Electromagnetic pumping of molten salts

Abstract

This paper investigates the possibility to control through electromagnetic pumping the molten salts flow in high temperature heat transfer applications. Based on finite element models there were evaluated and compared parameters of multi-phase induction pumps with cylindrical, annular or flat pumping channels and of conduction pumps with ac or quasi-dc electric power supply.

Full text

Electromagnetic Pumping of Molten Salts
J. Etay*, V. Fireţeanu**, Y. Fautrelle*, C. Roman**
* SIMPAP/EPM Laboratory, CNRS/INPG, PHELMA-Campus, BP 75, Grenoble, France
** EPM_NM Laboratory, POLITEHNICA University, 313 Splaiul Independentei, 060042 Bucharest, Romania
Abstract-This paper investigates the possibility to control
through electromagnetic pumping the molten salts flow in high
temperature heat transfer applications. Based on finite element
models there were evaluated and compared parameters of
multi-phase induction pumps with cylindrical, annular or flat
pumping channels and of conduction pumps with ac or quasi-dc
electric power supply.
I. INTRODUCTION
The concern on molten salt as liquid fluorides is
undergoing a revival [1]. Traditionally, used in primary
aluminum production, they are envisaged for high
temperature heat transfer for both nuclear and solar power
production. Indeed, on one hand, due to the high heat
capacity, they could act as excellent coolant, and on the other
hand, a part of the traditional knowledge in electrochemistry
using molten salts can be adapted to pyrometallurgy for
nuclear waste treatment.
As a coolant, on the nuclear side, three applications can be
foreseen for molten salts. The first application is the
substitution of the sodium in the secondary circuit of the
existing nuclear reactors. The second is the possible use of a
lithium fluoride salt inside a test module blanket of ITER, the
tokamak currently under construction in the South of France.
The third is attached to the Molten Salt Fast Reactor (MSFR),
one of the reactor which had been selected as a candidate for
the Generation IV nuclear reactors [4]. In this last application,
the liquid fluoride acts both as a coolant and as a vehicle for
mass transfer, i.e. as fuel. To reach these performances, the
molten salt will flow inside the primary exchanger and also
part of this salt will be pump to be regenerated.
The same heat transfer necessity is found in the field of
“high-temperature” solar energy, where large thermal storage
capacity systems are needed. Here also, molten salts are good
candidates [2].
The uses of such liquids raise common questions like for
example the flow control. The object of the work is to provide
insight for electromagnetic pumping technologies. Indeed, the
molten salts exhibit an electrical conductivity range lying
between 100 and 700 Ω-1m-1. While well below that of liquid
metals, from 106 to 107 Ω-1m-1, it is very superior to that of
seawater, from 1 to 8 Ω-1m-1. Because this latter was
sufficient for the Japanese testing of a Magnetohydrodynamic
ship propulsion to be successful in 1991 [4], it is worth to
investigate electromagnetic pumping of molten salts.
In this paper several electromagnetic pumps are proposed.
The most promising will be tested on a loop under building at
the LPSC research laboratory in Grenoble. This will be a
validation step before going to industrial scale experiments or
nuclear facilities.
The paper concerns the electromagnetic pumping of molten
salts using induction pumps with only one electric supply,
which generates a multi-phase inductor field, and conduction
pumps with ac or quasi-dc electric power supply. One of two
circuits of the conduction pumps controls the magnetic field
in the airgap where the pump channel is placed, and the
second controls the pumping current injected in the molten
salt inside the channel.
II. THE MULTI-PHASE MAGNETIC FIELD IN
CONDUCTIVE BODIES
The operation principle of multi-phase induction pumps for
conductive liquids is based on the generation inside the
pumping channel of induced currents, respectively of
electromagnetic forces. The magnetic field created by a
multi-phase linear inductor, expressed by the formula
B(t,x) = Bm cos(ωt - 2πx/λ), where ω = 2πf and λ = 2τ, called
traveling magnetic field, is characterized by the parameters
frequency supply f and pole pitch length τ of the inductor.
The intensity of currents induced by such a magnetic field in
a conductive body depends on the electric conductivity
σ = 1/ρ and magnetic permeability µ. Such a wave field,
generated by the one-side flat linear inductor in Fig. 1, with
the active face in the plan z = 0, travels along the Ox
axis with the synchronous speed vs = λ/T = 2fτ.
In a simplified analytical model of the one-side traveling
magnetic field in the conductive half space, [1], there is no
airgap and the active face of the inductor is the lower limit
z = 0 of the half space, Fig. 2. The inductor and the
Airgap
-
Liquid conductive
body
z
Linear flat inductor
yx
Fig. 1. Electromagnetic pumping in the traveling
magnetic field of a flat linear inductor.

