Liquid Metal MHD Flow Research Articles

Large eddy simulation of magnetohydrodynamic turbulent flow in an electrically conducting circular pipe with V-shaped strips

Pressure drops and velocity distributions of liquid metal MHD flow in pipes are closely related to the geometry of the cross-section. Liquid metal flows in two types of electrically conducting circular pipes under a uniform magnetic field applied transversely to the flow are investigated numerically using large eddy simulation with a coherent structure model developed in the OpenFOAM environment. One pipe has a typical circular cross-section (N-pipe), whereas the other has four V-shaped strips at the wall parallel and perpendicular to the magnetic field (F-pipe). The increasing transverse magnetic field causes a turbulent MHD flow evolves into a single-sided turbulent flow and a laminar flow in the N-pipe. The V-shaped strips on the Hartmann wall generate a low-velocity belt along the magnetic field direction in the center of the pipe and weak high-velocity jets near the V-shaped strips. Furthermore, the inflection points in the velocity profile improve instability and turbulence. The root mean square of the velocity fluctuation, in particular, the transverse components increase with the Hartmann number increasing along the magnetic field direction in the F-pipe. The V-shaped strips delay the MHD turbulent-laminar transition. However, the skin friction coefficient is slightly higher in the F-pipe than in the N-pipe, with the same dimensionless parameters. The research results can be applied to the turbulence promoter in the MHD pipe flow. Key words: Magnetohydrodynamic turbulent flow, large eddy simulation, pipe, V-shaped strips. Tables 5, Figs 9, Refs 23.

Mixed convection studies of liquid metal MHD flow in a horizontal square duct subjected to a strong uniform magnetic field

Mixed convection studies of liquid metal MHD flow in a horizontal square duct subjected to a strong uniform magnetic field

Liquid metal MHD flow and heat transfer in a rectangular duct with perfectly conducting walls perpendicular to the applied magnetic field

Several technological applications involve the flow of liquid metals in ducts under a magnetic field, for instance, the coolants of fusion reactors. In this paper, using a magnetohydrodynamic MHD formulation based on the electric potential, we obtain an analytical solution for the flow of a liquid metal in a rectangular duct with two insulating walls and two perfectly conducting walls perpendicular to the applied uniform magnetic field. As the Hartmann number increases, the flow displays high velocities in the boundary layers attached to the insulating walls and a quasi-stagnant flow at the core. The effect of this flow pattern on the forced convection heat transfer is then explored numerically considering a uniform heat flux on either the conducting or insulating walls. Compared to the hydrodynamic case, the MHD flow enhances the heat transfer as the Hartmann number increases only in the case when the heat flux is applied at the insulating walls where high velocities are present. The increase of the local Nusselt number as the Péclet number grows indicates an efficient heat removal from the heated wall.

3D modelling of MHD mixed convection flow in a vertical duct with transverse magnetic field and volumetric or surface heating

Understanding phenomena associated with the multiple effects/interactions of the fusion nuclear environment on liquid metal flow is required to correctly design liquid metal (LM) blankets for fusion facilities. These effects are investigated in the present work by numerically simulating 3D LM MHD flow. The simulated geometry consists of a straight, vertical duct which runs perpendicular to a strong, fringing applied magnetic field. There is also a region of applied heating as the primary goal is to explore buoyancy effects in MHD duct flows. Results are presented for both buoyancy assisted (upwards) and buoyancy opposed (downwards) flows in conducting and insulating ducts for a range of Hartmann numbers (Ha) up to 100, Reynolds numbers (Re) from 103 to 104 and Grashof (Gr) numbers from 107 to 108. While increasing Gr or decreasing Re increases buoyancy effects, increasing Ha was shown to increase maximum temperature through turbulence reduction. The extent to which the MHD mixed convection flows are quasi-2D is analyzed and buoyant effects, in competition with electromagnetic forces, are shown to bring about 3D flow features not seen in purely MHD flows. Volumetric nuclear heating with steep gradients is applied to the vertical MHD flows for comparison to flows with surface heating only. Surface heating generates stronger buoyancy effects than volumetric heating of the same total power; however, many of the same phenomena occur. Therefore, surface heating, the only option for lab experiments, can provide indication of the effects of volumetric heating in MHD flows.

