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Examples
Wave2000® Examples
In order to give you a better idea of the power and versatility of CyberLogic's ultrasound simulation software packages, we have included here several sample ultrasonic problems and their solutions using Wave2000®. These examples will give you a better idea of how Wave2000® can be used in your own application(s). Example 4 also shows some of Wave2000®'s specific model set-up windows, illustrating how easy the graphical user interface makes it to define a particular simulation model. Example 5 shows the use of phased arrays and infinite (absorbing) boundary conditions. In addition you can download the program, and obtain a free time limited license for program evaluation by registering with us and logging in. Information on pricing is also available. Please Contact Us if you have any questions or to discuss how you and/or your company would benefit from using Wave2000®.
Focussed (phased array) source transducer and infinite boundary conditions (this one gives a good view of some of the array phasing capabilities of the software).
Wave2500® Examples
In order to give you a better idea of the power and versatility of CyberLogic's ultrasound simulation software packages, we have included here a few sample ultrasonic problems and their solutions using Wave2500. These examples will give you a better idea of how Wave2500 can be used in your own application(s). You should also view the Wave2000® Examples, as the two programs share many of the same features, particularly the GUI. Indeed, users of either program will quickly be able to master the use of the other one. Please note that you can download the full featured program and obtain a free time limited license for evaluation by registering with us and logging in. Also, please Contact Us if you have any questions or to discuss how you and/or your company would benefit from using Wave2500.
Wave3000® Examples
In order to give you a better idea of the power and versatility of CyberLogic's ultrasound simulation software packages, we have included here a couple of sample ultrasonic problems and their solutions using Wave3000. These examples will give you a better idea of how Wave3000 can be used in your own application(s). You should also view the Wave2000® Examples, and Wave2500 Examples, as the three programs share many of the same features, particularly the GUI. Indeed, users of at least one of the programs will quickly be able to master the use of one or both of the other ones. Please note that you can download any or all of the full featured programs and obtain a free time limited license for evaluation by registering with us and logging in. Also, please Contact Us if you have any questions or to discuss how you and/or your company would benefit from using Wave3000 or our other ultrasound simulation programs.
Layered media measurements using pulse-echo ultrasound.
The figure below and associated legend represent a layered ultrasound propagation problem. Wave2000 has a pseudo-color display related to material definitions which is shown here. Thus, in this model there are three material layers making up the overall object, aluminum, titanium and chromium, going from left to right across the screen. Also shown is a 0.5 cm transducer located at the center of the left side of the object. This transducer has been defined in Wave2000 to operate in pulse-echo mode.
Wave2000 generates “step-by-step” images of the propagating ultrasound wave. The ultrasound “movie” below displays a 1 MHz sine wave with a Gaussian envelope propagating into the layered structure from the left surface. The diffraction spreading of the wave from the transducer can be seen, while the wave is reflected and transmitted at the boundaries of the layers. The boundaries are displayed as a light pixel value proportional to the gradient between the two regions.
Wave2000 plots and/or saves all transducer source and/or receiver data. The figure below displays a receiver plot associated with this layered simulation model. The graph shows the measurements associated with the pulse-echo receiver. As may be seen, the source waveform (in blue) is displayed at the very beginning of the plotted signal. The reflected waveform measured by the receiving portion of the pulse-echo transducer is shown in red. On this curve, the first identifiable waveform is the reflection from the first (aluminum/titanium) interface, occurring at about 4 us. Following that, the next main portion of the waveform is the reflection associated with the second (titanium/chromium) interface, occurring at about 8 us. The last well defined reflection is that associated with the vacuum portion of the object (i.e., the reflection associated with the chromium/vacuum interface at the right side of the object), and occurs at about 11 us. You can also observe the presence of later arriving signal energy, representing multiple reflections as well as mode conversions. Note that the stated arrival times are the round trip travel times for the ultrasound signals.
