Three-dimensional decaying magnetic field belonging to Beltrami flow

TL;DR

This paper investigates the decay of three-dimensional magnetic fields in Beltrami flows, using a Taylor vortex model to verify electromagnetic fluid flow calculations and analyze magnetic field characteristics under various conditions.

Contribution

The study introduces a benchmark test for electromagnetic fluid flow calculations using a 3D Taylor vortex with magnetic fields and analyzes magnetic field behavior and decay.

Findings

Magnetic pressure forms mesh patterns and distorted cubic structures.

Magnetic energy decreases with flow decay and turbulence transition.

Flow approaches stationary state after vortex decay.

Abstract

This study analysed a three-dimensional Taylor decaying vortex under an applied magnetic field as a benchmark test problem to verify the calculation method of an electromagnetic fluid flow and investigated the validity of the decaying magnetic field model. First, we observed the flow structure of a three-dimensional Taylor decaying vortex without an applied magnetic field. We investigated the changes in the error between the calculation result and the exact solution when the number of grid points and the Reynolds number varied and showed the effectiveness of the benchmark test. Next, we analysed a three-dimensional Taylor decaying vortex under an applied magnetic field and clarified the characteristics of the decaying magnetic field. When a magnetic field is applied, low magnetic pressure regions are connected in a mesh pattern, and the magnetic pressure distribution with a distorted cubic structure occurs to surround a high magnetic pressure region. In a stagnation region, the magnetic energy becomes low, and the magnetic flux line is similar to the streamline of the velocity field. High current densities occur in a grid pattern, and the magnetic flux lines swirl around the high current density region. The magnetic pressure and magnetic energy are high in the high current density region. When the Reynolds number and the magnetic Reynolds number vary, the decay trends of various energies agree well with the exact solution. The transition to turbulent flow occurs at a high Reynolds number, and the kinetic and total energies decrease rapidly. After the dissipation rate of kinetic energy becomes maximum, the vortex structure decays, and the flow field approaches a stationary state without magnetic fields. The three-dimensional Taylor decaying magnetic field belonging to the Beltrami flow is a valuable model for verifying the calculation method of electromagnetic fluid flows.