Beam forming and steering of helical guided waves in pipelike and platelike structures

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First Claim
1. A method of inspecting a pipe for flaws comprising:
 emitting ultrasonic waves in a helical pattern through the pipe from an array of ultrasonic transducer elements, wherein individual ultrasonic transducer elements of the array comprise at least one ultrasonic emitter and at least one ultrasonic receiver, and wherein the at least one emitter is configured to emit omnidirectional ultrasonic waves;
controlling the emission of the ultrasonic waves from the array such that a wave packet of the ultrasonic waves is emitted at a plurality of helical angles within a range of helical angles;
receiving reflections of the ultrasonic waves, the reflections of the ultrasonic waves caused by impingement of the ultrasonic waves on one or more flaws; and
determining at least one characteristic of the one or more flaws based on the received reflections of the ultrasonic waves based at least in part on the following formula;
Φ
=ϕ
Ξ
_{α}wherein Φ
is a Helmholtz scalar potential;
wherein Ψ
_{r}, Ψ
_{θ }and Ψ
_{z }are components of a Helmholtz vector potential;
wherein φ
, ψ
_{Tj};
j=1,2 and ψ
_{z }are arbitrary constants; and
wherein Ξ
_{η}, η
=α
,β
is a function of the form exp i (η
r cos (θ
−
θ
_{η})+k_{z}z−
ω
t),wherein at least one ultrasonic transducer element is configured to produce a direction of oscillation relative to waves propagating in the pipe or to an axis of the pipe.
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Abstract
A method of inspecting a pipe for flaws includes emitting ultrasonic waves, controlling the emission of the ultrasonic waves, receiving reflections of the ultrasonic waves, and determining at least one characteristic of one or more flaws. The ultrasonic waves are emitted in a helical pattern through the pipe from an array of ultrasonic transducer elements. The emission of the ultrasonic waves from the array is controlled such that the ultrasonic waves are emitted at a plurality of helical angles within a range of helical angles. The reflections of the ultrasonic waves are caused by impingement of the ultrasonic waves on the one or more flaws. The at least one characteristic of the one or more flaws is determined based on the received reflections of the ultrasonic waves.
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No References
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24 Claims
 1. A method of inspecting a pipe for flaws comprising:
emitting ultrasonic waves in a helical pattern through the pipe from an array of ultrasonic transducer elements, wherein individual ultrasonic transducer elements of the array comprise at least one ultrasonic emitter and at least one ultrasonic receiver, and wherein the at least one emitter is configured to emit omnidirectional ultrasonic waves; controlling the emission of the ultrasonic waves from the array such that a wave packet of the ultrasonic waves is emitted at a plurality of helical angles within a range of helical angles; receiving reflections of the ultrasonic waves, the reflections of the ultrasonic waves caused by impingement of the ultrasonic waves on one or more flaws; and determining at least one characteristic of the one or more flaws based on the received reflections of the ultrasonic waves based at least in part on the following formula;
Φ
=ϕ
Ξ
_{α}wherein Φ
is a Helmholtz scalar potential;wherein Ψ
_{r}, Ψ
_{θ }and Ψ
_{z }are components of a Helmholtz vector potential;wherein φ
, ψ
_{Tj};
j=1,2 and ψ
_{z }are arbitrary constants; andwherein Ξ
_{η}, η
=α
,β
is a function of the form exp i (η
r cos (θ
−
θ
_{η})+k_{z}z−
ω
t),wherein at least one ultrasonic transducer element is configured to produce a direction of oscillation relative to waves propagating in the pipe or to an axis of the pipe.  View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
 11. A device for inspecting a structure for flaws, the device comprising:
at least one ultrasonic emitter configured to emit waves in the structure, wherein the structure is a pipe; at least one ultrasonic receiver configured to receive reflections of the waves caused by impingement of the waves on one or more flaws; and a computing system configured to; control emission of waves from at least one ultrasonic transducer element in helical patterns based on one or more control parameters, the one or more control parameters comprising at least a windowed pulsed signal comprising at least a half oscillation of any shape; determine at least one characteristic of one or more flaws in the structure based on the signals emitted from an array of ultrasonic transducer elements and the reflections of the waves received by the array of ultrasonic transducer elements; and determine at least one characteristic of one or more flaws in the structure based at least in part on a time delay supplemented by amplitude control based on a minimum time delay increment, wherein the minimum time delay is a characteristic of hardware in the device; wherein at least one emitter is configured to emit omnidirectional ultrasound waves, wherein at least one ultrasonic transducer element comprises the at least one ultrasonic emitter and the at least one ultrasonic receiver, and wherein the at least one ultrasonic transducer element is configured to produce a direction of oscillation relative to waves propagating in the pipe or to an axis of the pipe.  View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24)
1 Specification
This application claims the benefit of U.S. Provisional Application No. 62/016,569, filed Jun. 24, 2014, the contents of which are incorporated herein by reference in their entirety.
