific embodiments by which the examples described herein may be practiced. It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the disclosure.

[0025] Many types of sensors can be mounted on the exterior of a conduit which are responsive to the pressure variations within the process fluid within the conduit. These include sensors that measure the strain in the exterior layer of the conduit and sensors that measure the acceleration of a sensor attached to the exterior of the conduit. The strain within, and the displacement, velocity and acceleration of, the external wall of a composite conduit is responsive to many types of disturbances which include being responsive to the internal acoustic and vortical pressure disturbances, as well as deformation on the conduit due to external forces and acceleration.

[0026] Heretofore, the measurement of the speed of sound within a process fluid utilizing two sensors installed on an exterior of a conduit which are responsive to pressure variations within the process fluid within a conduit has not been possible. Under certain circumstances, sound navigation and ranging (SONAR) processing techniques of the prior art are effective at determining propagation speed of coherent disturbance within pipes using an array of multiple ported pressure sensors and/or sensors mounted to the exterior of the conduit. These techniques rely on determining time and or phase delay information among coherent components of the measured time-resolved signals measured multiple locations disposed along a length of the conduit , where the length of the sensor array is referred to herein as the aperture of the array, and work best when the measured signals on each sensors contain significant signals associated with the propagation of one-dimensional acoustic waves within the conduit that are coherent over the distance aperture of the array of sensors. [0027] In general, there are typically many types of signals that conspire to confound the interpretation of the process fluid sound speed from an array of sensors installed on a conduit. These signals include, and can be caused by, coherent and incoherent electrical noise, vortical disturbances, vibrational, and structural disturbances. In monolithic flow conduits such as steel or poly vinyl chloride (PVC), structural disturbances are typically lightly damped and propagation of structural waves within a conduit, including bending, compression, and torsional waves, can result in significant coherent disturbances being measured at multiple sensors within an array of sensors. As is known in the prior art, these highly coherent and complex structural waves pose challenges in determining the speed at which sound propagates within a process fluid contained within a conduit using sensors that are responsive to strain within the conduit. One tool that designers can utilize to improve the ability of SONAR processing algorithms to extract the speed at which sound is propagating across an array of sensors is to increase the number of sensors within the array and to reduce noise caused by any of the coherent and incoherent electrical noise, vortical disturbances, vibrational, and structural disturbances.

[0028] . As an example, a typical linear sonar array system of the prior art can contain anywhere from a few dozen to hundreds of sensors, depending on the application and desired accuracy, with a "standard" example often being around 10-100 sensors arranged in a straight line along the array. In yet another example, the current state of the art of clamp-on gas void fraction meters is represented by Cidra Corporation SONARtrac clamp-on gas void fraction meter. It has been widely reported that this meter utilizes 8 strain-based sensors designed to measure temporal variations in the circumference of a conduit at 8 axial locations along the conduit and to process the output of the 8 strainbased sensors to determine the speed at which low frequency acoustic waves are propagating within the process fluid conveyed by the conduit on to which the array of 8 strain-based sensors are attached. The large number of sensors enable SONAR processing algorithms to distinguish a multiple number of coherent propagating disturbances along the array including acoustic, vortical, torsional, compression, and shear waves. As will be disclosed in more detail herein below, systems and methods of the current disclosure represent a significant improvement over the prior art by significantly reducing the number of clamp-on sensors required to determine the speed sound within a process fluid conveyed by a conduit, enabling the measurement of the process fluid sound speed within a conduit utilizing a pair of sensors mounted on the external surface of a conduit conveying the process fluid. Note that the term clamp-on sensor is defined herein as any sensors that can be mounted to the external surface of a conduit and wherein the sensor does not have any direct communication with the process fluid contained within the conduit.

[0029] Disturbances that convect with the flow within a conduit, including coherent vortical disturbances, also pose a challenge in determining the speed of sound with a system that includes a low sensor count array such as a system having fewer than the 8 sensor example disclosed above. As part of the current disclosure, it should be appreciated that the coherence between perturbations associated with vortical disturbances measured at two sensor locations along a conduit decreases when the distance between the sensor locations along the length of the conduit increases, where the distance is often normalized by an effective diameter of the conduit.

