**INHALTE**

#### Research Training Group

**Lorentz Force Velocimetry and Lorentz Force Eddy Current Testing**

Research area A: liquid metals

### A-1: Large-scale structure formation in liquid metal convection

Title | Large-scale structure formation in liquid metal convection |

PhD Student | Till Zürner |

Associated PhD Student | Sebastian Moller Wiebke Rösing Wenjun Liu |

Projectleader | Prof. J. Schumacher Dr. C. Resagk Dr. S. Eckert (HZDR) |

**Abstract**

Local Lorentz force velocimetry (LLFV) is a non-contact electromagnetic measurement technique to determine velocity profiles in electrically conducting fluids like liquid metal melts. Using this method, we measure the force on a tiny permanent magnet that interacts with the moving melt. After having successfully tested this method in the closed test loop GALINKA under isothermal and forced convection conditions, in its third generation the project aims to extend the technique towards three new aspects: (i) flow in large-aspect-ratio closed cells, (ii) non-isothermal conditions, i.e. the effect of an externally applied temperature gradient, and (iii) the effect of an externally applied homogeneous magnetic field of high flux density. Key questions to be answered are: can LLFV be used (i) to sense flow structures driven by thermal gradients, (ii) to measure convective heat transfer coefficients, (iii) to measure in the presence of a strong magnetic background field? To address these points we plan to perform high-precision model experiments using the low-melting alloy GaInSn as a test melt.

### A-2: Traceable multi-component force and torque measurement

Title | Traceable multi-component force and torque measurement |

PhD Student | Rafael Marangoni |

Projectleader | Prof. T. Fröhlich Prof. E. Manske |

**Abstract**

Lorentz force velocimetry is a contactless method to measure flow-rate, based on the interaction of a permanent magnet with a conductive liquid metal flow. It is also suitable to resolve local flow velocity when the magnet is small compared to the dimensions of the flow. To investigate the interaction of liquid metal flows and small permanent magnets, multi-component force/torque measurement systems are required which are able to measure three components of force and three components of torque simultaneously. The range of forces and torques to be measured is in the mN and µNm range and requires the application of high-precision multi-component measurement systems which are commercially not available. Project A2 aims to investigate metrological properties of 6-component force/torque measurement systems based on new measurement principles, provide methods for their traceable calibration, evaluation of measurement uncertainty for them as well as of the Lorentz force velocimetry for liquid metal flow, and to develop new methods like temperature shielding or compensation to allow robust measurement systems close to high temperature liquid metal flows.

### A-3: Direct numerical simulation of a turbulent liquid metal duct flow

Title | Direct numerical simulation of a turbulent liquid metal duct flow |

PhD Student | Sebastian Prinz |

Projectleader | PD Dr. rer. nat. habil. T. Boeck Prof. J. Schumacher |

**Abstract**

Project A3 is concerned with wall-bounded liquid metal flows in a straight duct in the presence of a magnetic field generated by an external magnet system. By means of direct numerical simulation (DNS) with a research code, we want to study fundamental effects of the interaction between the turbulent flow and magnetic field that are relevant for Lorentz force velocimetry. The field is therefore non-uniform and has a significant magnitude only over a section of the duct. The project will use an existing finite-volume code for a magnetohydrodynamic duct flow in which the boundary conditions for the magnetic field at the walls and in the exterior are treated by a boundary integral method. The main challenge in this project is to obtain realistic values for the magnetic Prandtl number which is of the order of 10^{-6} in real applications. It is therefore planned to combine a DNS for the magnetic field with a large-eddy simulation for the turbulent velocity field. Furthermore it is planed to implement turbulent in- and outflow conditions for the duct geometry.

### A-4: Two-phase flow measurements in a liquid tin channel

Title | Two-phase flow measurements in a liquid tin channel |

PhD Student | Ze Lyu |

Associated PhD Student | Majd Ali Daniel Hernandez Jonas Kühndel Sebastian Angermeier |

Projectleader | apl. Prof. C. Karcher Dr. C. Resagk |

**Abstract**

Lorentz force velocimetry (LFV) is a well-known technique which is used to determine velocity profiles or mass flux rates in a channel filled with an opaque liquid metal. The first goal of project A1 is to apply these methods to regimes where the magnetic Reynolds number Rem becomes finite. The dynamic coupling between turbulent flow and magnetic field gives, on the one hand, rise to several nontrivial phenomena such as magnetic field expulsion or vortex shedding and, on the other hand, makes this task very difficult to solve numerically without small-scale parametrizations (project A3). A high value of Rem can be obtained in a liquid tin channel (Tintelo), where the flow can be accelerated significantly. Here we plan to measure the velocity of liquid tin at temperatures as high as 400°C in a vertical or in a horizontal test section, respectively. A pump which propels a fluid can accelerate it up to several m/s that is enough to have finite Rem. The second goal is to study the particle transport in such a liquid metal flows and to reveal how the loading with inertial particles affects the flow. We want to detect such effects with Lorentz force velocimetry. Alternative measurement techniques, such as ultrasound probing, will help to benchmark the obtained LFV results.

