Real-Time Monitoring of Structural Displacements in Large-Scale Tokamaks due to Electromagnetic Forces

Conceptos Básicos

A combined electromagnetic-structural model order reduction approach enables real-time monitoring of mechanical stress and displacement in conductive structures of thermonuclear fusion devices due to electromagnetic loads.

Resumen

The paper presents a model order reduction (MOR) approach for the real-time estimation of structural deformations in large-scale conductive structures, such as the vacuum vessel (VV) of thermonuclear fusion devices, due to electromagnetic (EM) forces.

The key highlights are:

1. The EM problem is solved using either the Finite Element Method (FEM) or the Volume Integral Equation (VIE) method, with the latter accelerated by hierarchical matrices (H-matrices) to efficiently handle the fully populated matrices.

2. The structural problem is solved using the FEM, with the EM loads serving as the forcing term.

3. Proper Orthogonal Decomposition (POD) is employed to develop Reduced Order Models (ROMs) for both the EM and structural problems, minimizing the computational expense associated with coupling the two physics.

4. The time-dependent analysis is resolved efficiently by solving the linear DAE system representing the EM-ROM, and then computing the forcing term for the Structural-ROM.

5. Numerical results demonstrate the accuracy of the approach and its compatibility with real-time execution, even for realistic 3D VV models of thermonuclear fusion devices like ITER, in contrast to the prohibitive computational cost of the full-order models.

The proposed methodology enables the construction of a Digital Twin of the machine, serving as a virtual sensor for real-time monitoring of critical structural displacements, which is essential for the safe operation of current and future thermonuclear fusion devices.

Estadísticas

The trend of the total force over the VV during the vertical displacement event (VDE) evaluated with the 2D axisymmetric model in COMSOL, the full-order model (FOM), and the reduced-order model (ROM) shows excellent agreement.
The magnitude of the displacement field at t = 0.63 s evaluated with the ROM for the ITER-like VV is reported, with the displacement graphically amplified by a factor of 600.

Citas

"The numerical results illustrate the outstanding performance of the MOR procedure in accelerating the transient analysis of VDE, making it compatible with real-time simulation of the VDE phenomenon and allowing 'faster than real-time' highly accurate predictions suitable for incorporation in control algorithms."

Ideas clave extraídas de

Reduced Order Modeling for Real-Time Monitoring of Structural Displacements due to Electromagnetic Forces in Large Scale Tokamaks

by Francesco Lu... a las arxiv.org 05-03-2024

https://arxiv.org/pdf/2405.01406.pdf

Consultas más profundas

How can the proposed approach be extended to include other types of loads, such as thermal and seismic, acting on the vacuum vessel structure?

Incorporating other types of loads, such as thermal and seismic, into the real-time monitoring system for the vacuum vessel structure can be achieved by expanding the multiphysics framework used in the current approach.

Thermal Loads:

Thermal loads can be included by integrating thermal analysis models into the existing electromagnetic-structural coupling framework. This would involve considering the heat distribution within the vacuum vessel and its impact on structural deformation.
The thermal analysis can be coupled with the electromagnetic and structural models to account for the thermal expansion and contraction effects on the vessel structure.

Seismic Loads:

Seismic loads can be incorporated by introducing a seismic analysis module that considers the dynamic response of the vacuum vessel to seismic events.
The seismic analysis would involve evaluating the structural response of the vessel to ground motion and seismic forces, which can lead to additional deformations and stresses.

Multiphysics Integration:

The thermal, electromagnetic, and seismic models can be integrated into a comprehensive multiphysics framework to capture the combined effect of all loads on the vacuum vessel structure.
The real-time monitoring system can then provide a holistic view of the structural behavior under various loading conditions, enabling proactive maintenance and operational decisions.

How can the proposed approach be extended to include other types of loads, such as thermal and seismic, acting on the vacuum vessel structure?

Incorporating other types of loads, such as thermal and seismic, into the real-time monitoring system for the vacuum vessel structure can be achieved by expanding the multiphysics framework used in the current approach.