[0030] It has been discovered, as part of the current disclosure, that for applications in which pressure disturbances associated with vortical disturbances are of similar or larger amplitude levels as compared to the acoustic pressure disturbances, that it is possible to determine the speed at which sound propagates within the fluid of the conduit with the use of two externally mounted strain sensors. As disclosed in detail herein, the externally mounted strain sensors are responsive to pressure perturbations within a conduit and the distance between the sensors along the length of the conduit are separated by an sufficient distance, such as five times the effective diameter of the conduit within the aperture of the array (i.e. the aperture of the two sensor array is about 5 diameters or more in length ).The coherence of vortical signals continues to decrease with increasing distance. Note that the effective diameter is the nominal diameter for a conduit with a constant diameter and a circular cross section within the aperture. For non-circular conduits it is the effective hydraulic diameter, and for conduits in which the cross section varies, the effective diameter is the maximum effective diameter within the aperture. The - aperture as disclosed herein, with specific reference to FIGS. 8 and 10, enables systems and methods of the current disclosure to minimize the coherence of the vortical disturbances. This discovery further enables systems and methods to measure the speed of sound propagating within a conduit utilizing a two sensor arrangement of a pair of clamp-on sensors removably positioned on the exterior of the conduit. As disclosed in detail herein, the sensors of the current disclosure have sufficient sensitivity and are installed with sufficient spacing that they are able to effectively determine the speed at which acoustic waves propagate within a conduit conveying a process fluid with entrained gas.

[0031] It has also been discovered that there are advantages to utilizing an array of two sensors mounted on the external surface of a conduit in which the conduit is constructed of a composite material in which the composite material contains layers of elastomers and reinforcing fibers such as the type of construction often used for hydraulic hoses such as hose 120 and 130 of FIGS. 12 and 13 respectively. The reinforcing fibers can be made of a variety of materials including steel or fiberglass. Hydraulic hoses of this construction are widely used and are typically flexible in the lengthwise direction and capable of withstanding high internal pressures, often exceeding thousands of pounds per square inch, and are typically capable of withstanding external pressure associated with the pressure internal to the conduit to below the pressure on the outside of the hose.

[0032] It should be appreciated by those skilled in the art that composite hose tends to have high material damping characteristics compared to conduits constructed of monolithic materials. As such, composite hoses tend to dampen the propagation of structural waves that are common on conduits used to convey fluids in machines with high power densities such as mobile hydraulic equipment. Mobile hydraulic systems typically have an energy source, such as a diesel or electric motor, and one or more hydraulic pumps, placed within a compact environment, resulting in a high energy density environment. This high energy density environment results in high levels of noise and vibration, with significant structural vibration being imparted into hydraulic conduits. These structural vibrations can serve to confound prior art SONAR based methods, impairing their ability to accurately determine the speed at which sound is propagating within the fluid within the conduits utilizing sensors attached to the outer surface of the conduit. Challenges imposed to SONAR based sound-speed measurements by the structural vibrations decrease with the increase in structural damping associated with the conduits.

[0033] It should be noted that the challenge associated with structural vibrations of a conduit is more demanding for methods that utilize sensors attached to the external surface of the conduit than for methods that utilize ported pressure sensors. Ported pressure sensors are often designed to be insensitive to vibration and are often vibration compensated to minimize errors in the measured unsteady pressure variations associated with structural vibration of the conduit.

[0034] As part of the present disclosure, novel systems and methods are disclosed to measure time-resolved strain signals at one or more axial locations along the length of a conduit conveying or containing a process fluid in which the strain signals are representative of, and essentially proportional to, unsteady pressures within a conduit are disclosed. In one embodiment disclosed herein is a method that can use a strain measuring device to measure strain generated within in a beam clamped on to the outside of a conduit, where changes in the distance across the conduit generate bending in the bending member proportional to variations in the internal pressure within the conduit. One specific embodiment can be a piezoelectric strain gauge which utilizes a piezo-crystal strain measuring device coupled to the bending member which is attached to the conduit.

[0035] It should be appreciated by those skilled in the art that as part of the current disclosure, methods to measure internal variations in conduits constructed of a wide range of materials without limitation, including monolithic materials like steel and PVC to fiber or steel reinforced composite hose such as designs often used in hydraulic equipment.

[0036] Referring to FIGS. 1 and 2, there is shown a diameter strain translator (DST) 1 in accordance with the present disclosure. The DST 1 is comprised of a bending member 2 positioned on a pipe 3 and releasably affixed thereto by a pair of U-bolts 4, 5. In some embodiments, a pipe 3 having a nominal inside radius R of 1 inch, can be used with a suitably sized pair of U -shaped clamps 4, 5 secured on the pipe using bending member 2 and fastened thereto using fastener nuts 6-9. In this particular example, pipe 3 can be comprised of a relatively rigid material such as PVC, steel or the like or even a composite hose. DST 1 also includes strain measurement device 10 coupled to bending member 2 as will be disclosed in more detail herein after. An initial bending moment is applied to preload to bending member 2 to the conduit by tightening the fasteners on the ends of the U-shaped clamps 4, 5.