Effect of the length of the poloidal ducts on flow balancing in a liquid metal blanket

To address concerns associated with liquid metal (LM) flow balancing among multiple poloidal channels of a LM blanket, we investigate the factors (first of all the length of the channels) that influence the flow distribution when the duct walls are electrically insulated. We simulate LM MHD flow through multiple channels fed by a prototypical manifold for a range of channel lengths using a 3D MHD solver, HIMAG. The simplified manifold geometry consists of a rectangular, electrically insulated feeding duct which suddenly expands such that the duct thickness in the magnetic field direction abruptly increases by a factor of 4. After a short length downstream of the expansion, the flow is divided into three identical parallel channels. By measuring the flow rate in each of the channels, we conclude that flow balance among the channels is improved by increasing the length of the channels. An effort is made to obtain scaling laws that characterize flow balancing as a function of the flow parameters and the manifold geometry using a Resistor Network Model (RNM). Associated Hartman and Reynolds numbers in the computations were ∼103 and 102 respectively. Compared to the full 3D analysis, the proposed RNM suggests a relatively quick and simpler way of computing the blanket length that might be needed to provide balanced flow among the parallel channels.

Temperature fluctuations in a liquid metal MHD-flow in a horizontal inhomogeneously heated tube

The investigation of heat transfer characteristics during liquid metal flow in a horizontal tube with one-sided heating of the lower half of the tube is carried out. Experimental investigations are conducted using the mercury MHD complex of the Moscow Power Engineering Institute and the Joint Institute for High Temperatures, Russian Academy of Science, in the context of a long-term collaboration program. The characteristics of the averaged and fluctuation temperatures are considered in different sections over the length of the heating zone in the area of a homogeneous transverse magnetic field. The laminar liquid metal flow revealed the occurrence and development of a low-frequency quasi-harmonic temperature fluctuation with great intensity.

Numerical Study of Liquid Metal MHD Flow through a Square Duct under the Action of Strong Transverse Magnetic Field

umerical solution for steady MHD flow of liquid metal through a square duct under the action of strong transverse magnetic field has been investigated. The walls of the duct are considered to be electrically insulated as well as isothermal. The numerical solutions for velocity and temperature distributions have been obtained by finite difference method. The solutions for different values of Hartmann number and Prandtl number has been analyzed and are presented graphically. The MHD effect on velocity field and temperature field has been predicted in this investigation. Keywordsflow, liquid metal flow, electrically insulated wall, square duct.

Influence of blanket structural materials on liquid metal Pb–17Li flow in the FDS

The Dual-cooled Waste Transmutation Blanket design of the Fusion-Driven Sub-critical System is a dual-cooled liquid metal Pb–17Li and He system with Chinese Low Activation Martensitic steel structure. The effects of the structural material on liquid metal MHD flow, including pressure drop and heat transfer, are presented. The influences of the wall conductance of the duct wall on the MHD pressure drop have been analysed and estimated. The pressure drop is too large to be accepted when Pb–17Li coolant flows in these ducts without insulating coating. This can be improved by using Al 2O 3 electrically insulating coating, while heat transfer must also be cautiously considered.

Analysis on MHD Stability of Free Surface Jet flow in a Gradient Magnetic Fields

The simplified modeling for analysis on MHD stability of free surface jet flow in a gradient magnetic fields is based on the theoretical and experimental results on channel liquid metal MHD flow, especially, the results of MHD flow velocity distribution in cross-section of channels (rectangular duct and circular pipe), and the expected results from the modeling are well agreed with the recent experimental data obtained. It is the first modeling which can efficiently explain the experimental results of liquid-metal free surface jet flow.

Experimental and Computational Simulation of Free Jet Characteristics Under Transverse Field Gradients

ABSTRACTIn this paper, we present numerical and experimental studies of the behavior of a liquid metal jet in a constant and gradient magnetic field. The experiments were conducted in the Magnetic Torus Liquid Metal MHD flow test facility (MTOR). The experimental results have shown that free jets can be stabilized by the magnetic field. The Lorentz force significantly suppresses the motion of the liquid metal jet and delays the break-up position. Analysis based on linear theory has been applied to understand jet behavior under magnetic fields. In addition, numerical simulation based on B formulation has been performed and compared to the experimental results.

Three-Dimensional Simulation of MHD Flow with Turbulence. Reduction of Turbulence to Two-Dimensional One in Downstream.

A uniform transverse magnetic field is imposed on liquid metal MHD flows. Spatial development of Karman vortex between two insulator walls is numerically simulated. When a strong magnetic field is imposed, MHD diffusion reduces the vortices including three-dimensional component to quasi-two-dimensional ones in downstream. The condition for development of two-dimensional turbulence is discussed.

Three-Dimensional Simulation of MHD Flow with Turbulence. Reduction of Turbulence to Two-Dimensional one in Downstream.

A uniform transverse magnetic field is imposed on liquid metal MHD flows. Spatial development of Karman vortex between two insulator walls is numerically simulated. When a strong magnetic field is imposed, MHD diffusion reduces the vortices including three-dimensional component to quasi-two-dimensional ones in downstream. The condition for development of two-dimensional turbulence is discussed.

