COMSOL 6.4 - Hartmann Flow in Liquid Metal Blanket with Heat Transfer

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Hartmann Flow in Liquid Metal Blanket with Heat Transfer

This model demonstrates the flow of Lithium through an electrically insulated duct in a simple tokamak blanket design. In the frame of reference of the flowing material, the electromotive force induces a volumetric current, which in turn generates a Lorentz force opposing the flow velocity owing to the ambient magnetic field. The induced current closes the loop by returning in a thin layer near the electrically insulated, no slip surface.

Model Definition

The model is set up in 3D using the and physics interfaces coupled via a multiphysics node, as well as with the interface coupled to via a multiphysics node.

For the electromagnetic fields, an external magnetic flux density is defined on the duct boundaries contributing with electrical insulation, and the volumetric current is induced by the electromotive force as induced by the fluid velocity. The fluid flow is given no-slip wall conditions along the duct, and a pressure-driven base flow with a volumetric force contribution given by the Lorentz force. Heat transfer is treated by the convection–diffusion equation, where the convecting velocity is given by the flow field.

Figure 1 shows the velocity magnitude in the liquid metal blanket and highlights the shear flow near the no-slip surfaces of the blanket with a surface deformation plot. The direction of the externally applied magnetic field is indicated with arrows.

Figure 2 shows the induced current density and circulating current paths in a blanket cross section, displaying the main decelerating current in the center of the blanket, and the thin layers of return current near the electrically insulated no-slip surfaces.

Figure 1: The velocity magnitude of the liquid metal flowing in the blanket, with arrows indicating the direction of the applied magnetic field.

Figure 2: The current density y-component, and arrows displaying the current density direction.

ACDC_Module/Electromagnetics_and_Fluids/hartmann_flow_in_liquid_metal_blanket

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select > > .

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In the tree, select > .

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In the tree, select > .

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Add relevant physical parameters for the model.

Global Definitions

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In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
d	1[cm]	0.01 m	Half-distance between planes
U0	0.05[m/s]	0.05 m/s	Average inlet velocity
B0	0.02[T]	0.02 T	Magnetic flux density

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 40*d.

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In the text field, type 10*d.

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In the text field, type 2*d.

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Locate the section. In the text field, type -d.

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In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select > > .

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Click the button in the window toolbar.

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In the toolbar, click

to close the window.

Lithium, 200 °C (mat1)

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In the window for , locate the section.

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In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Heat capacity at constant pressure	Cp	200	J/(kg·K)	Basic

Add a multiphysics coupling node to treat advective heat transfer correctly.

Nonisothermal Flow 1 (nitf1)

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In the toolbar, click

and choose > .

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In the window for , locate the section.

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From the list, choose .

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From the ρref list, choose .

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In the αp,0 text field, type 1e-3[1/K].

The background magnetic field is applied as a boundary condition for the tangential vector potential.

Magnetic and Electric Fields (mef)

Background Magnetic Flux Density 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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Specify the Bb vector as


B0	Z

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Locate the section. From the list, choose .

Electric Insulation 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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button in the toolbar.

Laminar Flow (spf)

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In the toolbar, click

and choose .

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Select Boundary 1 only.

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the Uav text field, type U0.

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In the toolbar, click

and choose .

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Select Boundary 6 only.

Heat Transfer in Fluids (ht)

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In the toolbar, click

and choose .

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Select Boundaries 1 and 2 only.

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In the window for , locate the section.

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In the T0 text field, type 450.

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the Q0 text field, type 1e6*exp(-((y-0.1[m])/0.02[m])^2).

Refine the mesh near the boundary layers.

In the toolbar, click

and choose .

In the toolbar, click

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

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In the window, click .

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Select Boundary 1 only.

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Right-click and choose .

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In the window for , locate the section.

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In the dialog, type 1 2 4 6 in the text field.

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In the window for , locate the section.

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From the list, choose .

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In the text field, type 30.

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In the text field, type 10.

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Select the checkbox.

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In the window, right-click and choose .

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In the window for , locate the section.

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In the text field, type 40.

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In the toolbar, click

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Magnetic Flux Density (mef)

Fluid velocity and Magnetic field

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In the window, right-click and choose .

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In the dialog, type Fluid velocity and Magnetic field in the text field.

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In the window, expand the node, then click .

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In the window for , locate the section.

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Find the subsection. In the text field, type 5.

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Find the subsection. In the text field, type 0.

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Find the subsection. In the text field, type 0.

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type u.

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In the text field, type v.

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In the text field, type w.

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Locate the section.

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Select the checkbox. In the associated text field, type 0.5.

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In the window, right-click and choose .

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In the window for , locate the section.

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Find the subsection. In the text field, type 5.

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Find the subsection. In the text field, type 5.

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Find the subsection. In the text field, type 1.

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Locate the section. From the list, choose .

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type 1.

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Locate the section. From the list, choose .

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From the list, choose .

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Right-click and choose .

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Select Boundaries 2, 3, and 5 only.

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In the toolbar, click

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button in the toolbar.

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 35*d.

Current Density and Pathways

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In the toolbar, click

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In the window for , type Current Density and Pathways in the text field.

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type mef.Jy.

Arrow Surface 1

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In the window, right-click and choose .

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In the window for , locate the section.

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In the text field, type mef.Jx.

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In the text field, type mef.Jy.

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In the text field, type mef.Jz.

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Locate the section. From the list, choose .

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Select the checkbox. In the associated text field, type 5.0E-6.

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In the toolbar, click

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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button in the toolbar.

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In the window, expand the > node.

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type 1.

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Locate the section. From the list, choose .

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From the list, choose .

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Right-click and choose .

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Select Boundaries 2, 3, and 5 only.

In the window, under > right-click and choose .

Temperature (ht)

In the window, click .

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In the toolbar, click

and choose .

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In the window for , locate the section.

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In the text field, type T.

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Locate the section. Find the subsection. In the text field, type 5.

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Find the subsection. In the text field, type 0.

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Locate the section. From the list, choose .

Temperature (ht)

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In the window, click .

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In the toolbar, click

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button in the toolbar.