[0037] With DST 1 affixed to the pipe as described herein above, the U-shaped clamps 4, 5 are assumed to be significantly more rigid than the bending member, and any change in the cross-conduit dimension of the conduit 3, (typically the diameter 20 of a round conduit) results in a deformation of the bending member 2. As will be disclosed in more detail herein after, changes in the cross-conduit dimension of pipe 2, which can be caused by a plurality of factors including pressure variations which translate into changes in diameter 20 and circumferential dimension changes, results in a proportional bending strain in bending member 2. In some embodiments bending member 2 can be aluminum and U-shaped clamps 4, 5 can be steel wherein the bending stiffness of the U-shaped clamps 4, 5 is much higher than the bending stiffness of the bending member 2 and by contrast wherein the bending stiffness of the bending member is lower than the bending stiffness of the U-shaped clamps.

[0038] In the embodiment shown in FIGS. 1 , 2, strain measurement device 10 can comprise a Piezotronics RHM240A01 IEPE strain measurement device. The strain measurement device 10 utilizes a quartz crystal to measure strain (the change in the distance) between a pair of feet 12,13 of the housing of the strain measurement device. The strain measurement device 10 can be securely installed on bending member 2 utilizing a mounting bolt 16 that secures the strain measurement device to the bending member via a threaded hole in the center of the bending member. Proper torquing mounting bolt 16 creates a normal force the creates sufficient frictional force to ensure the pair of feet 12,13 are effectively bounded to the upper surface of the bending member 2, such that the output of the strain measuring device 10 generates a strain signal in proportion to the strain between the pair of feet 12, 13 of the strain measuring device. It should be appreciated by those skilled in the art that strain measurement device 10 is mounted at the midpoint of bending member 2 where the bending member is tangent with the wall 11 of pipe 3 and in alignment with the cross sectional centerline 19 of the pipe.

[0039] It should also be appreciated that the strain generated in the strain measurement device 10 is determined by the change in the distance between the feet 12, 13 of the strain measuring device divided by the nominal (non-strain condition) distance between the feet of the strain measuring device. For a bending member 2 of constant cross section, the strain measured by the strain measurement device 10 will closely approximate the strain in the outer surface of the bending member between the feet 12, 13 of the strain measurement device. In other embodiments, for example, with the strain amplification slots 17, 18, the strain generated in the strain measurement device remains the change in the distance between the feet 12, 13 of the strain measuring device divided by the distance between the feet in a non-strained condition of the strain measuring device. In such embodiments, the strain generated in the strain measurement device 10 no longer closely approximates the strain in the material of the bending member 2.

[0040] The use of strain amplification slots 17, 18 cutting into a bending member 2 are an embodiment that optimizes the strain generated in the strain measurement device 10 compared to the strain that would be generated in the same strain measurement device attached to a similar bending member 2 without the strain amplification slots. The strain amplification slots 17, 18 serve to both decrease the bending stiffness of the bending member as well as increase the strain generated in the strain measuring device 10 due to a given change in diameter 20 of the conduit 3.

[0041] Still referring to FIGS. 1 , 2, and as disclosed immediately herein above, bending member 2 can include strain amplification slots 17, 18 which serve to increase the amount of strain measured by the strain measuring device for a given amount of change in the diameter of the conduit. Optional strain amplification slots 17, 18 can be cuts that penetrate partially through the thickness of bending member 2 and are positioned equidistant from the midpoint of the length of the bending member wherein such an embodiment will increase the strain measured by the strain measuring device for a given dimensional change in the conduit. It is within the scope the current disclosure that many variations in the design of bending members including constant cross section bending element and bending elements having a plurality of regions of different bending stiffnesses that vary the bending stiffness and cross sectional properties over its length to increase the strain generated in the strain measuring device compare to a bending member of constant cross section area. These variations in design include modification of bending members through and additive process, i.e. adding additional elements to a baseline bending member, and a subtractive process, i.e removing material from a baseline bending member, such as the use of strain amplification slots 17, 18 described herein. A baseline bending member is defined herein as a bending member with constant cross sectional geometry over the length of the bending member, and a modified baseline bending member is a bending member that has been modified through additive or subtractive means to create a modified bending member on which a strain measurement device is attached to measure provide a signal indicative of the bending deformation of the modified bending member. For instance, a baseline bending member may comprise baseline member 2 of FIGS. 1 and 2 with the amplification slots 17, 18 omitted.

