Pogo Examples

Several NDT examples solved using the Pogo package.

A common test case in acoustics is scattering from an acoustic cylinder; this has quite a lot of complexity with refraction, reflection and diffraction all present, but can also be compared to an analytical solution. This is simulated in 2D below. Two models were created to demonstrate two approaches to the problem. The first model (left) utilises a mesh consisting of triangles which fully conform to the geometry of the cylinder. The second model (right) is the structured case in which a uniform mesh is used and the properties are locally adjusted to generate the cylinder shape. This will result in 'staircasing' around the cylinder boundary, which can produce strange results. The model is a square measuring 40 mm along the edge; a cylinder of radius 1 mm is located at the centre. The cylinder density and wave speed is double that of the surrounding region.

  • Simulation Details (Meshed Model)

  • Nodes: 741,918

  • Time steps: 4,500

  • Explicit time stepping stage: 1.61 sec

  • GPU: GeForce RTX 2080 Titan

  • Simulation Details (Structured Model)

  • Nodes: 641,601

  • Time steps: 1,800

  • Explicit time stepping stage: 0.65 sec

  • GPU: GeForce RTX 2080 Titan

Phased arrays are powerful tools for ultrasonic inspection, allowing arbitrary focusing in the domain. Here we demonstrate focusing with just such an array. The model measures 120 mm × 60 mm and 64 transducers are located along the top edge. The focal location is 15 mm from the back wall and 30 mm from the left-hand wall, shown in the animation below with a green plus (+).

  • Simulation Details

  • Nodes: 1,007,525

  • Time Steps: 26,833

  • Explicit time stepping stage: 6.77 sec

  • GPU: GeForce RTX 2080 Titan

A single-crystal transducer is considered here, fired down into the object and we look for reflections from both the notch and the backwall. The model measures 200 mm × 100 mm, with absorbing boundaries applied to the left, right and top walls. A 25 mm line transducer is located on the top wall, 20 mm to the right of the vertical centre line.

  • Simulation Details

  • Nodes: 1,202,938

  • Time steps: 8,227

  • Explicit time stepping stage: 3.71 sec

  • GPU: GeForce RTX 2080 Titan

History Plot

Full matrix capture (FMC) is an increasingly popular approach with phased arrays, where individual transducers are excited in turn and all transducers receive from all firings. This produces a 'matrix' of data, containing data from all the send-receive pairs, and is a very powerful technique because it allows the data to subsequently be used for imaging. Pogo can simulate an unlimited number of transducers, but here we limit the number for illustration purposes. The model measures 120 mm × 60 mm and eight transducers are located along the top edge. Each transducer signal and response is contained in an individual "shot".

  • Simulation Details

  • Nodes: 1,007,238

  • Time Steps: 26,833

  • Explicit time stepping stage: 56.06 sec

  • GPU: GeForce RTX 2080 Titan

Ultrasonic guided wave inspection of pipes is now used throughout the world, and is a powerful technique for screening long sections of pipes from a single location. Key to the success is the excitation of a single mode and proper understanding of the way that ultrasound scatters from any defects in the pipe, and FE has played a critical role in this. The model describes a 6 m long pipe with an outer diameter of 8 inches and a wall thickness of 10 mm. A Hann shaped defected is located at the axial midpoint and has a depth of 70% of the wall thickness. Absorbing boundaries measuring 0.5 m, are applied to each end of the pipe.

  • Simulation Details

  • Nodes: 461,184

  • Time steps: 10,092

  • Explicit time stepping stage: 8.77 sec

  • GPU: GeForce RTX 2080 Titan

History Plot of T(0,1)

History Plot of F(1,2)

Guided waves can also be used in plate-like structures. Here we consider a demonstration of guided waves scattering from a thinned region, which could correspond to a corrosion patch in an oil tank, for example. In this case, the S0 and SH0 modes are excited, and the centre frequency is 60 kHz. Model of a 3D plate measuring 1 m × 1 m × 10 mm. A Hann shaped defect with a radius 0.2 m and depth of 80% of the plate thickness is located at the centre of the model.

  • Simulation Details

  • Nodes: 13,823,051

  • Time steps: 8,074

  • Explicit time stepping stage: 61.13 sec

  • GPU: GeForce RTX 2080 Titan

Focused inspection of a 2D anisotropic weld using a phased array. The model measures 300 mm × 100 mm and utilises 32 transducers positioned along the top left edge. The theoretical focal location is shown in the animation below with a green plus (+). The true focal location differs from the theoretical location because of the different material properties of the grains within the weld region.

  • Simulation Details

  • Nodes: 1,560,653

  • Time steps: 5382

  • Explicit time stepping stage: 4.82 sec

  • GPU: GeForce RTX 2080 Titan

This model utilises a structured mesh approach to replicate the work done by Leckey, Wheeler, Hafiychuk et al. 2018 http://dx.doi.org/10.1016/j.ultras.2017.11.002 . Composites are difficult materials to simulate due to the range of scales present as well as variation of properties within and across layers. The chosen parameters are a trade-off between accuracy/stability of the code and the available computing power and runtime. Delamination of specimens is also of concern since this adds extra complexity to the model.

  • Simulation Details

  • Nodes: 1,125,000

  • Time steps: 25,000

  • Explicit time stepping stage: 32.07 sec

  • GPU: GeForce RTX 2080 Titan


Dr Peter Huthwaite

Imperial College London