Numerical method for analysis of turbulent liquid metal magnetohydrodynamic flow

Abstract This paper describes a numerical method for analyzing turbulent liquid metal magnetohydrodynamic flow in a rectangular duct under a transverse magnetic field. The main features of the proposed method are as follows: (1) a new iterative solution procedure is implemented to satisfy the conservation law for the electric current density; (2) Buleev's turbulence model is employed to calculate the turbulent intensities and shear stresses. The iterative solution procedure is tested and its ability is illustrated through solution of an example problem that corresponds to Hartmann's theoretical work. In order to verify the applicability of the turbulence model, the present method is applied to an analysis of Reed and Lykoudis's experimental data. The obtained numerical results agree well with the experimental data except for some slight differences.

[1]  Yutaka Shimomura,et al.  Large eddy simulation of magnetohydrodynamic turbulent channel flows under a uniform magnetic field , 1991 .

[2]  Richard David Nathenson,et al.  High-Efficiency Flow Coupler: A New Approach to Pumping Sodium in Liquid-Metal Reactors , 1988 .

[3]  R. J. Holroyd,et al.  Liquid lithium as a coolant for Tokamak fusion reactors , 1984 .

[4]  S. T. Wu.  Unsteady MHD duct flow by the finite element method , 1973 .

[5]  M. Hirata,et al.  TURBULENT HEAT AND MOMENTUM TRANSFER FOR ELECTRICALLY CONDUCTING FLUID FLOWING IN TWO-DIMENSIONAL CHANNEL UNDER TRANSVERSE MAGNETIC FIELD , 1978 .

[6]  F. Harlow,et al.  THE MAC METHOD-A COMPUTING TECHNIQUE FOR SOLVING VISCOUS, INCOMPRESSIBLE, TRANSIENT FLUID-FLOW PROBLEMS INVOLVING FREE SURFACES , 1965 .

[7]  Y. Gel'fgat,et al.  TURBULENT HARTMANN FLOW. , 1969 .

[8]  L. Barleon,et al.  MHD flow in liquid-metal-cooled blankets , 1991 .

[9]  A. Sterl,et al.  Numerical simulation of liquid-metal MHD flows in rectangular ducts , 1990, Journal of Fluid Mechanics.

[10]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[11]  P. Lykoudis,et al.  MAGNETO-FLUID-MECHANIC CHANNEL FLOW. II. THEORY. , 1967 .

[12]  Claude B. Reed,et al.  The effect of a transverse magnetic field on shear turbulence , 1978, Journal of Fluid Mechanics.

[13]  M. Aritomi,et al.  Numerical analysis for laminar and turbulent liquid-metal flow in a transverse magnetic field , 1989 .

[14]  T. Kunugi,et al.  Analysis of Liquid Metal MHD Fluid Flow and Heat Transfer Using the KAT Code , 1991 .

[15]  Genki Yagawa,et al.  Finite element analysis of magnetohydrodynamics and its application to lithium blanket design of a fusion reactor , 1982 .