[0042] It should be appreciated by those skilled in the art that many methods exist to analytically or experimentally evaluate the effectiveness of DST 1 set forth in this disclosure. The analysis provided herein below is but one example of one such analyses. It is noted that modifying various assumptions in any analysis could modify the results without departing from the inventive scope of this disclosure.

[0043] Assuming that bending member 2 is the only flexible component of DST 1 , any change in the cross -conduit dimension 11 of the pipe 3 can be related to the strain at the strain measurement location on the bending member as outlined in the following analysis.

[0044] Assuming that a change in the internal pressure of the conduit generates circumferentially symmetric hoop stress in the conduit and the conduit is made of a material that has a linear relationship between stress and strain sufficiently well modelled by Young’s modulus, the hoop stress o_pipe and hoop strain s_pipe in the conduit 3 can be related to the internal pressure P as follows:

Where E_pipe is the Young’s modulus of the pipe and t_pipe is the thickness of the wall 11 of the pipe. The change in radius R_pipe of the conduit can be related to the hoop strain in the conduit:

Note also that diametric strain is equal to the radial strain as follows:

[0045] One model to estimate the strain developed in the strain measuring device 10 is developed herein below. With additional reference now to FIG. 3, assuming the strain amplification slots 17, 18 effectively reduce the bending stiffness of the region under the slots to be significantly less than that of the rest of the bending member 2 due to the reduction in the area moment of inertia, the slots cause the bending member to effectively act as a hinge. As the radius R of the pipe expands under an increase in pressure, the distance d1 (diameter 20, FIG, 2) representing the cross-conduit dimension aligned with the contact point of the bending member on the conduit and the opposite side of the conduit of the pipe 3 to the center of the thickness of bending element 2 where it is in contact with the upper surface of the pipe, increases compared to that of the d2 of the bending element near the end, where its position is fixed relative the bottom of the pipe by the essentially rigid U-bolt clamps. The distance d1 - d2 (the change in diameter of conduit 3) is given by:

[0046] The expansion in the pipe 3 causes the outer region of the bending element 2 to effectively rotate as rigid bodied about the relatively flexible hinge point created by the strain amplification slots 17, 18 through a rotational deflection of the bending member denoted by A0 (FIG. 3) and the dotted line of bending element 2:

[0047] Where L_offset is the distance between the effective position of the hinge point created by the strain amplification slots 17, 18 and the line of action of the ll-bolt clamps 4, 5. This rotation causes the width of the slots on the upper surface of the bending element 2 to expand by a distance approximated by A0 t_hinge, where t_hinge is distance from the effective rotation point of the hinge to the upper surface of the bending element. One skilled in the art should appreciate that t_hinge is effectively the depth of the strain amplifying slots plus 14 of the thickness of the material remaining below the slot.

[0048] Assuming the pair of feet 12,13 of the strain measuring device 10 remain in contact with the surface of the bending element 2, span two regions having different bending stiffnesses, for example, are positioned on either side of strain amplification slots 17, 18 respectively, due to friction associated with the clamp-on force of the bolt 16 affixing the strain measuring device 10 to the bending element 2, the strain measured by the strain measuring device can be approximated as follows:

[0049] As described above, the use of the strain-amplifying slots 17, 18 results in a different bending stiffness and results in the strain being developed within strain measuring device 10 that is primarily the result of the changing the width of the gap L_gaUge between feet 12, 13, and the strain measuring device is not directly measuring strain within the material of the bending member 2.

[0050] Comparing the strain in the strain measuring device 10 to the strain in the pipe 3 and defining this strain amplification factor as a , yields the following:

Assuming that L_{O Se} ~ Rptpe

^£gauge > hinge a

^£pipe Lgauge

[0051] Thus, the relationship between the strain measured by strain measuring device 10 to the strain in the pipe increases with t_hinge and decreases with L_gauge . For the general dimensions contemplated herein, the ratio of the strain in the strain measuring device ^£gauge to the strain in the pipe e_{p ipe} is in the of order unity. It is noted, however, design parameters could be optimized to create strain ratios between the strain in the strain measuring device 10 and the strain in the pipe 3 the be either smaller or larger than unity.

[0052] The pressure that can be resolved by utilizing DST 1 disclosed herein can be expressed as a function of the resolvable strain as follows:

[0053] For instance, the specifications for the Piezotronics RHM240A01 IEPE strain measurement device indicate a sensitivity of 100 mV/ps with a resolution of 0.1 nanostrain. By way of example, assuming a PCB 102A44 Piezotronics ported pressure transducer has a reported sensitivity of 100 mV/psi with a reported resolution of 0.1 milli PSI Referring to FIG 4, there is shown the resolvable pressure variation based on the above analysis of steel pipes (elastic modulus of 30e06 psi) utilizing a strain gauge with a reported resolvable strain of 0.1 nano-strain for a range of three hinge thickness to pipe radius ratios (toR) The resolvable pressure for a PCB 102A44 ported pressure transducer is shown for comparison.

