Optimal Design for a Portable NMR-and MRI-Based Multiphase Flow Meter

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In this paper, an optimal design for nuclear magnetic resonance and magnetic resonance imaging based multiphase flow meter is presented. The overall apparatus consists of an electromagnetic coil surrounded by 12 rings of Halbach arrays of 12 magnets each. Both the coil and the magnets arrays were simultaneously and optimally designed using a three-dimensional (3-D) finite-element method (FEM) package and particle swarm optimization algorithm. The aim of the design is to uniformly prepolarize the hydrogen spins of the atoms composing the flowing fluid, with a predefined static magnetic field, before they enter into the measurement area within which they are homogenously polarized with a perpendicular ac magnetic field. Cheap and lightweight hardware are the other two design parameters of the design. Results of extensive 3-D simulations of the design indicate that an optimized and homogenous static magnetic field distribution could be achieved within an area of 40 mm diameter and 606 mm length. In addition, using a multiturn coil of 6 cm diameter and 2000 turns, an ac magnetic field of 13 mT amplitude and 112 ppm homogeneity could be achieved, which is enough to handle fluids flowing at speed of up to 2 m/s. Experimental validation, which was done using newly constructed two Halbach arrays of cuboid and trapezoid magnet elements, respectively, indicates a good match with FEM simulations.

Original languageBritish English
Article number8488665
Pages (from-to)6354-6361
Number of pages8
JournalIEEE Transactions on Industrial Electronics
Issue number8
StatePublished - Aug 2019


  • Halbach array
  • magnetic resonance imaging (MRI) particle swarm optimization (PSO)
  • nuclear magnetic resonance (NMR)


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