Traditional methods employing guided waves for inspecting pipes comprise two stages. The first stage is illustrated in
For the first stage, the disadvantage of traditional methods is that the flaws must necessarily be either material loss type or circumferentially oriented because of the direction of wave propagation. Because the energy of the wave is distributed throughout the circumference, the intensity of the wave is low leading to its premature dissipation when pipe is carrying fluid or is submerged or buried (see Hardie F, “Evaluation of the effectiveness of nondestructive testing screening methods for inservice inspection,” Report for the Health and Security Officer, UK, 2009, pages 2930).
The second stage can overcome the limitations of the first stage by providing high intensity ultrasound at the region of interest. The second stage is illustrated in
Focusing is typically achieved by actuating the array of sensors with time delayed signals through a system, such as the embodiment of a system depicted in
Other disadvantages of the focusing method relate to factors involving the hardware depicted in
The second stage is typically used to size and find the circumferential location of the flaw. Focused guided waves can also be optionally used to generate a Cscan or a detailed map of a pipe by inspecting it pointbypoint as the focal point of the wave axially and circumferentially shifted by manipulating the transducer elements'"'"' excitation.
All of the above methods are ineffective when there are two flaws with one flaw hidden behind the shadow of another, as illustrated in
Mixing of the ultrasound array parameters, namely, time delays and amplitude variation is known as apodization. Apodization has been suggested in literature as a method for improving spot size of the focused waves. The primary aim of apodization thus far has been to reduce the so called Fourier noise caused due to the finite geometrical extent of an array of transducers. Further, apodization is performed without taking into account the fact that the minimum time delay offered by hardware limits the frequency at which good quality beam forming is achieved. Recently, it was shown that time delays can be completely replaced by amplitude variation across the transducer elements (see Kannajosyula, H., et al., “Amplitude controlled array transducers for mode selection and beam steering of guided waves in plates,” Review of Progress in Quantitative Nondestructive Evaluation: Volume 32, American Institute of Physics, 2013).
By virtue of the principle of reciprocity, theories developed for beam steering have enabled the development of postprocessing algorithms in literature for tools that employ an array of ultrasonic sensors each of which discretely transmit and/or receive ultrasonic guided wave signals in the structure. Such postprocessing algorithms are able to filter flaw signatures from the received data and thereby image the structure. Such algorithms are commonly referred to as synthetic phased array method and tools employing such algorithms have been referred to as ultrasonic radar or ultrasonic guided wave radar.
Unfocused beam forming in plates has been shown to be possible (see, e.g., Kannajosyula, H., et al., “Amplitude controlled array transducers for mode selection and beam steering of guided waves in plates,” Review of Progress in Quantitative Nondestructive Evaluation: Volume 32, American Institute of Physics. 2013). In principle, wave propagation in a pipe of very large diameter and small wall thickness will be similar to that in a plate. However, this may not necessarily be true for pipes of smaller diameters. Hence extension of beam forming technique used in plates to beam forming in pipes is not straightforward. Conversely, a method for focused beam forming in plates has not yet been developed in literature. Theory used for pipes can be extended to plates by modeling plates as very large diameter pipes. However; current theory appears to need further development for this to be possible.
This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This summary is not intended to identify key features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.
In one embodiment, a method of inspecting a pipe for flaws includes emitting ultrasonic waves, controlling the emission of the ultrasonic waves, receiving reflections of the ultrasonic waves, and determining at least one characteristic of one or more flaws. The ultrasonic waves are emitted in a helical pattern through the pipe from an array of ultrasonic transducer elements. The emission of the ultrasonic waves from the array is controlled such that the ultrasonic waves are emitted at a plurality of helical angles within a range of helical angles. The reflections of the ultrasonic waves are caused by impingement of the ultrasonic waves on the one or more flaws. The at least one characteristic of the one or more flaws is determined based on the received reflections of the ultrasonic waves.
In one example, the at least one characteristic of the one or more flaws includes one or more of a location of the one or more flaws, a size of the one or more flaws, an orientation of the one or more flaws, or a shape of the one or more flaws. In another example, the at least one characteristic of the one or more flaws is determined based on a presence or an absence of an anomalous signature. In another example, the method further includes mapping the at least one characteristic based on at least one of an amplitude distribution in time, an amplitude distribution in frequency, arrival time, or direction of approach of the anomalous signature. In another example, the method further includes controlling one or more of an average value of the range of helical angles or a width of the range of helical angles.