[0054] Now referring to FIG. 5, there is shown another embodiment of DST 1 as part of the current disclosure. In this particular embodiment, bending member 50 has a dog-bone shaped configuration wherein the width w_g of the bending member is a reduced width region (as compared to the nominal width) for the region over which the strain measuring device 10 measures the strain. The reduction in the bending stiffness due to the dogbone configuration near the center of bending member 50 serves to amplify the strain measured by the strain measuring device 10 for a given pressure variation within pipe 3 compared to that measured by a strain measuring device associated with bending member 2 without the reduction in width. It should be appreciated by those skilled in the art that DST 1 has advantages prior art single point strain gauge measurements that measure the strain within to the conduit under the area of the strain measurement device, such as strain gauges or conformable strain measurement devices such as PVDF films and macro fiber composites for applications in which bending vibrations within the conduit may be significant. During bending vibrations of a circular conduit or any symmetric conduit, the cross-sectional dimension of the conduit is essentially unaltered by the bending stress. Embodiments of DST 1 of the current disclosure primarily generates strain in the bending member which is primarily responsive to changes in the cross sectional dimension of the conduit, i.e. the diameter of the circular conduit that bisects the bending element along centerline 19 (FIG. 2), the DST of the current disclosure is largely unresponsive to strain in the pipe due to bending stress, in which the strain in the pipe is asymmetric about the neutral axis of the bending vibration and does not result in significantly changes in the cross sectional diameter.

[0055] For the reasons set forth immediately herein above, the clamped-on nature of a bending member (2 or 50) on to the exterior surface of a conduit 3, as disclosed herein, results in a strain measurement in the bending member that is proportion to the circumferential strain the conduit that is sensitive to strain developed due to internal pressure variation, but that is not sensitive to strain associated with transverse bending of the conduit, along centerline 14 (along its length). It should be appreciated that embodiments of the DST 1 of the present disclosure, in addition to embodiments that utilize Piezotronics RHM240A01 IEPE strain measurement device, is well-suited for use with many other types strain measuring devices as well, such as piezo films, macro fiber composition, resistive strain gauges, optical strain gauges, etc.

[0056] Now referring to FIG. 6, the U-bolts 4,5 of DST 1 are replaced with bolts 61 , 62, 63 and 64 and stiff bending element 65. The bolts 61 , 62, 63 and 64 include associated fasteners such as fastening nuts to clamp the bending member 2 and the base element 65 to an outside surface of pipe 3 to produce a an preload and initial bending moment in bending member 2 by tightening the fasteners on the ends of the strain bolts. The base element 65 is, in relative terms, much stiffer than bending element 2. In other words, base element 65 should have sufficient stiffness to generate sufficient strain within the bending element 2 onto which the strain measuring device 10 is attached when subjected to pressure variations within pipe 3. The stiffer the base element 65, the more the circumferential strain within the pipe due to internal pressure variations will be isolated with the bending element 2 on which the strain measuring device 10 is attached.

[0057] Referring now to FIG. 7 there is shown another embodiment of DST 1 in accordance with the current disclosure. As shown, this embodiment utilizes two strain measuring devices 10a, 10b and two bending members 2 along with strain bolts 61 , 62, 63 and 6. Strain bolts 61 , 62, 63 and 64 include fastening nuts to clamp the bending members 2 an outside surface of pipe 3 to produce a predetermined initial bending moment in bending members 2 by tightening the fasteners on the ends of the strain bolts.