Research area B: electrolytes

### B-1: Flow instabilities at the interface between liquid metal and salt solution

Title | Flow instabilities at the interface between liquid metal and salt solution |

PhD Student | Andreas Wiederhold |

Projectleader | Dr. C. Resagk apl. Prof. C. Karcher |

**Abstract**

The research in project B-1 during the third RTG generation will focus on applying Lorentz force velocimetry (LFV) to very low conducting fluids, two-fluid systems with liquid metals and molten salts, and two-phase flows. We will apply high magnetic field LFV to a saltwater-air-bubbles flow in an electrolyte channel using superconducting magnets and weight compensation together with noise reduction and force compensation methods. Investigating hot liquid metal - salt melt systems with LFV will open new applications for energy storage facilities and liquid metal batteries. Here, it is especially important to detect impurities and to characterize interface instabilities. Finally, fundamental investigations for two-phase flow with low electrical conductivity shall identify particle dynamics, inertia, and flow profiles as well as aggregation and separation effects in salt melts and liquid metals

### B-2: High-resolution Lorentz force measurement at interface between liquid metal and salt solution

Title | High-resolution Lorentz force measurement at interface between liquid metal and salt solution |

PhD Student | Na Yan |

Projectleader | Prof. T. Fröhlich |

**Abstract**

Project B-2 aims to resolve measurements of micro forces in the horizontal direction in combination with high dead load. These forces, namely the Lorentz Force (LF), originating downstream to relative motion when the magnetic field of high power rear-earth permanent magnets, by total weight of about 1kg, are transversely exposed to weakly conducting electrolyte flow. In general, the character of measurements is limited by “zero point stability” problem that in contrast to dead load of magnets is strongly subject to environmental effects, mainly thermal expansion of supporting material and ground vibrations. The goal of Project B2 is to further improve the existing experimental set-up with commercial ultra-precision electromagnetic force compensation balances or direct LF compensation method together with the existing electrolyte flow channels and new channels developed by project B1 and to investigate the measurement uncertainty of the Lorentz force velocimetry for weakly conducting electrolyte flow together with project B1. Secondly to design and build a ultra-precision force measurement system operating at low temperatures (77 K) using high-temperature superconductor bulk magnets as permanent magnets together with project B3 and B1.

### B-3: Innovative magnet systems based on high-temperature superconductors

Title | Innovative magnet systems based on high-temperature superconductors |

PhD Student | Oleksii Vakaliuk |

Projectleader | Dr. B. Halbedel Prof. E. Rädlein |

**Abstract**

Project B-3 will focus on using high-temperature superconductors to enhance the magnet systems necessary for Lorentz force velocimetry of weakly conducting fluids. Special cooling systems are required for this purpose.

Our current research results will provide the base on which we will further develop, construct, and test a cooling system for high-temperature superconductor bulks that are optimized regarding mass and functions. Testing and evaluating such a magnet system will be done together with project B-1 using the available fluid flow measurement setup.

We will collaborate with project B-2 in our aim to embed the force measurement system into the cooling system design. The application possibilities of our newly developed cooling system will be tested theoretically through simulation and practically through use on channels containing salt melts and glass melts. This requires project B-3 to closely cooperate with the theoretical project B-4.

### B-4: Lorentz force anemometry: Numerical simulation including shielding and disturbance

Title | Lorentz force anemometry: Numerical simulation including shielding and disturbance |

PhD Student | Ninh Tran |

Projectleader | PD Dr.-Ing. habil. U. Lüdtke |

**Abstract**

Lorentz force anemometry is a well-known contactless method used to determine the flow of electrically conducting fluids by measuring the Lorentz force using magnet systems. It is necessary to numerically simulate Lorentz force anemometry in order to investigate the influence of shieldings (electrically conducting tubes, for instance) on how accurately and sensitively we can perform our measurements. Our special focus lies on the optimized magnet systems by Alferenok (project B-4, 1st doctoral generation) and Terzijska (project B-4, 2nd doctoral generation) or experimental arrangements investigated by Heinicke (project A-1, 1st doctoral generation) and Hernández (associated project, 2nd doctoral generation).

The numerical investigations of Lorentz force anemometry will be extended to include moveable disturbances such as bubbles in the fluid. Bubbles can be considered using a two-phase model including the “Volume of Fluid” (VoF) method. The material properties of the bubbles produce varying results: a) The electrically conductivity is zero (saltwater, air bubbles) or b) the electrically conductivity is high (saltwater, metal particles). Project B-4 closely cooperates with the experimental project B-3. Furthermore, project B-4 contributes conceptual formulations to the theoretical project B-5, which investigates optimization methods.