Thermal Loads:

Thermal loads can be included by integrating thermal analysis models into the existing electromagnetic-structural coupling framework. This would involve considering the heat distribution within the vacuum vessel and its impact on structural deformation.
The thermal analysis can be coupled with the electromagnetic and structural models to account for the thermal expansion and contraction effects on the vessel structure.

Seismic Loads:

Seismic loads can be incorporated by introducing a seismic analysis module that considers the dynamic response of the vacuum vessel to seismic events.
The seismic analysis would involve evaluating the structural response of the vessel to ground motion and seismic forces, which can lead to additional deformations and stresses.

Multiphysics Integration:

The thermal, electromagnetic, and seismic models can be integrated into a comprehensive multiphysics framework to capture the combined effect of all loads on the vacuum vessel structure.
The real-time monitoring system can then provide a holistic view of the structural behavior under various loading conditions, enabling proactive maintenance and operational decisions.

How can the proposed approach be extended to include other types of loads, such as thermal and seismic, acting on the vacuum vessel structure?

Incorporating other types of loads, such as thermal and seismic, into the real-time monitoring system for the vacuum vessel structure can be achieved by expanding the multiphysics framework used in the current approach.

Thermal Loads:

Thermal loads can be included by integrating thermal analysis models into the existing electromagnetic-structural coupling framework. This would involve considering the heat distribution within the vacuum vessel and its impact on structural deformation.
The thermal analysis can be coupled with the electromagnetic and structural models to account for the thermal expansion and contraction effects on the vessel structure.

Seismic Loads:

Seismic loads can be incorporated by introducing a seismic analysis module that considers the dynamic response of the vacuum vessel to seismic events.
The seismic analysis would involve evaluating the structural response of the vessel to ground motion and seismic forces, which can lead to additional deformations and stresses.

Multiphysics Integration:

The thermal, electromagnetic, and seismic models can be integrated into a comprehensive multiphysics framework to capture the combined effect of all loads on the vacuum vessel structure.
The real-time monitoring system can then provide a holistic view of the structural behavior under various loading conditions, enabling proactive maintenance and operational decisions.

How can the proposed approach be extended to include other types of loads, such as thermal and seismic, acting on the vacuum vessel structure?

Incorporating other types of loads, such as thermal and seismic, into the real-time monitoring system for the vacuum vessel structure can be achieved by expanding the multiphysics framework used in the current approach.

Thermal Loads:

Thermal loads can be included by integrating thermal analysis models into the existing electromagnetic-structural coupling framework. This would involve considering the heat distribution within the vacuum vessel and its impact on structural deformation.
The thermal analysis can be coupled with the electromagnetic and structural models to account for the thermal expansion and contraction effects on the vessel structure.

Seismic Loads:

Seismic loads can be incorporated by introducing a seismic analysis module that considers the dynamic response of the vacuum vessel to seismic events.
The seismic analysis would involve evaluating the structural response of the vessel to ground motion and seismic forces, which can lead to additional deformations and stresses.

Multiphysics Integration:

The thermal, electromagnetic, and seismic models can be integrated into a comprehensive multiphysics framework to capture the combined effect of all loads on the vacuum vessel structure.
The real-time monitoring system can then provide a holistic view of the structural behavior under various loading conditions, enabling proactive maintenance and operational decisions.

How can the proposed approach be extended to include other types of loads, such as thermal and seismic, acting on the vacuum vessel structure?

Incorporating other types of loads, such as thermal and seismic, into the real-time monitoring system for the vacuum vessel structure can be achieved by expanding the multiphysics framework used in the current approach.

Thermal Loads:

Thermal loads can be included by integrating thermal analysis models into the existing electromagnetic-structural coupling framework. This would involve considering the heat distribution within the vacuum vessel and its impact on structural deformation.
The thermal analysis can be coupled with the electromagnetic and structural models to account for the thermal expansion and contraction effects on the vessel structure.