In Wave2000, ultrasound simulations can be easily adapted to model various changes to the interrogated object. For example, Wave2000 can model the effects of non-parallel material layers as easily as it simulates this parallel interface model. It is interesting to note in this example that the source transducer gives rise to a significant amount of diffraction spreading and as a result a related amount of non-normal incidence of the ultrasonic wavefront onto the boundaries (and the associated shear waves generated by mode conversion). These phenomena are all accounted for in a Wave2000 simulation.
Porosity effects and material characterization.
The figure below is a single “slice” of a micro-computed tomographic image of a cylinder of human calcaneal (heel) trabecular bone. The bone trabeculae (with thicknesses on the order of 100 microns) are represented by the light regions and the marrow spaces are represented by the black regions. (The bone imaging data is courtesy of Dr. John Kinney of Lawrence Livermore Laboratories, Livermore, CA.)
Use Wave2000 to study highly scattering structures. The ultrasound “movie” below is comprised of 3 images of an ultrasound wave propagating through the trabecular bone slice shown in the previous figure. As may be seen, there is a large amount of scattering of the 1 MHz ultrasound pulse (produced by a 1 cm source transducer located on the left side of the object), in what may be described as a “mode stirring” phenomenon. A longitudinal receiver (also not shown) is configured in “through transmission mode,” i.e., is located “coaxially” with respect to the source on the right side of the sample. Note that Wave2000 displays only the boundaries between disparate materials in an interrogated object during a simulation, so that the propagating wave can be visualized.
A variety of source waveforms can be utilized in Wave2000 simulations. The plot below shows the ultrasound source waveform transmitted into the bone by a transducer on the left side of the sample. Wave2000 has a set of source waveform types that may be used in a simulation. In addition, users may incorporate their own waveforms (e.g., data from a particular transducer in their lab) by using a Wave2000 “source file option.”
Through transmission measurements are simple to define in Wave2000. The plot below shows the ultrasound waveform measured by a through transmission receiver on the right side of the bone. The received waveform displays characteristics often observed in “real world” measurements. For example, there appears to be phase cancellation distortion towards the end of the main pulse. Also, there is significant amount of signal energy received after the main pulse comes through, showing a remarkable similarity to reported observations.
Wave2000 has “built-in” analysis routines. Although Wave2000 allows the user to plot and save receiver measurements in an ASCII file (for subsequent processing by a user’s own custom software), Wave2000 also comes with a small set of “built-in” analysis routines. The one shown below is a “transit time” velocity calculation which allows the user to compute the apparent velocity of the ultrasound wave measured at a specified receiver, with respect to a specified source. It also displays several velocities based on distinct “arrival time” criteria. Not shown but also included in the Wave2000 Analysis features is the ability to compute the frequency-dependent attenuation of a receiver waveform with respect to a given source waveform.
Wave2000 can be used in practically any materials characterization problem. The user may explore how, for example, porosity and architecture (structure) affect the propagation (e.g., velocity and attenuation) of ultrasound. In addition, Wave2000 can be used to test a new idea for material characterization (e.g., a novel positioning of a receiver on an interrogated object). One can also explore how changing the material properties of the constituents making up the interrogated object affects the propagation. For example, in this bone assessment application, it is of interest to examine the effects of replacing blood by water or fat or void in the marrow spaces of the bone sample. Such modifications are simple to do with Wave2000.
Flaw Detection (scattering from a crack)
Wave2000 has an easy to use graphics file format to represent arbitrary structures. With Wave2000 we say: “If you can draw it, you can simulate it.” A simple example of this is shown in the figure below which is a “PCX” graphics file representing an object to be ultrasonically interrogated. It represents a solid block of Plexiglas, within which is a small (1 mm x 3 mm) crack. The “crack” is a void (vacuum) region, represented in Wave2000 by a (reserved) pixel value of 255. By changing the grey level associated with the crack region, a crack containing virtually any liquid or solid can be simulated.
In this example, a 1 MHz Gaussian modulated sine wave is input into the block with a 1.5 cm source transducer (not shown) located on the left side of the object. The transducer is defined to operate in pulse-echo mode, thus allowing the backscattered ultrasound signal to be measured (i.e., plotted and saved in an ASCII file). The “movie” below shows the beautiful structure of the scattered ultrasound wave. Note that only a few frames of the propagating wavefront are shown; Wave2000 of course allows the user to control the “relative frequency” of display on their own computer.