Time-varying MHD flows with free surfaces

The numerical requirements for liquid metal MHD flows with free surfaces are considerable. A stable, time-accurate Navier–Stokes solver is needed, with the ability to handle free surfaces in the presence of strong internal circulations. In addition, the solver must avoid numerical instabilities associated with the free surface motion. Another requirement is the flexibility to calculate the two-way coupling between liquid flow and evolution of the electromagnetic field. Furthermore, in some circumstances it is necessary to calculate the evolving field both inside and outside the liquid domain. Finally, there is the issue of turbulence modelling, complicated by the anisotrophic character of the turbulent energy induced by the magnetic field. To do this with any efficiency requires substantial segregation of the variables in the algorithm. This paper describes an approach using operator splitting and conjugate gradient methods, and developed with the partial differential equations solving program Fastflo. The paper emphasizes the computational electromagnetic aspects associated with the motion of the free surface.

Liquid-metal MHD flow in rectangular ducts with thin conducting or insulating walls: laminar and turbulent solutions

This paper treats the steady, fully-developed flow of a liquid metal in a rectangular duct of constant cross-section with a uniform, transverse magnetic field. Thin conducting wall boundary conditions at the top/bottom walls (perpendicular to the magnetic field) are extended to allow electrical currents to return through either the wall or the Hartmann layers. Hence, a unified analysis of flows in ducts with wall conductance ratios in the range of interest of fusion blanket applications, namely, from thin conducting to insulating wall ducts, is conducted. The flow in laminar and turbulent regimes is investigated through a composite core-side-layer spectral collocation solution which explicitly resolves the flow in the side layers (parallel to the magnetic field) even for very large Hartmann numbers. Turbulent profiles are obtained through an iterative scheme in which turbulence is introduced through an eddy viscosity model from the renormalization group theory of turbulence [Yakhot, V. and Orsag, S.A., J. Sci. Comput., 1986, 1 (1), 3]. The transition from a flow in a duct with thin conducting walls to one with insulating walls is clearly displayed by varying the wall conductance ratio from 0.05 to 0 for Hartmann numbers in the range 10 3–10 5. In turbulent regime, Reynolds numbers vary in the range 5 × 10 4–5 × 10 5. For thin conducting wall duct flows, turbulence is concentrated in the increased side layers while the core remains unperturbed. In insulating wall ducts, the flow remains in the laminar regime within the considered range of Reynolds numbers.

Heat transfer in laminar and turbulent liquid-metal MHD flows in square ducts with thin conducting or insulating walls

The heat transfer in fully-developed liquid-metal flows in a square duct with a uniform, transverse magnetic field is analyzed. Velocity profiles obtained for laminar and turbulent regimes [Cuevas, S., Picologlou, B. F., Walker, J. S. and Talmage, G., Int. J. Engng Sci., 1997, 35, 485] are employed to solve the heat transfer equation through finite differences, in a duct with one side wall (parallel to the magnetic field) uniformly heated and three adiabatic walls. Turbulent effects are introduced through eddy viscous and thermal diffusivity models from the renormalization group theory of turbulence [Yakhot, V. and Orszag, S. A., J. Sci. Comput., 1986, 1(1), 3]. Analysis focuses in determining how the structure of the side-layer flow, influenced by the wall conductance ratio and Hartmann and Péclet numbers in the ranges of interest of fusion blanket applications, affects the heat transfer processes. Numerical calculations for liquid lithium show that for thin conducting wall duct cases, the laminar MHD heat transfer mechanism, characterized by high-velocity side-wall jets, appears to be more efficient than turbulent mixing in the boundary layer for a given Péclet number.

MHD flow in rectangular ducts with inclined non-uniform transverse magnetic field

Abstract This paper examines the three-dimensional liquid metal MHD flow in rectangular ducts with thin conducting walls and with an inclined non-uniform transverse magnetic field. The Hartmann number and interaction parameter are assumed to be large and the magnetic Reynolds number is assumed to be small. Under these assumptions, viscous and inertial effects are confined to thin boundary layers adjacent to the walls. Outside these layers, the governing equations are significantly simplified. For validation of the numerical solutions, exact analytical solutions are derived for the case of a rectangular duct of equal wall thickness and with a uniform magnetic field. Comparisons of the exact analytical and numerical solutions give excellent agreement. Variation of the fully developed flow pressure gradient with the wall conductance ratio, aspect ratio, and magnetic angle is discussed. Numerical solutions are presented for flow in the varying field region where the flow is perturbed due to three-dimensional effects. The three-dimensional pressure drop, i.e. in excess of the locally fully developed pressure, is presented and its implication to a fusion blanket is discussed. The velocity distributions are also presented.