0 0
1
( ,0, ) , ( , , ) 0
x
x
BA
H x t J A x t
z
∂
= =− = ∞ =
µ µ ∂
0 0
0
, ( / ) ,
( / )
z z
x z
sm sm
z
sm
B J e B j J e
J j J e
−γ −γ
−γ
π
=µ =− µ γ
τ
=− ωµ σ γ
conductive half space are extended to infinity along the x and
y coordinates, Fig. 1, and the conductive half space is
extended to infinity in z > 0 direction. The magnetic core of
the inductor has no slots, is nonconductive and has infinite
permeability.
The multi-phase electric supply of the flat linear inductor
can modeled by the vector Js [0, Js(x,t), 0] of the current
sheet line density in the plane z = 0, Fig. 2, where
Js(x,t) = Jsmcos[ωt –(π/τ)x].
The vector of the current density in the half space has the
structure J[0, J(x,z,t), 0], the magnetic vector potential,
defined by the formula B = curl A, is oriented along the same
Oy axis, A[0, A(x,z,t), 0] and the vector of magnetic flux
density has the structure B[Bx(x,z,t), 0, Bz(x,z,t)]. The
unknown A(x,z,t) satisfies the equation:
(1)
The two boundary conditions:
(2)
express the known value of the magnetic field at the interface
between the magnetic core and the conductive half space and
the property of field vanishing to infinity of z coordinate.
The complex image A(z) of the magnetic potential, defined
by the transformation A(t,x,z) = Real{A(z)⋅exp[j(ωt - πx/τ)]}
that is the solution of the equation (1) with the boundary
conditions (2) is A = (µ0Jsm/γ)e-γz, where
γ = [(π/τ)2 + jωµ0σ]0.5. The complex images of the two
components of magnetic flux density and of the induced
current density in the 1D computation domain z ≥ 0, are:
(3)
The modulus of these quantities varies with respect the
coordinate z as follow:
(4)
where γ is the modulus of γ and the parameter δ = 1/Real(γ)
represents the penetration depth of the traveling field. This
parameter characterizes the decrease in the direction z of the
electromagnetic field inside the conductive half space.
The penetration depth can be expressed by the formula
δ = (τ/π){2/[(1 + ε2)0.5 + 1]}0.5, where the parameter
ε = ωµ0σ/(π/τ)2 = vslc/[1/(µ0σ)] is
called Reynolds magnetic number. This parameter is
function of travelling wave speed vs, of the characteristic
length lc = τ/π and of the magnetic diffusivity 1/(µ0σ).
For reduced values of the electric conductivity σ and/or of
the frequency f and/or of the pole pitch τ, respectively for
ε << 1, the approximation of penetration depth is δ ≈ (τ/π). In
this case, the depth of the electromagnetic field penetration is
independent on σ and f. In such cases a good penetration of
the field implies high values of the pole pitch length τ . The
field space structure, Fig. 3a, depends only on τ and it is
independent on σ and f.
For values of frequency f and pole pitch length τ leading to
the condition ωµ0σ >> (π/τ)2, respectively for ε >>1, the
approximation of penetration depth given by the formula
δ ≈ [2/(ωµ0σ)]0.5 is independent on τ. In this case, a good
penetration of the traveling field implies reduced values of
the frequency f. The field penetration, Fig. 3b, depends on σ
and f and is independent on the parameter τ.
2 2
0
2 2
A A A
t
x z
∂ ∂ ∂
+ =µ σ ∂
∂ ∂
Fig. 2. Simplified model of traveling field in the conductive half space.
x
y
z
×× × × ×
µ = ∞
σ = 0
0τ
-τ
µ0, σ
Conductive half space
Current sheet
Magnetic core
/ /
0 0
/
0
, ( / )( / ) ,
( / )
z z
x sm z sm
z
sm
B J e B J e
J J e
− δ − δ
− δ
= µ = π τ µ γ
= ωµ σ γ
τ/2 τ
-τ -τ/2
z
x
z
x
-τ -τ/2 τ/2 τ
a) ε << 1
b) ε >> 1
Fig. 3. Penetration of traveling magnetic field in the conductive half space.

