TEAM Benchmarks
Problem 27:
Eddy Current NDT and Deep Flaws
Problem Description
This problem expands on previous non-destructive evaluation/testing benchmarks by looking at flaws in the depth of
the sample, rather than on the surface that is being probed. The sample is a cylinder of aluminium with a hole down
the centre.
Table 1: Cylinder dimensions
Outer radius (mm)
Inner radius (mm)
Height (mm)
Conductivity (S/m)
25
5
20
22.7e6
Figure 1: Model outline used in the simulation. The three flaws are created in the model and switched on and off via appropriate
material properties.
Three shapes of flaw are simulated; these are located on the inner surface of the cylinder. The extent of the flaws is
modelled explicitly. All three flaws are physically present in each simulation – the “active” flaw is determined by setting
the material properties of the corresponding region to those of air. A fourth model is also used in which no flaw is
present. This method allows us to use the same mesh for each model and thereby exclude mesh-related numerical
inaccuracies.
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TEAM Benchmarks
Problem 27:
Eddy Current NDT and Deep Flaws
Table 2: Flaw dimensions
Flaw 1
Flaw 2
Flaw 3
p(mm)
2
2
2
h(mm)
1
2
4
l(mm)
4
2
1
w(mm)
0.3
0.3
0.3
The probe is a coil of wire and a pair of Hall Effect sensors. The coil is positioned co-axially with the sample. The
probes are located level with the base of the drive coil, at a distance of 5mm from the axis. One sensor is directly
above the flaw; the other is diametrically opposite.
Table 3: Coil dimensions
Outer radius (mm)
Inner radius (mm)
Height (mm)
Liftoff (mm)
Turns
Wire diameter (mm)
12.35
6.5
3.95
0.5
445
0.2
The current in the coil is switched off suddenly, and the sensors detect the magnetic flux density from the induced
eddy currents. The probes themselves are not explicitly modelled – we simply sample the field components at the
appropriate locations in the model.
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TEAM Benchmarks
Problem 27:
Eddy Current NDT and Deep Flaws
We use a Biot-Savart coil – this provides a drive to the model but does not form a part of the mesh. The coil is located
in a region which uses a reduced magnetic vector potential formulation. The background air region also uses reduced
potential; all other regions – sample, flaws, and the air region in the centre of the sample – use total magnetic vector
potential.
The model uses reflection symmetry in the plane passing through the centre of the flaw (and through both Hall Effect
sensors), with magnetic fields set to be tangential to this plane. This allows us to reduce the resource requirements for
model solution.
The problem definition is to observe the difference in horizontal flux at the two sensors following the turn-off of the coil
currents. For I in Amps and t in milliseconds, the specified waveform is:
‫ܫ‬ሺ‫ݐ‬ሻ = ൜
1.5,
0,
‫ < ݐ‬35
‫ ≥ ݐ‬35
The initial 35ms allows any transients induced by the turn-on of the coil to decay away. Measurements begin at
t=35ms.
Solution Method
We use the time-transient solver ELEKTRA/TR. The solution begins at time=0 with a DC current of 1.5A in the coil.
Modelling the first time-point as DC allows us to skip the initial 35ms, as we are only interested in the effects of the
current turn-off, not the turn-on. After this initial solution, the current is switched off. We use an adaptive time-step
method to accurately capture the effects of this sharp transient.
The problem definition states that the current is generated by a tension of the same shape as the desired current
waveform. We ignore this for this problem and use a fixed current drive instead. In doing so, we do not require the coil
to be a part of the finite element mesh: fields from the coil are calculated using the Biot-Savart integral within air
volumes. These regions use a reduced magnetic vector potential; all other regions use a total magnetic vector
potential.
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TEAM Benchmarks
Problem 27:
Eddy Current NDT and Deep Flaws
Results
Figure 2: Eddy current magnitude at t=5.0e-4s for each flaw simulation.
Flaw 1
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TEAM Benchmarks
Problem 27:
Eddy Current NDT and Deep Flaws
Flaw 2
Flaw 3
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