MHD flow in rectangular ducts with inclined non-uniform transverse magnetic field

Abstract This paper examines the three-dimensional liquid metal MHD flow in rectangular ducts with thin conducting walls and with an inclined non-uniform transverse magnetic field. The Hartmann number and interaction parameter are assumed to be large and the magnetic Reynolds number is assumed to be small. Under these assumptions, viscous and inertial effects are confined to thin boundary layers adjacent to the walls. Outside these layers, the governing equations are significantly simplified. For validation of the numerical solutions, exact analytical solutions are derived for the case of a rectangular duct of equal wall thickness and with a uniform magnetic field. Comparisons of the exact analytical and numerical solutions give excellent agreement. Variation of the fully developed flow pressure gradient with the wall conductance ratio, aspect ratio, and magnetic angle is discussed. Numerical solutions are presented for flow in the varying field region where the flow is perturbed due to three-dimensional effects. The three-dimensional pressure drop, i.e. in excess of the locally fully developed pressure, is presented and its implication to a fusion blanket is discussed. The velocity distributions are also presented.

Analysis of liquid metal MHD flow in multiple adjacent ducts using an iterative method to solve the core flow equations

A computationally fast and efficient method for analyzing MHD flow at high Hartmann number and interaction parameter is presented and used to analyze a multiple duct geometry. This type of geometry is of practical interest in fusion applications. Because the Hartmann number and interaction parameter are generally large in fusion applications, the inertial and viscous terms in the Navier-Stokes equation can often be neglected in the core flow region, making this equation linear. In addition, because the magnetic fields in a fusion reactor vary slowly and the magnetic Reynolds number is small, the induced magnetic field can be neglected. The resulting equations representing core flow have certain characteristics which make it possible to reduce them to two dimensional without losing the three dimensional characteristics. The method which has been developed is an “iterative” method. A velocity profile is assumed, then Ohm's law and the current conservation equation are combined and used to solve for the potential distribution in a plane in the fluid, and in a surface in the duct wall. The potential variation along magnetic field lines is checked, and if necessary, the velocities are adjusted. This procedure is repeated until the potentials along field lines vary to within a specified error. The analysis of the multiple duct geometry shows the importance of global effects. The results of two basic cases are presented. In the first, the average velocity in each duct is the same, but the wall conductance ratios of the walls perpendicular to the magnetic field vary from duct to duct. The total pressure drop in the electrically connected ducts was greater than or equal to the total pressure drop in the same ducts electrically isolated. In addition, the velocity profile in the ducts can be significantly affected by the presence of neighboring ducts. In the second case, the wall conductance ratios are the same for each duct, but the average velocity varies from duct to duct. The overall pressure drop is the same as if the ducts were electrically isolated, but the velocity profile and side layer flow rate can be very different from the electrically isolated case.

Numerical simulation of liquid-metal MHD flows in rectangular ducts

To design self-cooled liquid metal blankets for fusion reactors, one must know about the behaviour of MHD flows at high Hartmann numbers. In this work, finite difference codes are used to investigate the influence of Hartmann number M, interaction parameter N, wall conductance ratio c, and changing magnetic field, respectively, on the flow.As liquid-metal MHD flows are characterized by thin boundary layers, resolution of these layers is the limiting issue. Hartmann numbers up to 103 are reached in the two-dimensional case of fully developed flow, while in three-dimensional flows the limit is 102. However, the calculations reveal the main features of MHD flows at large M. They are governed by electric currents induced in the fluid. Knowing the paths of these currents makes it possible to predict the flow structure.Results are shown for two-dimensional flows in a square duct at different Hartmann numbers and wall conductivities. While the Hartmann number governs the thickness of the boundary layers, the wall conductivities are responsible for the pressure losses and the structure of the flows. The most distinct feature is the side layers where the velocities can exceed those at the centre by orders of magnitude.The three-dimensional results are also for a square duct. The main interest here is to investigate the redistribution of the fluid in a region where the magnetic field changes. Large axial currents are induced leading to the ‘M-shaped’ velocity profiles characteristic of MHD flow. So-called Flow Channel Inserts (FCI), of great interest in blanket design, are investigated. They serve to decouple the load carrying wall from the currents in the fluid. The calculations show that the FCI is indeed a suitable measure to reduce the pressure losses in the blanket.

The effect of magnetic field on two-phase liquid metal flow

In this paper, the basic equations of two-phase liquid metal flow in a magnetic field are derived, and specifically, two-phase liquid metal MHD flow in a rectangular channel is studied, and the expressions of velocity distribution of liquid and gas phases and the ratioK0 of the pressure drop in two-phase MHD flow to that in single-phase are derived. Results of calculation show that the ratioK0 is smaller than unity and decreases with increasing void fraction and Hartmann number because the effective electrical conductivity in the two-phase case decreases.