2
*2
02
1 0.5
Re { } Im ( )
21
z
xz sm
f al J B ag J e
−δ
π ε
 
= − × = γ µ
 ÷
τ
  +ε
Taking into account the values f1 = 50 Hz, τ1 = 0.72 m and
the conductivity σ = 300 Ω-1m-1 of the molten LiF at 850 °C, it
results ε1 = 0.62⋅10-2. This corresponds to the first case; the
value
of the
penetration depth is δ1 = 229.2 mm.
If the frequency is much higher, f2 = 100 kHz, it results
ε2
=
12.4. This corresponds to the second case, when the
penetration depth is δ2 = 91.9 mm.
The vector of the electromagnetic force density in the
conductive half space is evaluated with the formula:
(5)
where the sign* signifies the complex conjugate of the
affected quantity. The two components are
the pumping electromagnetic force density,
(6)
,
oriented along the direction x of the traveling field
propagation, and the levitation electromagnetic force density,
(7)
normally oriented with respect the active face of the inductor.
If ε >> 1, the levitation component fz is greater than the
pumping component fx, respectively fz = [(ε-1)/2]0.5fx. For
ε << 1, the levitation
component fz is negligible with
respect the pumping
component fx. For ε = 2√2 the two component of the
electromagnetic force density are equal, fz = fx.
The integral from z = 0 to infinity of the force density gives
the
electromagnetic force generated by the traveling field in the
conductive half space related to the unit of surface in xOy
plane, Fig. 2. The pumping force Fx and the levitation force
Fz have the expressions:
(8)
The equation ∂Fx/∂ε = 0 gives the optimum value ε o = √3
of the Reynolds magnetic number, for which the pumping
action of the traveling field is maximum.
The density pJ of the active power corresponding to the
Joule effect of the induced currents in the conductive half
space is computed with formula:
(9)
The line integral from z = 0 to infinity of pJ gives the active
power PJ generated in the conductive half space related to the
unit of surface in xOy plane, Fig. 2:
(10)
The ratio between the pumping force Fx and the induced
power PJ is Fx/PJ = 1/(2fτ). Consequently, an efficient
electromagnetic drive of the conductive half space,
characterized by high value of the pumping force and reduced
value of the Joule power, implies reduced values of the
frequency.
III. TRAVELING MAGNETIC FIELD INDUCTION PUMPS
The 2D finite element models of induction pumps for
molten LiF at 850°C presented in this section concern a
cylindrical linear pump (CLIP), an annular linear pump
(ALIP) and a flat linear pump (FLIP). The main interest is to
evaluate correlations between the geometrical, physical and
supply parameters of the pumps that are able to ensure the
reference value pe = 105 N/m2 of the electromagnetic
pressure. This pressure is the ratio between the pumping
electromagnetic force in the molten salt inside the pumping
channel and the area of the
inner transversal cross section
of the channel.
A. Cylindrical linear
induction pump
(CLIP)
The geometry in Fig. 4
corresponds to a cylindrical
three-phase two poles inductor,
with eight circular coils per
phase. The pole pitch length is
720 mm and the inductor
2
*2
02
1 0.5
Re { }
21
z
zx sm
f al J B J e
−δ
π ε
 
= × = µ
 ÷
τ
  +ε
*
1{ }
2
J
p J J= ×
σ
22
2 2
2 ( / )
41 1 1
sm
J
J
P
π τ ε
=σ+ε + +ε
Fig. 4. Cylindrical pump.
* *
1
[ , 0, ] Re 0 0
2
0
x z
x z
i j k
f f f al J
B B
=
r r r
r