In another embodiment, a device for inspecting a structure for flaws includes at least one ultrasonic emitter configured to emit waves in the structure, at least one ultrasonic receiver configured to receive reflections of the waves caused by impingement of the waves on one or more flaws, and a computing system. The a computing system is configured to control emission of waves from the at least one ultrasonic transducer in helical patterns based on one or more control parameters and determine at least one characteristic of one or more flaws in the structure based on the signals emitted from the array and the reflections of the waves received by the array. The one or more control parameters includes at least a windowed pulsed signal comprising at least a half oscillation of any shape.
In one example, the one or more control parameters further includes at least one of: a continuous oscillation of signal amplitudes, a variance of signal frequency over time, a prescribed range of frequencies, or a variance of one or more of time delays, amplitudes, number cycles, pulse lengths, or frequencies. In another example, the device further includes an array comprising the at least one ultrasonic emitter and the at least one ultrasonic receiver. In another example, the device further includes at least one additional ultrasonic receiver configured to receive one or more of the waves emitted by the array or the reflections of the waves, where the at least one additional ultrasonic receiver is separate from the array. In another example, the computing system is further configured to determine the at least one characteristic of the one or more flaws based on the characteristics of reflected or transmission of waves received by the at least one additional ultrasonic receiver. In yet another example, the computing system is configured to evaluate and select one or more of a guided wave subtype of the waves, helical paths of the waves, or a focal point of the waves.
In another example, the structure is a pipe. In another example, the pipe comprises at least one of a circular crosssection, a square crosssection, a triangular crosssection, any other polygonal crosssection, or a crosssection that rotates along an axis of the pipe. In another example, at least one emitter is configured to emit omnidirectional waves, where at least one ultrasonic transducer element comprises the at least one ultrasonic emitter and the at least one ultrasonic receiver, and where the at least one ultrasonic transducer element is in a configuration determined by a direction of oscillation relative to waves propagating in the pipe or to an axis of the pipe.
In another example, the oscillation is along a thickness of the pipe, where the at least one ultrasonic transducer element is a thickness mode piezoelectric transducer or a particularlyshaped 13 piezocomposite transducer. In another example, the oscillation is along the axis of the pipe, where the at least one ultrasonic transducer element is a circularshaped macrofiber composite with piezoelectric fibers oriented perpendicular to the axis and comprises electrodes arranged along the axis of the pipe. In another example, the oscillation is tangential and orthogonal to the axis of the pipe, where the at least one ultrasonic transducer element is a circularshaped macrofiber composite with piezoelectric fibers oriented perpendicular to the axis and comprises electrodes arranged perpendicular to the axis of the pipe. In another example, the oscillation is tangential and orthogonal to the waves, where the at least one ultrasonic transducer element is a circularshaped macrofiber composite with piezoelectric fibers forming an annular array and comprises electrodes oriented radially from the center of the annular array. In another example, the oscillation is tangential and parallel to the waves, where the at least one ultrasonic transducer element comprises electrodes forming an annular array, and where the at least one ultrasonic transducer element is a circularshaped macrofiber composite with piezoelectric fibers oriented radially from the center of the annular array.
In another example, the at least one ultrasonic emitter is configured to emit waves both unidirectionally and bidirectionally. In another example, the structure comprises a platelike structure. In another example, the computing system is further configured to determine at least one characteristic of one or more flaws in the structure based at least in part on the following formula:
where Φ is a Helmholtz scalar potential, where Ψ_{r}, Ψ_{θ} and Ψ_{z }are components of a Helmholtz vector potential, where ϕ, ψ_{Tj}; j=1, 2 and ψ_{z }are arbitrary constants, and where Ξ_{η}, η=α,β is a function of the form exp i(ηr cos (θ−θ_{n})+k_{z}z−ωt). In another example, the computing system is further configured to determine at least one characteristic of one or more flaws in the structure based at least in part a time delay supplemented by amplitude control based on a minimum time delay increment, and the minimum time delay is a characteristic of hardware in the device.