Pulse-echo configurations are just one of Wave2000’s many transducer options. Shown below is a plot of the receiver and source waveforms. The source waveform, appearing at the left side of the graph, is a sinusoid with a Gaussian envelope. The reflected wave, due to the presence of the crack, appears later in time (at about 8 microseconds).
Explore many “what if” scenarios with Wave2000. It is straightforward in Wave2000 to modify the simulation model to address a variety of questions. In the context of this simulation example, these may include: What happens to the reflected wave if the crack is made longer or shorter, thicker or thinner, is oriented obliquely or off-center with respect to the source, or contains some (non-void) material (e.g., water)? These and similar questions may be addressed with Wave2000 usually as easily as this one shown here. In general, “if you can draw it you can simulate it” with Wave2000.
Pipe cross-section and Wave2000's model definition windows.
This is an example designed to illustrate how Wave2000’s graphical user interface makes it easy to setup a simulation model.
Wave2000 can synthesize a variety of 2D objects. For example, one can create images with various geometries such as the “pipe with a crack” structure shown below. In addition, Wave2000 can import from many “paint type programs” so that there is basically no limit to the variety of complex structures which can be simulated with Wave2000. In this example, a Gaussian modulated 2.25 MHz waveform is transmitted into a brass pipe containing water, with a small crack (0.3 mm wide by 1 mm long) in the pipe located equidistant between the source (in green) and receiver (in blue).
Wave2000 can simulate practically any material. By using the Materials Properties window shown below, you can specify the elastic constants of a particular material used in a simulation. One also specifies the grey level of the material which is to be associated with a particular region or set of regions in the object image. The familiar acoustic (longitudinal and transverse) impedances, velocities and attenuations are displayed at the bottom right portion of the page, associated with each material.
Wave2000 comes with a Material Library containing about 50 predefined materials. One page from that Library is shown below. You can also add materials to the Library, or create your own library or set of libraries.
Wave2000 has an easy to use graphical user interface (GUI) for defining both sources and receivers, which the figures below respectively display. The commands, many of which are controlled by a single click of the mouse, can set up specific simulation conditions, as for example, with pulse-echo and/or through transmission definitions. Additionally, source waveforms can be chosen from a list of functions (including data from a user’s own experimental measurements). Moreover, receiver data can be saved as an ASCII text file, for subsequent processing and analysis.
Simulation of the cracked pipe, which was set up using Wave2000’s GUI in a matter of a few minutes, is shown below. This simulation can be useful for evaluating the effect of different size cracks (e.g., length and thickness) on the propagation of ultrasound down the pipe, from the transmitter to the receiver.
Data from simulations are plotted and saved to file. The longitudinal receiver measurements are displayed below. A similar plot (not shown) can be made for the shear measurements.
Focussed (phased) array source transducer and infinite boundary conditions.
n this example of a Wave2000 simulation, a demonstration is given of a focussed source array in a 20 mm wide x 24 mm high water bath. It also displays Wave2000’s “infinite boundary condition” feature.
Wave2000 has phased arrays, even allowing arbitrary phasing or delays. In this example, a focussed 2.4 cm long source array located on the left edge of the water bath (shown in the figure below as a thin blue line with a grey backing) with focal length 10 mm emits a 1MHz sine Gaussian longitudinal pulse. It is received by two “point” (i.e., very short) receivers (much like 2 hydrophones) both located 10 mm from the left side of the water bath. One receiver is located at the focus itself (in the center of the water bath) while the other receiver is located 3 mm (laterally) below the focus. The figure below also shows three (3) infinite boundary conditions (denoted by the green borders), located on the top, bottom and right side of the water bath, respectively.
Wave2000 has infinite boundary conditions. As may be seen below, the array generates a wavefront which focusses at the center of the water tank. Note also that the wave does not reflect from the edge of the water tank, but simply “disappears” as if it were propagating off into an “infinite” size water tank. This avoids the need to “window out” reflections from the tank boundaries when analyzing the data.