length is 1690 mm. The pumping cylindrical channel has the
inner radius Ri = 100 mm, and the inner and outer radius of
the inductor are 145 mm, respectively 425 mm. The slots
cross section has the dimensions 50 mm x 100 mm and the
mean value of the current density over the coils cross-section
is 6 A/mm2. The nonlinear magnetic core of the inductor is
characterized by the saturation 1.4 T and the initial relative
permeability is 300.
In order to create the reference value of the electromagnetic
pressure pe in the molten salt, the value of the rated pumping
force generated by the CLIP pump is Fec = pe⋅π Ri2 = 3140 N.
The dependences of the electromagnetic force, of the Joule
power in the molten salt and of the ratio electromagnetic
force/Joule power on the inductor supply frequency presented
in Figs. 5 – 7 offers the following findings:
- the maximum of the pumping force corresponds to a fre-
quency around 280 kHz;
- a higher value of the pumping force/Joule power ratio im -
poses a value of the supply frequency as low as possible.
The rated value 3140 N of the pumping force corresponds
to the rated frequency fc = 30.5 kHz. Figs. 8 – 11 show the
corresponding results related the magnetic field lines, the
magnetic flux density chart and the pumping force density, all
for the phase 60 degrees, and the current density in the molten
salt. The rated values of the Joule power in the molten salt is
Pc = 116 MW and of the reactive power of the pump is Qc =
8090 MVAr.
0
2
4
6
8
10
12
14
16
0 50 100 150 200 250 300
Frequency (kHz)
Pumping Force, F
x
(kN)
Fig. 5. Dependence on frequency of the pumping force.
0
1
2
3
4
5
6
7
8
0 50 100 150 200 250 300
Frequency (kHz)
Joule Power P
J
, (GW)
Fig. 6. Dependence on frequency of the Joule power.
0
5
10
15
20
25
30
35
40
0 50 100 150 200 250 300
Frequency (kHz)
Pumping Fo rce / Jou le Power (kN/GW)
Fig. 7. Pumping force/Joule power ratio versus frequency.
If all the eight coils of a phase of the CLIP inductor are
series connected and each coil has w turns, it result the rated
values of the phase current in [A] and of the phase-to-phase
supply voltage in [V]:
I = 30000/w , U =155877w (11)
Fig. 8. Magnetic field lines. Fig. 9. Magnetic flux density chart.
Fig. 10. Pumping force density. Fig. 11. Induced current density.

If all the eight coils are parallel connected, the rated phase
current of the CLIP pump in [A] and the rated phase-to-phase
supply voltage in [V] are:
I = 240000/w , U = 19484w (12)
Independent on the number w of turns, the rated values of
the current and voltage given by the formulas (11) and (12)
are very high and, consequently, the CLIP medium frequency
pump, 30.5 kHz supplied, is out of the practical interest.
B. Annular linear induction pump (ALIP)
The geometry of the model in Fig. 12 corresponds to the
ALIP pump, with an annular pumping channel. The ALIP
inductor is similar with the CLIP inductor, with eight circular
coils per phase. The pole pitch is 720 mm length and the
inductor length is 1640 mm. The pumping channel has
annular cross-section with the two radius R1/R2 = 160 mm/
200 mm. The inner and outer radiuses of the inductor are
245 mm, respectively 445 mm. The slots cross-section and
the mean value of the current density over the coils
cross-section are the same as of CLIP pump.
The nonlinear magnetic core
of the inductor is characterized
by the saturation 2.0 T and the
value 3000 of the initial relative
permeability.
In order to create the
reference value of the
electromagnetic pressure in the
molten salt, the value of the
ALIP rated pumping force is
Fea = pe⋅π (R22 – R12) = 4524 N.
The dependences on the
supply frequency of the
pumping force, of the Joule
power in the molten salt and of
the ratio electromagnetic
force/Joule power, similar to
those presented in Figs. 5 – 7,
show that the maximum of the
pumping force corresponds to
the frequency 150 kHz. But the
rated value 4524 N of the
pumping force corresponds to the ALIP rated frequency
fc = 5.9 kHz. Figs. 13 – 16 show the corresponding results
related the magnetic field lines, the magnetic flux density
chart and the pumping force density, all for the phase 60
degrees, and the current density in the molten salt. The
rated Joule power in the molten salt is Pa = 47.8 MW and the
rated reactive power of the pump is Qa = 3420 MVAr.
Fig. 13. Magnetic field lines. Fig. 14. Magnetic flux density chart.
If all the eight coils of a phase of the ALIP inductor are
series connected and each coil has w turns, it result the rated
values of the phase current in [A] and the phase-to-phase
supply voltage in [V]:
I =30000/w, U = 65896w (13)
Fig. 12. Annular pump.
Fig. 17. Flat double-sided pump.