The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated as the same become better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein:
This subject matter disclosed herein relates to systems and methods for unfocussed and focused beam forming and steering of ultrasonic helical guided waves in pipe and platelike structures. In one embodiment, a pipelike structure is approximated as a perfectly circular cylinder that is constructed out of metal, plastic, or inhomogeneous materials of some regularity, as exemplified by carbon fiber reinforced polymer (CFRP) composite. Beam forming and steering of ultrasonic helical guided waves is possible due to formulating guided waves in pipes that provides improved understanding of the phenomena. In one embodiment, a system and method directs guided waves along a specific helical angle providing significant advantages over previous systems and methods.
The concept of unfocussed beam forming and steering is illustrated in
The concept of focused beam forming is illustrated in
An example method 68 of controlling actuation of the transducer array for unfocussed beam forming and steering is depicted in
An example method 90 of controlling actuation of the transducer array for focused beam forming is depicted in
In general, ultrasonic transmitters do not need to have direct access to load carrying layers if the waves can be generated in the nonloadcarrying layers using a given transmitter. For example, in the case of a guided wave phased array transducer, the phased array may be installed on the coated structure (e.g., coated pipe) without removal of the coating layer. The advantage includes not requiring the full removal of the coating layer installation of the transducer array a mandatory practice in conventional methods of installation. This is, in particular, desirable when the full circumference of the pipeline is not accessible. Examples of using phased array transducers are described in U.S. Patent Application No. 62/103,315, filed Jan. 14, 2015, the contents of which are hereby incorporated by reference in their entirety.
In addition, in some embodiments, the subject matter disclosed herein employs mixed time delay and amplitude control to improve beam forming of high frequency ultrasonic guided waves and thereby further improve the resolution of the inspection system. As a departure from traditional apodization methods, the amplitude variation is used to compensate for the lack of precision in the time delays offered by current hardware. In some embodiments, the subject matter disclosed herein may also be used for focused beam forming in platelike structures. In some embodiments, the subject matter disclosed herein enables nondestructive scanning of pipelines for flaws of any shape and orientation at higher speeds with better resolution and improved accuracy, some of the reasons for which are described in the next section.
Example Advantages of Disclosed Embodiments
One of the advantages of the subject matter disclosed herein is that flaws of all orientations can be detected, located, and sized simultaneously without necessarily requiring a second stage because of the variable helical path of the guided waves. Because of the variability of helical angles, a given flaw can be interrogated from multiple directions. In some embodiments, the directionality is controlled on demand by a user or a control algorithm. An example of this capability is depicted in
Further, due to the reasons that apply to the guided wave focusing technique (e.g., namely the constructive interference of ultrasound from multiple transducers), the intensity of the resulting ultrasound will be high when compared to the first stage of the traditional approach depicted in
The hidden flaw may also be detected by observing signals from that are as a result of multiple reflections, as depicted in
The guided wave beam generated by this direction will be unidirectional, unlike traditional approaches that are bidirectional. In other words, traditional approaches generate beams in both directions along the axis of the pipe. This may be considered an advantage as the readability of the acquired data is vastly superior because of absence of reflections from features in one or more directions. However, the embodiments disclosed herein can optionally be made to act bidirectionally. In one embodiment, the unidirectional capability is used for detailed sizing and location of flaws after bidirectional capability is used to detected the flaws.
Wave Types and Transducer Designs
Preliminary results indicate that generation of special wave types is possible under certain embodiments. In some embodiments, such waves are generated by particular transducer designs. Some examples of such waves and transducer design are depicted in
Transducer arrays do not need to be of the shape illustrated in
Array Control Parameters
The first step of the algorithms illustrated in
In
The term group velocity in
As a departure from traditional methods, mixed time delay and amplitude control may be used to achieve high frequency guided wave propagation. Such a mixing of time delays and amplitude variation has been suggested in literature without taking into account the fact that the minimum time delay offered by hardware limits the frequency at which good quality beam forming is achieved. Time delays can be completely replaced by amplitude variation across the transducer elements. Further, amplitude control can be expressed in terms of time delay. Changing of time delays is much faster than amplitude change, particularly if the change in amplitude is large in value. In some of the embodiments disclosed herein, time delays may be used as much as possible. However, when the minimum time delay increment is not sufficiently small, amplitude control may be used to correct the deficiency. In such a scenario the amplitude change may be small and can be achieved at very high speeds. This will improve the resolution of the inspection system in proportion to the frequency that becomes possible.