Receiver (hydrophone-like) measurements are easy to make. As may be seen, the displacement at the receiver located 3 mm below the focus (appearing as blue and labeled as “L – focus + 3mm”) is much less than that at the receiver located in the focal point of the source array (appearing as red and labeled as “L – focus”). Also shown is the source waveform (appearing as green and labeled as “L – Left Long. (Source)”).
Setting up the phased array parameters are simple in Wave2000. The figure below shows the Wave2000 Source Array Configuration page for setting up the array parameters. A similar page exists for defining a receiver array as well.
This example displays Wave2000’s ability to generate phased array behavior. The program allows the user to set a deflection angle and/or focal length, as well as to adjust element size and spacing. The program accounts for all aspects of the acoustic wave propagation problem, with no need for any simplifying assumptions. Wave2000 allows you to explore a whole host of configurations and determine the effects of an almost unlimited number of variables on the propagating ultrasound wave and on the receiver measurements.
Reflection, refraction and mode conversion studies.
This is an example designed to illustrate how Wave2000 simulates reflection and refraction of an ultrasonic wave impinging on a boundary at an oblique angle.
Here, a Gaussian modulated 1 MHz sine wave is generated by a 2 cm source transducer located on the left edge of the object. The material on the left side of the boundary (oriented at 30 degrees from the vertical) is polystyrene; the material on the right side of the boundary is steel. In Wave2000, only the boundaries between materials are shown during an ultrasound simulation, in order that the propagating wave can be visualized.
As may be seen, both longitudinal and shear waves are reflected and transmitted at the boundary between the two materials. The distinct angles of propagation for the two modes are apparent from the simulation. If desired, one or more receivers could be defined at arbitrary positions (even within the object) to quantitatively measure the reflected/refracted ultrasound signals. You can define both longitudinal and shear transducers in Wave2000 (i.e., a single transducer can operate as both a longitudinal and shear source and/or receiver simultaneously). In fact, any number of sources and receivers can be defined within the same simulation!
These examples display only a small portion of the full features of Wave2000. You can find out more by reading About Wave2000 or by downloading a full-featured evaluation copy by registering with us and logging in. Information on pricing is also available. Please Contact Us to discuss your intended application(s) or for any other additional information on Wave2000 you would like to have.
Ultrasound detecting a crack in an oil pipeline using computer simulation
Introduction
Around the world, there are millions of kilometers of high-pressure pipelines, many of which are used to transport oil. Generally, distribution of crude oil through pipelines is one of the most secure methods. However, defects may occur and grow in the pipeline until the pipeline ruptures, with obvious serious consequences. Therefore, it requires that special attention be made to non-destructive testing of the pipeline, and in particular to cracks that may be present, especially to stress corrosion cracking. Currently, there are pipeline assessment devices (called “pigs”) available that use ultrasonic technology to detect pipeline wall cracks. This equipment is transported inside the pipeline by the flowing crude oil, while at the same time ultrasound measurements are performed. This method can be used to assess up to hundreds of kilometers of pipeline in one run.
The figure below is a schematic view illustrating such a device; as may be seen, the tail (back of the “pig”) contains the sensors. Universal joint connections between all the units allow the whole unit to run along curves. The first pressure vessel (A) is equipped with batteries that ensures power for several days. A second pressure vessel (B) contains the electronic components as well as a recording mechanism to store the ultrasound data. Sensor carrier (C) contains a number of sensors (T), to ensure that the pipe wall is assessed in all directions (360 degrees).
Simulation Model
Ultrasound is often used in non-destructive testing, for example for crack detection in an oil pipeline. In this example, we will show you how to create a computer simulation model that demonstrates how ultrasound can detect a crack in pipeline. In the figure below, the upper part shows a sector of a pipeline, and a plane “A” intersecting the pipeline perpendicularly. The lower part shows the enlarged cross section; the circle represents the steel wall of the pipeline, with the inside filled with petroleum (in grey), and the outside surrounded by water. (Note that it is simple to replace water with another material, e.g., air.) The letter “T” indicates that there is an ultrasound transducer placed inside the pipe, which emits an ultrasound signal towards the wall and receives the reflected signal, i.e., the transducer is operating in pulse-echo mode. The rectangle marked as ROI is the region that will be simulated in this example.
