Contactless Inductive Flow Tomography (CIFT)

Contactless inductive flow tomography (CIFT), developed at HZDR, is able to visualise the three-dimensional flow profile of fluids with high electrical conductivity. It employs the principle of the induction of electrical currents due to the movement of a conducting material through a magnetic field. Because of its contactless operating principle, it is well-suited for hot and chemically agressive melts, such as those encountered in continuous steel casting or semiconductor crystal growth.

Working principle for two-dimensional flows

The working principle of CIFT can be illustrated using a mainly two-dimensional flow profile inside a continuous steel casting mould. Figure 1 shows a sketch of a mould with a submerged entry nozzle with outlets facing sideways. From these outlets, the liquid metal flows into the mould. When a static magnetic field is applied in the vertical direction, an electric current is generated inside the melt because of its motion relative to the magnetic field. This electric current, in turn, generates a magnetic field that can be measured outside the mould. This magnetic field carries information about the flow structure in the melt. From the laws of Ohm and Biot-Savart, a linear model of this induction process can be derived. By inverting this model and applying appropriate regularization techniques, the flow in the mould can be reconstructed from the magnetic field measurements made outside the mould.

Application example: two-phase flow inside a model mould

Figure 2 displays a realization of this method in a model experiment, where the static magnetic field is generated by a rectangular coil around the mould. The superposition of the applied magnetic field and the flow induced magnetic field is measured with 7 sensors positioned along both narrow faces of the mould. In this setup a time resolution of 1 Hertz is achieved. The videos in Figure 3 show two different flow regimes in the mould that were provoked by two different amounts of gas which were injected into the submerged entry nozzle. In the video shown in Figure 3(right) an undesired change from the so-called double-roll flow to a single-roll flow can be observed.

Challenges for the measurement

The challenges of this measurement technique are the numerical solution of the linear inverse problem, as well as the measurement of the very small flow-induced magnetic fields. The strengths of the induced magnetic fields are typically two to five orders of magnitude smaller than the applied magnetic field. For example, an applied magnetic field of about 1 mT creates a flow-induced magnetic field of approximately 100 nT. By comparison, Earth's magnetic field is about 50,000 nT. Thus it appears that the smallest magnetic disturbances, arising e.g. from the switching of electric devices, arc-welding activities or solar activity, interfere with the measurement signal and must be filtered out. This can be achieved by excitation with an AC magnetic field of a constant frequency of order 1 Hz. Then, as occurs in lock-in amplifiers, only the signal with the precisely-defined excitation frequency is extracted and noise signals in other frequency ranges are filtered out.

Besides Fluxgate sensors, air-core coils are applied for robust magnetic field measurements. These have the advantage by comparison with Fluxgate probes that they have no intrinsic upper range limit. However, they require a large number of turns in order to detect the tiny flow-induced magnetic fields. Currently, induction coil sensors with a diameter of 29 mm and 340,000 turns are used. With the help of an analog-digital-converter with a dynamic range of 100 dB, the small flow-induced magnetic fields can be measured. Figure 4 shows a typical Fluxgate sensor and some different induction coils.

CIFT as an online process control tool

The developement of the fast reconstruction algorithm was a milestone for the CIFT method: The precalculation of the inverse matrizes for different Tikhonov regularisation parameters λ enabled solving the inverse problem on off-the-shelf GPUs in less than a second. This made possible the use of CIFT as an online process control tool.

Figure 5 depicts the scheme of a CIFT-based process control loop, which controls the strength of an electromagnetic brake (EMBr) in response to the reconstructed velocity field inside the mould. Strong hysteresis effects of the EMBr due to its ferromagnetic parts are compensated for by an advanced mathematical model (cf.  Glavinic et al., 2022).

This control loop was succesfully applied in a model laboratory experiment:

The common problem of nozzle clogging in steel casting is simulated by an artificial blockage of the right-hand outlet port of the submerged entry nozzle (cf. Fig. 6 middle and right), which diminishes the flow velocities and shifts the jet impingement point (marked by blue arrow) of the right-hand side of the mould. The CIFT-based control loop reliably detects the difference in height between the left- and right-hand impignement points and initiates a shut-down of the EMBr, mitigating the height difference.

Three-dimensional reconstruction

When a three-dimensional flow has to be reconstructed, it is not sufficient to apply only one single magnetic field. In this case, at least one additional magnetic field must be applied in a different direction. An approach with one horizontal and one vertical field yields good results. For a single reconstruction, first the horizontal magnetic field is applied and the resulting flow-induced magnetic field is measured. Then the vertical magnetic field is applied and the flow-induced magnetic field is measured again. From both measurements the three-dimensional flow can be reconstructed.