Flaw Characterization
Flaw characterization involves the determination of one or more of the existence, location, size, shape and orientation of any flaw. Features that can be characterized as flaws include inclusions, cracks, corrosion, dents, attachments, welds, or any other type of nonuniform feature. The characteristics of the flaws will be extracted from the ultrasonic data received by the elements of transmitter array, a traveling or scanning receiver sensor, and/or a dedicated receiver array consisting of at least one sensor element that may be placed anywhere on the pipe. The receiver array, if any, may have its sensor elements distributed in any fashion, for example they may be distributed circumferentially or linearly. The signatures that help determine the existence of a flaw correspond to reflection of ultrasound from a flaw and/or an unexpected absence of ultrasonic signals. In one embodiment, the location is determined by taking into account the helical angle at which ultrasonic beam is launched at the transmitter and, in case of a signature caused due to reflection of ultrasound from a flaw, the properties of signature (e.g., its amplitude distribution in time or frequency domain), its arrival time relative to the time at which the beam was launched, or the helix angle of the reflected beam when it was received.
The helix angle of the received reflection signal can be determined by several methods. In case of single receiver, the original transmit helix angle, the relative location of the receiver and arrival time of the received signal may be used to triangulate the location of the flaw. If a receiver is used, then, in addition signal processing methods (e.g., Fourier transforms) may be used to determine the angle of arrival. In all of the calculations, the lookup table is calculated using the theory discussed below. An example method 246 for mapping and/or obtaining a scanned image of pipe is illustrated in
The method 246 beings with three steps that can be performed in series or in parallel. At block 248, a dataset variable is set to an initial value, such as D=1. At block 450, stored datasets are retrieved. In some embodiments, the stored datasets are retrieved using the methods depicted in
At block 258, a helix angle of arrival and intensity of patterns are calculated. In one embodiment, the helix angle of arrival and the intensity of patterns are calculated using Fourier transforms and/or receiver array data. At block 260, a determination is made whether an anomalous pattern exists. If no anomalous pattern exists, then the method 246 proceeds to block 262 where the dataset variable is incremented and then the method 246 returns to block 254. However, if an anomalous pattern exists, the method 246 proceeds to block 264. At block 264, a helix angle of arrival and an intensity of patterns are calculated. In one embodiment, the helix angle of arrival and the intensity of patterns are calculated using Fourier transforms and/or receiver array data. At block 266, the defect is triangulated and characterized and corresponding values are transferred to a defect map. In some embodiments, the defect is triangulated and characterized using a mean helix angle of generation, the distance between transmitter array and receiver element at which anomaly was detected, and/or the angle of arrival of anomaly and look up table of velocities. The method 246 then proceeds to block 262 where the dataset variable is incremented and then the method 246 returns to block 254.
Other Applications
The embodiments disclosed herein may be used for applications employing ultrasonic guided waves that achieve improved performance in the presence of high intensity ultrasound. Examples of such applications include nonlinear ultrasonic testing, ultrasonic deicing, ultrasonic cleaning, and processing involving sonochemistry.
As already mentioned, the subject matter disclosed herein includes methods for unfocussed and focused beam forming and steering of helical guided waves. The methods depicted in
Bulk Wave Solutions
The governing equation for elastic wave propagation in an isotropic elastic medium is given by the balance of momentum and the Hooke'"'"'s Law, which are respectively expressed as follows:
where, σ is the stress tensor, u is the particle displacement vector and ϵ=(∇u+∇u^{T})/2 is the strain tensor and t is time. Combine Equations 1a and 1b the final equation of motion (or Navier'"'"'s equation) is obtained as follows:
In order to solve Equation 2 the Helmholtz decomposition of u is employed that can be expressed as follows:
u=∇Φ+∇×Ψ 3a
∇·Ψ=f(r,t) 3b
where, Φ and Ψ are the Helmholtz scalar and vector potentials; f(r, t) is an arbitrary function and in terms of physical components with respect to the cylindrical coordinate system (r, θ, z), Equations 3a and 3b are
The Equation 3b is also called as Helmholtz'"'"' gauge invariance criterion. Substituting Equation 3a in Equation 2, the latter can be decomposed into a system of 4 partial differential equations, given by
where, the scalar Laplacian operator ∇^{2 }is given by
Assuming a trial solution, Φ=ϕe^{i(αr cas θ+k}^{z}^{zωt)}, where ϕ is an arbitrary constant and substituting in Equation 4a it can be shown
For a non trivial ϕ,
Similarly, assuming the trial solution Ψ_{z}=ψ_{z }e^{i(βr cos θ+kz−ωt)}, ψ_{z }being an arbitrary constant, and substituting in Equation 4d the following can be demonstrated.