### B-5: Multi-objective optimization of heterogeneous functions

Title | Multi-objective otimization of heterogeneous functions |

PhD Student | Jana Thomann |

Associated PhD Student | Julia Niebling |

Projectleader | Prof. G. Eichfelder |

**Abstract**

In several projects of the Research Training Group optimization problems arise which have two or more conflicting objectives. Such problems are called multi-objective optimization problems. For instance, for the Lorentz force velocimetry it is important to find geometric arrangements of magnets such that the weight of the magnets is small while the measurable Lorentz force is large. These two objectives are competing and have to be optimized simultaneously. While the first is comparatively easy to evaluate, the values for the second objective can only be obtained by a time consuming (‘expensive’) numerical simulation run.

Therefore, the goal of project B-5 is to develop a general procedure for multi-objective optimization problems where one of the objective functions is simulation based/expensive. A special focus of the project will be on the heterogeneous character of the objective functions. The procedure will be implemented and numerically tested. The algorithm will also be applied to optimization problems which arise in other projects of the Research Training Group as for instance that of the project B-4 from 2013-2015. The PhD student will further use his or her knowledge in mathematical optimization to perform a deep theoretical investigation of the algorithm. It is the aim to show its convergence and its ability to solve the problems of interest with a pre-defined quality.

Research area C: solid bodies

### C-1: Design of a portable Lorentz force eddy current testing system

| Design of a portable Lorentz force eddy current testing system |

PhD Student | Jan-Marc Otterbach |

| Dr. H. Brauer |

**Abstract**

Lorentz Force Evaluation (LFE) is a new contactless, nondestructive evaluation method for conductive materials. The Lorentz force exerting on a permanent magnet moving relative to the electrically conductive material specimen is measured. In the presence of a defect, perturbations in the measured force signals occur. These perturbations allow the reconstruction of the defect geometry and location. The aim of the C-projects is the development of a portable Lorentz force eddy current testing system (PLET).

The aim of the project C-1 is the design of a portable Lorentz force eddy current testing system, including construction, testing and improvement. With PLET a system of permanent magnets (PM) is moving due to periodic excitations in the vicinity to a fixed nonmagnetic specimen, causing the induction of eddy currents in the body under test. The resulting forces and moments, acting on the PM, are perturbed in the presence of a defect and change the oscillation behavior of the controlled Lorentz force oscillator. The study includes the proof-of-concept of a rotating cylindrical dipolar magnet configuration is used, and should compare the concepts based on a highly constant velocity and a two-sensor difference system, respectively. The experimental study has to be realized in close collaboration with projects C-2 and C-3. Finally, a sensitivity analysis of the mechatronic system shall be performed.

### C-2: Modeling and simulation of a portable Lorentz force eddy current testing system

Title | Modeling and simulation of a portable Lorentz force eddy current testing system |

PhD Student | Reinhard Schmidt |

Associated PhD Student | Ahmad Warda |

Projectleader | Dr. H. Brauer Prof. K. Zimmermann Prof. H. Töpfer |

**Abstract**

Lorentz Force Evaluation (LFE) is a new contactless, nondestructive evaluation method for conductive materials. The Lorentz force exerting on a permanent magnet moving relative to the electrically conductive specimen is measured and evaluated. In the presence of a defect, perturbations in the measured force signals occur. These characteristic perturbations allow to reconstruct the geometry of the defect and its location. The aim of the C-projects is the development of a portable Lorentz force eddy current testing system.

In particular, the objective of project C-2 is to model a portable Lorentz force eddy current testing (PLET) system, including numerical simulations and optimization. The design process has to be performed in close collaboration with project (C-1). The perturbed eddy current fields caused by harmonically oscillating permanent magnets in the presence of defects have to be determined. The resulting forces and moments exerting on the permanent magnet are going to be derived and validated together with project C-1. The studies have to be realized in close consultation with project C-3 to provide numerical simulations for the reconstruction of defects. Finally, a sensitivity analysis of the electromagnetic system shall be performed to provide information about the characteristics and robustness of PLET systems.

### C-3: Identification of conductivity anomalies using a portable Lorentz force eddy current testing system

Title | Identification of conductivity anomalies using a portable Lorentz force eddy current testing system |

PhD Student | Eva-Maria Dölker |

Projectleader | Prof. J. Haueisen Dr. H. Brauer |

**Abstract**

Lorentz Force Evaluation (LFE) is a new contactless, nondestructive evaluation method for conductive materials. The Lorentz force exerting on a permanent magnet moving relative to the conductive material specimen is measured. If a defect is present in the specimen, perturbations in the measured force signals are observed. These perturbations allow for the reconstruction of the defect geometry. The aim of the C-projects is the development of a portable Lorentz force eddy current testing system. The aim of the project C-3 is the identification of conductivity anomalies using this portable Lorentz force eddy current testing system. Because the new system will produce qualitatively different data compared to our existing systems, novel reconstruction algorithms for LFE need to be developed. Emphasis is put on the development of frequency domain LFE and the combination of time and frequency domain source reconstruction. Realistic anomalies (e.g. shallow defects like cracks, flaws, welding seams, etc.) shall be considered and an uncertainty analysis shall be performed.