The figure below is the simulation model, with the region simulated being the same as the ROI shown in the above figure. The program used for this example is Wave2000 Plus. In the 2D model, there are three layers of materials, the top layer is 1 mm of water, the middle layer is 6.34 mm of steel and the bottom layer is 5.66 mm of petroleum. The infinite boundary conditions (in green) are used to simulate the large region surrounding the ROI. The figure shows a 2 mm long vertical crack in the steel wall of the pipe; the crack is 0.008 mm thick and is assumed in the model to be filled with water (again it is easy to replace the water-filled crack with any material, including air). A source ultrasound transducer (9.54 mm in length) is placed in the petroleum at an angle of 16.5 degrees. It emits a “Sine Gaussian Pulse” with a center frequency of 5 MHz. A receiver is placed at the same location as the source. The source-receiver pair work together in pulse-echo mode. For comparison purposes, the same model as the one described above but without the crack is also simulated.
Results
Each Wave2000 Plus model requires about 10 minutes to simulate on a desktop computer (Intel CORE i7 970, 3.2 GHz 6-core CPU) the 15 microseconds that are displayed in the animated gif images below. The figure below shows the simulation result for the model with the crack:
The figure above shows clearly that there is a signal that has propagated to the crack and been reflected back to the receiver transducer. For comparison, the simulation result of a model without crack is shown in the following figure. As may be seen, no signal is reflected back from a crack.
To quantitatively measure the reflected signals, the following plot shows the time-domain signals received for the two simulation models, with and without the crack, respectively. (Note that the software allows the user to save the received waveforms in files for post-processing and analysis.)
The plots above show that model with a crack in the pipe has an associated “crack signal” that appears at about 13 us, and that no such signal exists for the simulation model without a crack. The signal strength and shape will be affected by the crack size, shape, position and orientation, all of which are easy to examine with appropriate modifications to the simulation models.
Wave2000 Plus models
The Wave2000 Plus model files for the two models can be downloaded from our Download page. If you want to run the simulations or create your own models, you can use Wave2000 Plus with a free evaluation license. For more information, please go to the Download page.
Important tips about these simulations, in case you want to try some of your own for pipe-crack detection:
(1) When you add a source in Source Configuration, check “Shear Mode” and use “None” as Time Function;
(2) Also in Source Configuration, after setting up all the parameters for “xmitter”, check “Pulse-Echo” and click on “Apply” and then “OK”. Then open Receiver Configuration, rename “xmitter Echo’ to another name, e.g., “xmitter_echo”, and change Data Type to “Pressure”, and click “Apply” and “OK”. The last step is to start Source Configuration again, un-check “Pulse Echo” and click on “Apply” and then “OK”.
Cladded Rod
The figure below shows a steel rod cladded with a plastic tube. The steel rod is 20 mm in diameter and the overall diameter is 40 mm, and the length is 30 mm. As with all Wave2500 simulations, the object is shown as a cross-section, since a single cross-section is sufficient to characterize the entire (axisymmetric) object. In Wave2500, the upper left corner of the object image is the r=0, z=0 point, while the bottom right is r=rmax and z=zmax, where rmax and zmax are the maximum values of the radius, r, and height, z, of the object, respectively. Thus the upper left corner of the 2D image is actually the center of the top face of the cylinder, while the bottom left corner is the center of the bottom face of the cylinder, and the entire left side is the central cylindrical axis. Note that the 2D image shown here is actually 1/2 of the entire cross-section of the cylinder. Think of the actual object being generated by revolving this cross section around the cylinder axis (i.e., rotating by 360 degrees the cross-section around its left edge).