Let Ξ_{β} be any function that also satisfies Equation 4d. Differentiating Equation 4d with respect to r and substituting Ψ_{z}=Ξ_{β}, the following equation is obtained:
Using Equation 7, it can be shown that Equations 4b and 4c are simultaneously satisfied if the Ψ_{r }and Ψ_{θ} have the following form:
where, as before ψ_{Tj}; j=1, 2 are arbitrary constants and the subscript T stands for the term transverse. It may be noted that the expressions e^{i(αr cos θ+kz−ωt) }and e^{i(βr cos θ+kz−ωt) }represent plane waves propagating in the x−z plane. The solutions presented thus far can be modified to the more general case of a plane wave propagating at any orientation in the r−θ plane. Before proceeding in this direction, new notations need to be introduced, viz. Ξ_{θ}=e^{i(ηr cos(θ−θη)+k}^{z}^{zωt)}, where η=α,β_{Z}, β_{T}. Using this new scheme of notation, the solutions are recapitulated as follows:
where, although β_{Z}=β_{T}=β that
The final step before writing down the most general solution for Φ and Ψ, it is necessary to consider the Helmholtz gauge invariance criterion (Equation 3b). The choice of f (r, t) on the right hand side of Equation 3b is arbitrary. It can be shown that f (r, t) vanishes whenever
(−β^{2}ψ_{T1}+ik_{z}ψ_{z})Ξ_{β}=0 10
From here on the convention Ξ_{β}_{T}=Ξ_{β}_{T}=Ξ_{β} will be employed. The general solution for Φ and Ψ can be written as:
where, Ξ_{η}=e^{iηr cos(θ)}, η=±α, ±β; ϕ^{±} and ψ_{m}^{±}, m=T2, z are arbitrary coefficients corresponding to ±α and ±β, respectively. For convenience the number “2” in the subscript T2 will be dropped from the equations henceforth. Substituting Equations 12a and 12b in Equations 3a3c, the expressions for the particle displacement vectors can be obtained as follows:
Formulation for Guided Waves
The field of guided wave propagation in isotropic pipes includes as study of several fundamental problems including propagation in rods, submerged pipes, fluid carrying pipes and multilayered pipes. For the sake of simplicity, only the formulation and analysis of guided waves in a single layered pipe is presented.
For modeling guided waves the traction vector components on the pipe surface are required and are given by:
General Solution: Nonlinear Helicity
For a singlelayered pipe the formulation is achieved by traction free boundary conditions at both the surfaces of the pipe. Let the pipe wall thickness be 2ΔR and the mean radius of the pipe wall be given by R. Substitution of vanishing traction vectors in Equation 13, evaluated at R+ΔR and R−ΔR, the following expression is obtained
where E^{±} stands for the diagonal matrix whose entries are given by e^{±iαΔR cos θ}, e^{±iβΔR cos θ} and e^{±iβΔR cos θ}, respectively. For nontrivial X, the following condition must be satisfied:
Γ:=det[G]=0 15
where det[G] stands for the determinant of the matrix G.
Equation 15 is termed as the dispersion relation that may be solved for different combinations of θ, θ_{α}, θ_{β}. For each such combination dispersion curves that are a function of ω, k are obtained. For each point on the dispersion curve, Equation 15 may be numerically solved for X^{(±)}(R), from which the arbitrary coefficients ϕ^{±}, ψ_{T}^{±}, ψ_{z}^{±} and subsequently, the displacement and traction components may be evaluated. It will be shown later that for some special cases analytical expressions for the dispersion curves are possible. For further discussion the following new notation is introduced:
g_{z}=g_{z}(θ,ω): ={k_{z}: Γ(k_{z},θ,ω)=0} 16
where, g_{z }is the wavenumber of guided wave (which is denoted by the superscript). Equation 17 makes explicit an otherwise implicit assumption in guided wave modeling that in general the axial wavenumber, k_{z }is an independent quantity while g_{z}, the wavenumber of the guided waves are given by a subset of values of k_{z }that satisfy Equation 15 and that therefore, g_{z }does not remain an independent quantity. This notion or notation is used in subsequent derivations to avoid confusion, particularly when differentiation with respect to wavenumbers is involved.
The phase of the guided wave may therefore be expressed as P=g_{z}z−ωt. The phase, P represents the guided wave front whenever it is constant. Thus its derivative relative to time results the following expression:
The coefficients of the time derivatives in Equation 17 give the wavevector components, one of which is
that can be evaluated by solving Equation 16. The other coefficient gives the wavevector along the circumferential direction and may be expanded as follows:
where g_{θ} is the angular wavenumber. The phase helical angle,
Equations 18b and 18c show that the angular wavenumber of the guided wave is dependent on the axial distance as well. Since g_{z }is independent of z, it follows that the helical guided waves may tend to become circumferential guided waves. Thus the solutions in this section indicate the possibility of guided waves with nonlinear helicity. It will be numerically shown later that most guided waves of nonlinear helicity are lossy and will therefore propagate only over short axial distances.