Seismic Loads:

Seismic loads can be incorporated by introducing a seismic analysis module that considers the dynamic response of the vacuum vessel to seismic events.
The seismic analysis would involve evaluating the structural response of the vessel to ground motion and seismic forces, which can lead to additional deformations and stresses.

Multiphysics Integration:

The thermal, electromagnetic, and seismic models can be integrated into a comprehensive multiphysics framework to capture the combined effect of all loads on the vacuum vessel structure.
The real-time monitoring system can then provide a holistic view of the structural behavior under various loading conditions, enabling proactive maintenance and operational decisions.

How can the proposed approach be extended to include other types of loads, such as thermal and seismic, acting on the vacuum vessel structure?

Incorporating other types of loads, such as thermal and seismic, into the real-time monitoring system for the vacuum vessel structure can be achieved by expanding the multiphysics framework used in the current approach.

Thermal Loads:

Thermal loads can be included by integrating thermal analysis models into the existing electromagnetic-structural coupling framework. This would involve considering the heat distribution within the vacuum vessel and its impact on structural deformation.
The thermal analysis can be coupled with the electromagnetic and structural models to account for the thermal expansion and contraction effects on the vessel structure.

Seismic Loads:

Seismic loads can be incorporated by introducing a seismic analysis module that considers the dynamic response of the vacuum vessel to seismic events.
The seismic analysis would involve evaluating the structural response of the vessel to ground motion and seismic forces, which can lead to additional deformations and stresses.

Multiphysics Integration:

The thermal, electromagnetic, and seismic models can be integrated into a comprehensive multiphysics framework to capture the combined effect of all loads on the vacuum vessel structure.
The real-time monitoring system can then provide a holistic view of the structural behavior under various loading conditions, enabling proactive maintenance and operational decisions.

How can the proposed approach be extended to include other types of loads, such as thermal and seismic, acting on the vacuum vessel structure?

Incorporating other types of loads, such as thermal and seismic, into the real-time monitoring system for the vacuum vessel structure can be achieved by expanding the multiphysics framework used in the current approach.

Thermal Loads:

Thermal loads can be included by integrating thermal analysis models into the existing electromagnetic-structural coupling framework. This would involve considering the heat distribution within the vacuum vessel and its impact on structural deformation.
The thermal analysis can be coupled with the electromagnetic and structural models to account for the thermal expansion and contraction effects on the vessel structure.

Seismic Loads:

Seismic loads can be incorporated by introducing a seismic analysis module that considers the dynamic response of the vacuum vessel to seismic events.
The seismic analysis would involve evaluating the structural response of the vessel to ground motion and seismic forces, which can lead to additional deformations and stresses.

Multiphysics Integration:

The thermal, electromagnetic, and seismic models can be integrated into a comprehensive multiphysics framework to capture the combined effect of all loads on the vacuum vessel structure.
The real-time monitoring system can then provide a holistic view of the structural behavior under various loading conditions, enabling proactive maintenance and operational decisions.

How can the proposed approach be extended to include other types of loads, such as thermal and seismic, acting on the vacuum vessel structure?

Incorporating other types of loads, such as thermal and seismic, into the real-time monitoring system for the vacuum vessel structure can be achieved by expanding the multiphysics framework used in the current approach.

Thermal Loads:

Thermal loads can be included by integrating thermal analysis models into the existing electromagnetic-structural coupling framework. This would involve considering the heat distribution within the vacuum vessel and its impact on structural deformation.
The thermal analysis can be coupled with the electromagnetic and structural models to account for the thermal expansion and contraction effects on the vessel structure.

Seismic Loads:

Seismic loads can be incorporated by introducing a seismic analysis module that considers the dynamic response of the vacuum vessel to seismic events.
The seismic analysis would involve evaluating the structural response of the vessel to ground motion and seismic forces, which can lead to additional deformations and stresses.

Multiphysics Integration:

The thermal, electromagnetic, and seismic models can be integrated into a comprehensive multiphysics framework to capture the combined effect of all loads on the vacuum vessel structure.
The real-time monitoring system can then provide a holistic view of the structural behavior under various loading conditions, enabling proactive maintenance and operational decisions.