A 3D viewer allows the user to visualize the actual object (see the figure below). Not shown but defined for this simulation are a 40 mm diameter circular source transducer centered on the top of the cladded rod, and a 40 mm diameter circular receiver transducer defined on the opposite face (at the bottom) of the cylinder, operating in through transmission mode. Thus both the source and receiver cover the entire top and bottom faces of the object, respectively.
Wave2500 generates “step-by-step” images of the propagating ultrasound wave. The ultrasound “movie” below displays a 1 MHz sine wave with a Gaussian envelope propagating down the cladded rod.
Wave2000 plots and/or saves all transducer source and/or receiver data. The figure below displays a receiver plot associated with this cladded rod simulation model. The graph shows the measurements associated with the through transmission receiver. As may be seen, the source waveform (in blue) is displayed at the very beginning of the plotted signal. The transmitted waveform measured by the receiver at the bottom of the cladded rod is shown in red and green, representing the longitudinal and shear signals at the receiver, respectively.
Defect in Rectangular Solid
The figures below show a rectangular block (a “cuboid”) of plastic of dimension 10 mm (X) x 10 mm (Y) x 20 mm (Z). In the center of the plastic block is a void defect in the shape of a “pancake”; the defect is 2 mm in diameter and 1 mm thick. The axis of the pancake is along the z-axis of the block. The block is shown in the second figure “cut-in-half” to display the defect. A source tansmitter is placed on the entire face at z=o, and emits a broadband 1 MHz signal with a Gaussian envelope. The final figure shows in 3D rendered format the propagating wave as it encounters the defect. Note that the wavefront is square which reflects the fact that the source is effectively square itself since it covers the entire (square) face at z=0.
Note that in the 3D rendered view of the propagating wave only the defect (and source transducer) are shown in order to be able to visualize the wave itself.
Ultrasound Propagation Through Bone
Shown below is a 3D-rendered image of a human finger bone using micro-computed tomography (micro-CT).
The figure below shows the 3D propagation of ultrasound through a short length of cortical bone taken from the midshaft of the finger bone above. The signal is a 1 MHz Gaussian shaped pulse, which propagates from right to left. The materials are bone and blood. As may be seen there is a great deal of scattering of the wavefront, but the initially arriving wavefront emerges at the other side in a somewhat coherent way. Note that receivers can be defined anywhere within or on the object, and the data stored to disk for subsequent processing and analysis.
Another example demonstrates propagation through trabecular bone taken from the human heel bone, shown below. This image data was also acquired using micro-CT. The core is approximately 1 cm in diameter and 1.2 cm in length. The propagation is carried out again with a 1 MHz broadband pulse, and the source is placed on the face at one end of the cylinder. Blood is assumed to fill all of the pore spaces and to surround the core as well.
An animated graphic of the propagating wave is shown in the figure below. (Note that the core has been rotated so that the left face is now on the left side.) As may be seen the wave appears to be scattered greatly by the trabeculae. The images of the propagating wave seem to be an “inverse” image of the bone (i.e., the pore spaces); this is likely due to the fact that the displacements are much larger in the pores (fluid) relative to the displacements in the bone material per se.
Annular Source and Receiver
This is an example designed to illustrate how easy it is to define and use annular sources and receivers in a Wave2500 simulation.
Here, a Gaussian modulated 1 MHz sine wave is generated by a 5 mm wide “ring” source transducer located on the top of a cylinder of water. The following figure displays a “movie” of the ultrasound wave as it propagates through the water. Note that a number of separate rings could be defined and each given a prescribed delay for focussing. Not shown are the measurements of an annular ring transducer located within the cylinder. Receiver “rings” could also be phased for focussing.
These examples display only a small portion of the full features of Wave2500. You can find out more by reading About Wave2500 or by downloading a full-featured evaluation copy by registering with us and logging in. Information on pricing is also available. Please Contact Us to discuss your intended application(s) or for any other additional information on Wave2500 you would like to have.
CyberLogic is a leader in biomedical and electrical engineering, specializing in state-of-the-art ultrasound technologies for bone health assessment and medical imaging.
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