Although the components of phase velocity may be expressed as
phase velocity is a term that is frequently used in guided wave literature, in most practical scenarios, the group velocity is the more important and directly measurable quantity. The corresponding components of group velocity ν_{z}, ν_{θ} are given by:
Consequently, we may define a group helical angle,
The group helical angle has thus far not been reported in literature. The concept is analogous to skewing of guided waves propagating in an anisotropic plate.
With these general derivations, it may be inferred that wave propagation in pipes may be more complex than it is otherwise thought to be. The formulation presented till now allows several inferences that are not as straightforward when using Bessel'"'"'s function based solutions to be made. The first nontrivial inference that can be drawn from Equations 14 and 15 is that the dispersion relation propagation in a pipe does not depend upon the mean radius of the pipe. The effect of curvature is however, manifested through the dependence of G on θ. The dispersion curves will scale relative to the wall thickness, a feature that is also observed in case of plates. In the subsequent section formulation restricted to guided waves of linear helicity will be presented.
Guided Waves of Linear Helicity
For the analysis of guided waves of linear helicity, consider the terms representing the phases of Ξ_{α }and Ξ_{β}:
P_{α}=αr cos(θ−
P_{β}=βr cos(θ−
The corresponding wavevectors are obtained by taking the vector gradient of the Equations 20a and 20b which in component form are:
k_{α}=[α cos(θ−
k_{β}=[β cos θ−
The quantities enumerated in the vectors in Equations 21a and 21b are the radial, circumferential and axial wavenumbers, respectively. To provide a relationship between
α sin θ−
That is the tangential components of the wavevector are unique, which is an extension of the concept from two and three dimensional plate guided wave theory. If this rule is violated then as also observed in the previous section, the wave propagation will be attenuated because of destructive interference of the waves.
Using Equation 19, introducing the notations,
Note that for numerical stability, it is advisable to replace D^{±} with
g_{θ}=k_{θ} 25a
g_{z}=g_{z}(g_{θ},ω):={k_{z}:Γ(k_{z},g_{θ},ω)=0} 25b
Alternately,
g_{z}=k_{z} 25c
g_{θ}=g_{θ}(g_{z},ω):={k_{z}: Γ(g_{z},k_{θ},ω)=0} 25d
Thus linear helical guided waves are independent of the physical angle θ. This suggests that the dispersion relations for guided wave in pipe may be equivalent to those in plates. The formulation in this section may also be interpreted to mean that due to the phenomenon of interference the orientations,
For the purpose of generating the lookup table as illustrated in the flowcharts (e.g., in
g_{p}=g_{p}(
Subsequently, the group velocity components v_{v }and v_{t }along the helix angle
Consequently, we may define a group helical skew angle,
The skew angle,
A particular case of helical guided wave propagation is the circumferential guided wave for which
Numerical Results
In this section, numerically calculated dispersion properties corresponding to some helical angles including axial guided waves and circumferential guided waves will be explored. The example case of a steel pipe of 8.4 mm wall thickness is considered. The bulk longitudinal velocity, c_{1 }and the bulk shear velocity, c_{2 }and the density, ρ are assumed to be 5.94 mm/μs, 3.25 mm/μs and 7.8 g/cc; respectively. The dispersion curves were traced using Muller'"'"'s method.
First, consider the phase velocity dispersion curves corresponding to axially propagating modes (
The variation of the dispersion curves for guided waves along 0°, 30°, 60° and 90° helical angles are illustrated in
For designing transducers for generation and reception of helical guided waves, it is important to investigate the respective distribution of particle displacement vector components (or “wavestructure”) of the guided wave modes with the variation in helical angle. The comparison is restricted to only the modes that are common to all the helical angles. For the sake of brevity, the displacement patterns are further restricted to the outer radius of the pipe and to only the axial and torsional components of the normalized displacement vector.
Finite Element Simulation
Finite element simulations were performed to verify the possibility of unfocussed beam forming. Finite element methods are based on a separate mathematical formulation. This formulation can be found in the manuals of the opensource software FEniCS, which was used to program the finite element simulations for this patent. The finite element formulation also involves time marching for which several schemes exist in literature. For the results presented herein, the timemarching scheme corresponds to the implicit Euler method, unless otherwise stated. The simulations performed thus far have verified the beam steering of only the T_{0 }mode. From the results in
Summary of Select Disclosed Embodiments
The disclosed subject matter includes a method and a system for unfocused and focused beam forming and steering of ultrasonic guided waves in a pipe along helical path.
