Magnetohydrodynamic Analyses of a Miniature, Dual-Stage Electromagnetic Pump for Lead and Sodium In-Pile Test Loops

Abstract

To support the development of Generation IV nuclear reactors, in-pile and out-of-pile test loops with miniature, submersible direct-current electromagnetic pumps (DC-EMPs) are used to investigate compatibility and corrosion issues of nuclear fuel and structure materials with flowing molten lead and alkali liquid metals. Owing to the absence of detailed experimental measurements and because of its simplicity and low computational cost, the equivalent circuit model (ECM) is widely used to predict the pump characteristics. The simplifying assumptions in the ECM contribute to overpredicting the pump characteristics by >10%. To gain insight into the pump operation and assess the effect of various assumptions in ECM, not possible even experimentally, this work performed three-dimensional (3-D), magnetohydrodynamic (MHD) analyses of a 66.8-mm-diameter, submersible, dual-stage DC-EMP, recently developed by the authors, for circulating molten Pb and liquid Na at up to 500°C. The solution of the coupled electromagnetism equations and the momentum and energy balance equations calculates the pump characteristics and provides 3-D images of the flow, electric current, and magnetic field strength distributions in the flow duct. The grid convergence index (GCI) criterion confirmed the adequacy of the employed numerical mesh refinement and the results conversion. Results demonstrate strong dependence of the magnetic field strength distribution in the flow duct on the value and the distribution of the electric current but negligible effects of the fluid temperature on joule heating and pump characteristics. The Lorentz force highest densities occur at the entrance of the two pumping stages, and approximately 10.0% of the total force occurs in the fringe regions upstream and downstream of pumping stages. The MHD pump characteristics are in general agreement with, but consistently lower than, the ECM predictions. For molten lead and liquid sodium, the difference between the calculated characteristics increases with increased flow rate and input current, up to 12% and 14%, respectively.

Keywords:

• Miniature
• dual-stage direct-current electromagnetic pump
• 3-D magnetohydrodynamic analyses
• heavy and alkali liquid metals
• equivalent circuit model

Acronyms

CFD:	=	computational fluid dynamics
DC-EMP:	=	direct-current electromagnetic pump
ECM:	=	equivalent circuit model
FEMM:	=	Finite Element Method Magnetics
GCI:	=	grid convergence index
MHD:	=	magnetohydrodynamic
N:	=	magnetic north pole
RANS:	=	Reynolds-averaged Navier-Stokes
S:	=	magnetic south pole
2-D:	=	two-dimensional
3-D:	=	three-dimensional

Nomenclature

$\vec{A}$ =	=	magnetic vector potential
$\mathit{a}$ =	=	flow duct width (m)
$\vec{B}$ =	=	magnetic flux density (T)
$\mathit{b}$ =	=	flow duct height (m)
$C_p$ =	=	fluid specific heat (J/kg∙K)
$\mathit{c}$ =	=	length of current electrode (m)
$\vec{E}$ =	=	electric field gradient (V/m)
$\mathit{e}$ =	=	absolute relative error
$\overrightarrow{F_l}$ =	=	Lorentz force (N)
$F_s$ =	=	safety factor
$\mathit{I}$ =	=	electric current (A)
$I_{\mathit{in}}$ =	=	electrode input current (A)
$\vec{J}$ =	=	electrical current density in flow duct (A/m2)
$\mathit{k}$ =	=	thermal conductivity (W/m∙K)
$\mathit{L}$ =	=	pump total length (m)
$l_{\mathit{ext}}$ =	=	extension length of pump duct (m)
$l_p$ =	=	length of pump duct (m)
$l_{\mathit{sep}}$ =	=	separation distance between two pumping stages (m)
$\vec{n}$ =	=	normal vector to the boundary surface
$\mathit{P}$ =	=	pumping pressure (Pa)
$\mathit{p}$ =	=	apparent order
$\mathit{Q}$ =	=	flow rate of working fluid (m3/h)
$\mathrm{R}{\mathrm{e}}_m$ =	=	magnetic Reynolds number
$\mathit{r}$ =	=	grid refinement factor
$\mathit{T}$ =	=	temperature (oC)
$\mathit{U}$ =	=	mean velocity of the working fluid (m/s)
$\vec{u}$ =	=	flow velocity (m/s)
$u_d$ =	=	developed velocity (m/s)
${\vec{u}}^{\mathit{T}}$ =	=	turbulence velocity (m/s)

Greek

${\delta }_{\mathit{ins}}$ =	=	electrical insulation thickness (m)
${\delta }_m$ =	=	magnet thickness (m)
${\delta }_w$ =	=	duct wall thickness (m)
${\epsilon }_o$ =	=	magnetic permittivity (F/m)
$\mathit{\eta }$ =	=	fluid dynamic viscosity (Pa∙s)
${\eta }_T$ =	=	fluid turbulence viscosity (Pa∙s)
$\mathit{\mu }$ =	=	fluid magnetic permeability (H/m)
$\mathit{\rho }$ =	=	fluid density (kg/m3)
${\rho }_e$ =	=	electric charge density (C/m3)
$\mathit{\sigma }$ =	=	electric conductivity (S/m)

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This is partially funded by Battelle Energy Alliance, LLC award number DE-AC07-051D14517 to The University of New Mexico (UNM) and by the UNM’s Institute for Space and Nuclear Power Studies. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the U.S. Department of Energy or Battelle Energy Alliance, LLC. We thank The University of New Mexico’s Center for Advanced Research Computing, supported in part by the National Science Foundation, for providing access to the high-performance computing capabilities used in this work. This research also made use of the resources of the High-Performance Computing Center at Idaho National Laboratory, which is supported by the Office of Nuclear Energy of the U.S. Department of Energy and the Nuclear Science User Facilities.