[0058] Now referring to FIG. 8, there is shown a schematic of a system 80 for determining a speed at which sound travels within a fluid contained within a conduit 81 and a GVF of the fluid thereby. System 80 includes a length of conduit 81 , a first sensor 82, a second sensor 83 wherein the sensors are positioned along a length L of the conduit. First sensor 81 and second sensor 82 can comprise a DST 1 (FIGS. 1 -3, 5, 6) disclosed herein above electrically coupled to a processing unit 84 by electrical connectors 85, 86 spaced apart by a known distance L along the length of the conduit. It should be appreciated by those skilled in the art that the known distance L forms an aperture length of conduit 81 between first sensor 82 and second sensor 83 within which unidirectional sound waves travel. Processing unit 84 can comprise any suitable computing device and includes software capable of determining the speed at which sound travels within a fluid contained within a conduit 81 based on signals provided by the first sensor 82 and second sensor 83. As disclosed herein above, conduit 81 can comprise any suitable conduit such as steel, PVC and fiber or steel reinforced composite hose. Examples of prior art composite hose include rubber coated helically wound steel reinforced hose 120 (FIG. 12) and steel over braided hose 130 (FIG. 13). Flexible composite hose compromised of elastomers and reinforcing fibers and/or wires, where the reinforcing fibers and /or wires, can consist of any material the has an elastic modulus that is significantly larger than the elastomer. The reinforcing fibers and/or wires can consist of a material such as steel, fiberglass, Dacron, etc. The composite hose tends to have high material damping characteristics. High damping characteristics of composite conduits impair the ability of the conduit to support structural wave propagation with long coherence lengths compared to conduits made from monolithic materials. Composite hoses are widely used for their flexibility and their ability to withstand high pressures. Although the composite hoses are capable of withstanding relatively high pressures, the effective elastic modulus of the hose is relatively low compared to other conduits that can withstand similar pressures.

[0059] An example of a GVF measurement system 100 of the current disclosure can be seen with reference to FIGS. 9 and 10. With specific reference to FIG. 9, there is shown and embodiment of DST 1 similar to that disclosed herein above and shown in FIG. 6 coupled to the exterior of conduit 90 in the manner disclosed herein above. GVF measurement system 100 includes two DST sensors 1a, 1 b installed on the exterior of a conduit 90, where the sensors are responsive to pressure variations within the conduit as disclosed herein above. DST sensors 1 a, 1 b installed at different axial locations along the known distance of length L of the centerline of conduit 90, and where the conduit can comprise a composite of multiple types of materials such as hydraulic hoses which utilize steel and or other high strength fiber-like materials to reinforce one or more layers, or embedded within, elastomer-like materials, such as rubber and can contain a fluid such as hydraulic fluid. DST sensors 1 a, 1 b are electrically coupled to a processing unit 84 (FIG. 8) that interprets the output from the DST sensors to determine the speed representative of speed of sound in the fluid contained within the conduit. Also shown in FIG. 10 are ported acoustic pressure sensors 101a, 101b positioned within couplings fitted to either end of conduit 90 and in fluid communication with the fluid contained within the conduit and also electrically coupled to the processing unit that interprets the output from the ported acoustic pressure sensors to determine the speed representative of speed of sound in the fluid contained within the conduit the system and method of which is set forth in co-pending Patent Cooperation Treaty application number PCT/US24/18340, filed 04 March 2024, the disclosure of which is incorporated herein its entirety.

[0060] Referring next to FIG. 11 there is shown a graphical representation of the GVF reported by GVF measurement system 100 using DST sensors 1a, 1 b in accordance with the current disclosure plotted against the GVF as measure by ported pressure sensors 101a, 101 b. It should be appreciated by those skilled in the art that there is good agreement over a range of gas void fraction of between ~3% to -12% between the two distinctly different systems and methods of sensing acoustic pressures within conduit 90 and determining the GVF of the fluid within the conduit. In performing testing to produce the data shown in FIG. 11 , the bubbler shown in FIG. 10 was used wherein hydraulic hose 90 was filled with water, and a small amount of air was introduced through an aerated stone at the base of the bubbler combine to aerate the water within the column. The amount of air injected was varied to vary the gas void fraction within the column. Two static pressure sensors were also installed at the top and bottom of the bubbler column (not shown). A reference gas void fraction within the column was measured by comparing the measured static pressure difference across the column that is expected based on a liquid of known density in accordance with the following relationship:

Where AP is the measured pressure difference, p_Uq is the density of the liquid (in this case water), g is the acceleration due to gravity, and h is the vertical distance between the sensors.

[0061]The graphical representation of FIG. 11 shows the gas void fraction measured based on the interpretation of the sound speed measured utilizing the compressive clamp-on sensors DST 1 a, 1 b disclosed herein above at the locations shown wherein L=17 inch and wherein L represents the aperture of GVF measurement system 100. In the embodiment shown, conduit 90 comprises a 1-inch inner diameter composite hydraulic hose. As shown the two methods are in good agreement over a GVF of -3% to -12%, demonstrating the utility of the methods described herein. [0062] The foregoing disclosure provides illustration and description but is not intended to be exhaustive or to limit the implementations to the precise form disclosed. Modifications may be made in light of the above disclosure or may be acquired from practice of the implementations. As used herein, the term “component” is intended to be broadly construed as hardware, firmware, or a combination of hardware and software. It will be apparent that systems and/or methods described herein may be implemented in different forms of hardware, firmware, and/or a combination of hardware and software. The actual specialized control hardware or software code used to implement these systems and/or methods is not limiting of the implementations. Thus, the operation and behavior of the systems and/or methods are described herein without reference to specific software code - it being understood that software and hardware can be used to implement the systems and/or methods based on the description herein. As used herein, satisfying a threshold may, depending on the context, refer to a value being greater than the threshold, greater than or equal to the threshold, less than the threshold, less than or equal to the threshold, equal to the threshold, and/or the like, depending on the context. As used herein, the terms acoustic pressure sensor, acoustic transducer and transducer are used to mean the same element and include a device configured to measure the unsteady pressure of a fluid are different and distinguished form devices configured to measure steady (or DC) pressures a fluid. Although particular combinations of features are recited in the claims and/or disclosed in the specification, these combinations are not intended to limit the disclosure of various implementations. In fact, many of these features may be combined in ways not specifically recited in the claims and/or disclosed in the specification.