In one embodiment, a device includes an array of at least two ultrasonic transducers elements that can excite and receive sound or elastic waves in the pipe, or any implementation of such an array, exemplified by macrofiber composites. The device includes an electronic system that can control or drive the ultrasonic transducer elements in the array. The control parameters may comprise one or more of the following: a continuously oscillating signal amplitude, a windowed pulsed signal comprising at least half an oscillation of any shape, signal whose frequency content may vary with time, a prescribed range of frequencies, varying time delays and/or amplitudes and/or number of cycles (or pulse length) and/or frequencies. In one embodiment, the device includes an optional array of at least one ultrasonic receiver. In another embodiment, the device includes an electronic system that can amplify and conditioning the signals received from each transmitting and/or receiving sensor.
In one embodiment, a method includes evaluation and selection of guided wave subtypes, helical paths and focal points enabled by new method of formulating guided waves in pipes. The above parameters are evaluated based on the above selection for electronically controlling the waves generated in the pipe. Detection of the defects and features in the pipe may be based on the presence or absence of anomalous signatures, such as reflections and transmissions of ultrasound from the defects. The features based on the amplitude distribution in time and/or frequency, arrival time and direction of approach of such signatures are mapped.
In one embodiment, a method for inspecting the pipe wherein the inspection includes detecting, locating and sizing flaws by processing the reflections resulting from beam formed waves that impinge on the flaws at multiple angles of incidence, where such reflections are received as signals by the above mentioned system of arrays and electronics. Further, the flaws may include a shape and/or orientation with a minimum size determined by the period or alternately the frequency of oscillation of the generated wave in time and space.
In one embodiment, a method for using special transducer array elements—that individually generate omnidirectional waves—whose configuration is determined by the direction of oscillation relative to the rays comprised by the propagating wave in the pipe or to the axis of the pipe. In some examples, the oscillation is one of: oscillation along the wall thickness of pipe using a traditional thickness mode piezoelectric transducer or specially shaped 13 piezocomposite; oscillation tangential and along the axis of the pipe using a circular shape macrofiber composite with piezoelectric fibers oriented perpendicular to the axis and the electrodes arranged along the axis; oscillation tangential and orthogonal to the axis of the pipe using a macrofiber composite that is circular in shape but the piezoelectric fibers are oriented along the axis of the pipe whereas the electrodes are oriented perpendicular to the axis; oscillation tangential but orthogonal to the rays comprised by the wave a circular shaped macrofiber composite where the fibers form an annular array and the electrodes are oriented radially from the center of the annular array; oscillation tangential but parallel to the rays in the wave using a circular shaped macrofiber composite where the electrodes form an annular array but the piezoelectric fibers are oriented radially from the center of the annular array; or other transduction mechanisms, such as electromagnetic acoustic transducers or magnetostrictive transducers.
In some embodiments, the devices disclosed herein are capable of generating both bidirectional and unidirectional beams. In some embodiments, the devices disclosed herein are capable of being used for focused beam forming and steering in platelike structures. In some embodiments, the methods disclosed herein can also be used for postprocessing ultrasonic radar data. In some embodiments, the devices disclosed herein can also be used for applications that require high intensity ultrasound, such as are nonlinear ultrasonic testing, ultrasonic deicing, ultrasonic cleaning, and processes involving sonochemistry.
It should be noted that for purposes of this disclosure, terminology such as “upper,” “lower,” “vertical,” “horizontal,” “inwardly,” “outwardly,” “inner,” “outer,” “front,” “rear,” etc., should be construed as descriptive and not limiting the scope of the claimed subject matter. Further, the use of “including,” “comprising,” or “having” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. Unless limited otherwise, the terms “connected,” “coupled,” and “mounted” and variations thereof herein are used broadly and encompass direct and indirect connections, couplings, and mountings.
The principles, representative embodiments, and modes of operation of the present disclosure have been described in the foregoing description. However, aspects of the present disclosure which are intended to be protected are not to be construed as limited to the particular embodiments disclosed. Further, the embodiments described herein are to be regarded as illustrative rather than restrictive. It will be appreciated that variations and changes may be made by others, and equivalents employed, without departing from the spirit of the present disclosure. Accordingly, it is expressly intended that all such variations, changes, and equivalents fall within the spirit and scope of the present disclosure, as claimed.