This could be demonstrated in the following experiment, shown in Figure 7. In an acrylic glass cylinder the flow of the liquid metal GaInSn is driven by a propeller in the centre of the container. The guiding blades at the top of the container allow for the creation of two different flow structures: When pumping upwards, the guiding blades dampen the rotation of the fluid and a dominating poloidal flow is created, whereas pumping downward creates a toroidal flow in addition to the poloidal flow. Figure 8 shows the reconstructed flow for an experiment where the fluid was first pumped downward and then upward.

Application example: liquid metal convection

Thermally driven movements in liquid metals occur inside stars and planets and are likewise present in technical applications, e.g., semiconductor crystal growth. A deep understanding of the non-linear dynamics of such hydrodynamic systems can be achieved with so-called Rayleigh-Bénard convection (RBC) model experiments. Liquid metal RBC experiments are substantially different from experiments with water with respect to fluid density and thermal conductivity, and the opaqueness of liquid metals places high demands on the measurement techniques used. CIFT, for the first time, has enabled a complete view of the global 3D flow field as a function of time even in large RBC geometries. Figure 9 depicts an experimental RBC set-up at HZDR. The central liquid metal-filled cylinder with a height of 640 mm and a diameter of 320 mm is surrounded by the CIFT excitation coils, 42 fluxgate probes (inset) and additional sensors. This enables the reconstruction ofthe global flow field in the whole cylinder as shown in Figure 10.

Literature

• Sieger, M.; Gudat, K.; Mitra, R.; Sonntag, S.; Stefani, F.; Eckert, S.; Wondrak, T.
  Two-Field Excitation for Contactless Inductive Flow Tomography
  Sensor 24(2024), 4458.
• Mitra, R.; Sieger, M.; Galindo, V.; Vogt, T.; Stefani, F.; Eckert, S.; Wondrak, T.
  Design of a Contactless Inductive Flow Tomography system for a large Rayleigh–Bénard convection cell with aspect ratio 𝛤 = 0.5
  Flow Measurements and Instrumentation 100(2024), 102709.
• Wondrak, T.; Sieger, M.; Mitra, R.; Schindler, F.; Stefani, F.; Vogt, T.; Eckert, S.
  Three-dimensional flow structures in turbulent Rayleigh-Bénard convection at low Prandtl number Pr = 0.03
  ournal of Fluid Mechanics 974(2023), A48
• Glavinic, I.; Galindo, V.; Stefani, F.; Eckert, S.; Wondrak, T.
  Contactless Inductive Flow Tomography for real-time control of electromagnetic actuators in metal casting
  Sensors 22(2022), 4155
• Glavinic, I.; Muttakin, I.; Abouelazayem, S.; Blishchik, A.; Stefani, F.; Eckert, S.; Soleimani, M.; Saidani, I.; Hlava, J.; Kenjereš, S.; Wondrak, T.
  Laboratory Investigation of Tomography-Controlled Continuous Steel Casting
  Sensors 22(2022), 2195
• Ratajczak, M.; Wondrak, T.; Stefani, F.
  A gradiometric version of contactless inductive flow tomography: theory and first applications
  Phil. Trans. R. Soc. A, vol. 374, nr. 2070, Juni 2016.
• Stefani, F.; Gundrum, T.; Gerbeth, G.
  Contactless inductive flow tomography
  Physical Review E, vol. 70, 2004.
• F. Stefani und G. Gerbeth
  A contactless method for velocity reconstruction in electrically conducting fluids
  Measurement Science & Technology, vol. 11, pp. 758–765, 2000.
• F. Stefani und G. Gerbeth
  On the uniqueness of velocity reconstruction in conducting fluids from measurements of induced electromagnetic fields
  Inverse Problems, vol. 16, pp. 1–9, 2000.

Patents

• F. Stefani u. a., „Verfahren und Anordnung zur kontaktlosen Bestimmung von räumlichen Geschwindigkeitsverteilungen in nicht-kugelförmigen elektrisch leitfähigen Flüssigkeiten“, DE 100 26 052 B4, 17. März 2005.
• F. Stefani u. a., „Verfahren und Anordnung zur kontaktlosen Bestimmung von Geschwindigkeitsverteilungen eines flüssigen Metalls in einer Stranggießkokille“, DE 10 2008 055 034 A1, 01. Juli 2010.