[0063] Although each dependent claim listed below may directly depend on only one claim, the disclosure of various implementations includes each dependent claim in combination with every other claim in the claim set. No element, act, or instruction used herein should be construed as critical or essential unless explicitly described as such. Also, as used herein, the articles “a” and “an” are intended to include one or more items and may be used interchangeably with “one or more.” Further, as used herein, the article “the” is intended to include one or more items referenced in connection with the article “the” and may be used interchangeably with “the one or more.” Furthermore, as used herein, the term “set” is intended to include one or more items (e.g., related items, unrelated items, a combination of related and unrelated items, and/or the like), and may be used interchangeably with “one or more.” Where only one item is intended, the phrase “only one” or similar language is used. Also, as used herein, the terms “has,” “have,” “having,” or the like are intended to be open-ended terms. Further, the phrase “based on” is intended to mean “based, at least in part, on” unless explicitly stated otherwise. Also, as used herein, the term “or” is intended to be inclusive when used in a series and may be used interchangeably with “and/or,” unless explicitly stated otherwise (e.g., if used in combination with “either” or “only one of”).

Claims

CLAIMS WHAT IS CLAIMED IS:

1 . A method for determining the speed at which sound propagates in a fluid within a conduit, comprising: positioning a first sensor and a second sensor on an external surface of the conduit, wherein the first and second sensors are spaced apart by a known distance along a length of the conduit; measuring a first signal generated by the first sensor in response to pressure variations within the conduit; measuring a second signal generated by the second sensor in response to pressure variations within the conduit; and calculating the speed at which sound propagates in the fluid within the conduit based on the first and second signals and the known distance between the first and second sensors.

2. The method of claim 1 in which the method wherein the known distance defines an aperture.

3. The method of claim 2 wherein the first sensor and the second sensor form an array and wherein the aperture is at least five times an effective diameter of the conduit within the aperture of the array.

4. The method of claim 1 in which the method wherein the first sensor and a second sensor each comprise: a bending member configured to be positioned on the external surface of the conduit; one or more clamping elements releasably securing the bending member to the conduit; and a strain measuring device attached to the bending member, wherein the strain measuring device generates a strain signal proportional to a strain in the bending member caused by dimensional changes in the conduit.

5. The method of claim 4, wherein the bending member comprises a plurality of regions having different bending stiffnesses and wherein the strain measuring device spans at least two regions having different bending stiffness.

6. The method of claim 5, further comprising creating the different bending stiffnesses using a subtractive process.

7. The method of claim 5, further comprising creating the different bending stiffnesses using an additive process.

8. The method of claim 4, wherein the bending member includes at least one strain amplification slot extending partially through a thickness of the bending member to increase the strain measured by the strain measuring device for a given dimensional change in the conduit.

9. The method of claim 4, wherein the clamping elements comprise U-bolts and associated fasteners, wherein tightening the associated fasteners preloads the bending member against the conduit.

10. The method of claim 4, wherein the strain measuring device comprises a piezoelectric strain gauge secured to the bending member.

11 . The method of claim 10, wherein the piezoelectric strain gauge includes a pair of feet in contact with the surface of the bending member and a mounting bolt configured to apply a normal force for maintaining contact between the pair of feet and the bending member.

12. The method of claim 4, wherein the bending member is fabricated from a material having a lower bending stiffness compared to the clamping elements.

13. The method of claim 4, wherein the bending member has a dog-bone configuration with a reduced width region at a location aligned with the strain measuring device.

14. The method of claim 4, further comprising a base element positioned between the clamping elements and the conduit, wherein the base element is more rigid than the bending member.

15. The method of claim 3, wherein the first sensor and the second sensor are electrically connected to a processing unit configured to interpret the first signal and the second signal as representative of internal pressure variations within the conduit.

16. The method of claim 15, wherein the internal pressure variations are comprised at least in part of one-dimensional acoustic waves propagating within the aperture.

17. The method of claim 1 , wherein the conduit is a composite hose comprising layers of elastomers and reinforcing fibers.

18. The method of claim 17, wherein the reinforcing fibers are selected from the group consisting of steel, fiberglass, and Dacron.

19. The method of claim 17, wherein the composite hose has high material damping characteristics to reduce structural wave propagation.

20. The method of claim 1 , wherein the fluid within the conduit contains a gas void fraction (GVF), and the method further comprises determining the GVF based on the speed at which sound propagates.

21 . The method of claim 1 , further comprising filtering the first signal and the second signal to reduce noise caused by any of vortical and structural disturbances.

22. The method of claim 15, wherein the processing unit utilizes SONAR processing techniques to measure the speed at which one-dimensional acoustic waves propagate within the aperture utilizing the first signal and the second signal.

23. A system for determining the speed at which sound propagates in a fluid within a conduit comprising: a first sensor and a second sensor positioned on an external surface of the conduit, wherein the first and second sensors are spaced apart by a known distance along a length of the conduit; the first sensor is configured to generate a first signal in response to pressure variations within the conduit; the second sensor is configured to generate a second signal in response to pressure variations within the conduit; and a processing unit configured to determine the speed at which sound propagates in the fluid within the conduit based on the first and second signals and the known distance between the first and second sensors.

24. The system of claim 23, wherein the known distance defines an aperture, the first sensor and the second sensor form an array and wherein the aperture is at least five times an effective diameter of the conduit within the aperture of the array. i

25. The system of claim 23, wherein the first sensor and the second sensor are electrically connected to the processing unit and wherein the processing unit is further configured to interpret the first signal and the second signal as representative of internal pressure variations within the conduit.

26. The system of claim 25, wherein the internal pressure variations are comprised at least in part of one-dimensional acoustic waves propagating within the aperture.

27. The system of claim 26, wherein the processing unit utilizes SONAR processing techniques to measure the speed at which one-dimensional acoustic waves propagate within the aperture utilizing the first signal and the second signal.

28. The system of claim 23, wherein the first sensor and a second sensor each comprise: a bending member configured to be positioned on the external surface of the conduit; one or more clamping elements releasably securing the bending member to the conduit; and a strain measuring device attached to the bending member, wherein the strain measuring device generates a strain signal proportional to a strain in the bending member caused by dimensional changes in the conduit.

29. The system of claim 28, wherein the bending member comprises a plurality of regions having different bending stiffnesses and wherein the strain measuring device spans at least two regions having different bending stiffness.

30. The system of claim 29, further comprising creating the different bending stiffnesses using a subtractive process.

31 . The system of claim 29, further comprising creating the different bending stiffnesses using an additive process.

32. The system of claim 28, wherein the bending member includes at least one strain amplification slot extending partially through a thickness of the bending member to increase the strain measured by the strain measuring device for a given dimensional change in the conduit.

33. The system of claim 28, wherein the clamping elements comprise U-bolts and associated fasteners, wherein tightening the associated fasteners preloads the bending member against the external surface of the conduit.

34. The system of claim 28, wherein the strain measuring device comprises a piezoelectric strain gauge secured to the bending member.

35. The system of claim 34, wherein the piezoelectric strain gauge includes a pair of feet in contact with the surface of the bending member and a mounting bolt configured to apply a normal force for maintaining contact between the pair of feet and the bending member.

36. The system of claim 28, wherein the bending member is fabricated from a material having a lower bending stiffness compared to the clamping elements.

37. The system of claim 28, wherein the bending member has a dog-bone configuration with a reduced width region at a location aligned with the strain measuring device.

38. The system of claim 28, further comprising a base element positioned between the clamping elements and the conduit, wherein the base element has a higher bending stiffness than the bending member.

39. The system of claim 23, wherein the conduit is a composite hose comprising layers of elastomers and reinforcing fibers.

40. The system of claim 39, wherein the reinforcing fibers are selected from the group consisting of steel, fiberglass, and Dacron.

41 . The system of claim 39, wherein the composite hose has high material damping characteristics to reduce structural wave propagation.

42. The system of claim 23, wherein the fluid within the conduit contains a gas void fraction (GVF), and wherein the processing unit is further configured to determine the GVF based on the speed at which sound propagates.

43. The system of claim 23, wherein the processing unit is further configured to filter the first signal and the second signal to reduce noise caused by any of vortical and structural disturbances.