Fig. 15. Pumping force density. Fig. 16. Induced current density.
If the eight coils are parallel connected, the rated phase
current of the ALIP pump in [A] and the rated phase-to-phase
supply voltage in [V] are:
I = 240000/w, U = 8237w (14)
Independent on the number of turns w, the rated values of
the current and/or of the voltage given by (13) and (14) are
very high and, consequently, the ALIP pump 5.9 kHz
supplied, is also out of the practical interest. But, with a
cylindrical magnetic core inside the annular pumping
channel, the performances of this pump increases, the supply
frequency decreases and the rated values of the phase current
and supply voltage should become acceptable.
C. Flat linear double-side induction pump (FLIP)
Fig. 17 presents the geometry of the 2D model of a flat
linear induction pump with three phases, two poles, double-
side inductor, and four coils per phase on each inductor side.
The pole pitch length is 720 mm, the inductor length is
1840 mm and the pump height is 930 mm.
The pumping channel has a rectangular cross-section with
the inner thickness a = 40 mm. The pump airgap has the
thickness 130 mm. The width of the two magnetic core sides,
respectively the depth considered for the 2D computations, is
b = 300 mm. The slots cross-section and the mean value of
the current density over the coils cross-section are those of
CLIP and ALIP pumps, respectively 50 mm x 100 mm and
6 A/mm2. The nonlinear magnetic core is characterized by
the saturation 2.0 T and the initial relative permeability 3000.
In order to create the reference value of the electromagnetic
pressure in the molten salt, the rated pumping force is
Fef = pe⋅a⋅b = 1200 N.
From the dependences on the supply frequency of the
pumping force, the Joule power in the molten salt and the
ratio electromagnetic force/Joule power it result that the
maximum of the pumping force is reached for 30 kHz.
The rated value 1200 N of the pumping force is obtained
for the FLIP rated frequency ff = 114 Hz. The rated Joule
power in the molten salt is Pf = 422 kW and the rated reactive
power of the pump is Qf = 97.8 MVAr. Since the frequency f f
is not so far from the industrial network value, the version
FLIP50, with 50 Hz frequency supply, was studied. This flat
double-side pump version has the pole pitch length 1020 mm,
the inductor length is 2540 mm, the inductor height is
1330 mm and the slot cross-section dimensions are 60 mm x
120 mm. The laminations of magnetic cores are characterized
by high saturation 2.4 T and initial relative permeability
4000.
The rated value of the pumping force 1200 N is obtained
with FLIP50 for a mean value of the current density over the
coils cross-section of only 3.6 A/mm2, lower than the value
6 A/mm2 in case of CLIP and ALIP pumps.
The FLIP50 results are the pumping force Fef50 = 1212 N,
the rated Joule power in the molten salt, Pf50 = 252.5 kW and
the rated reactive power Qf50 = 51.7 MVAr.
With the two sides of FLIP50 inductor connected in
parallel and the four coils of a phase per side connected in
series, it result the rated phase current in [A] and the rated
phase-to-phase supply voltage in [V]:
I = 51840/w , U = 576.5w (15)
For w1 = 8 turns/coil it results U1 = 4612 V and
I1 = 6480 A and for w2 = 18 turns/coil, U2 = 10376 V and
I2 = 2880 A. These rated values of the FLIP50 electric power
supply parameters are technically acceptable.
Figs. 18 – 21 show the FLIP50 results of the magnetic field
lines, of the magnetic flux density chart and of the pumping
Fig. 19. Magnetic field lines.
Fig. 20. Pumping force density.
Fig. 21. Induced current density.

force density for the phase 60 degrees and of the current
density in the molten salt.
The flat linear pump FLIP50, 50 Hz three-phase supplied,
it is an acceptable solution for molten LiF electromagnetic
pumping. Since the pole pitch length 1020 mm of the FLIP50
pump is much higher than the magnetic core width, equal
with the inner dimension 300 mm of the pumping channel,
the evaluations in this paper, based on a 2D model should be
very approximate. Consequently, further 3D investigation of
this pump it is necessary in order to prove or not this opinion.
IV. ELECTROMAGNETIC PUMPS OF CONDUCTION TYPE
The electromagnetic pumps of conduction type can be
advantageous in comparison with the induction pumps for the
electromagnetic pumping of molten salts, which have the
resistivity much higher than the molten metals. If in the
induction pumps the current density in the molten salt is more
or less proportional with the magnetic flux density in this
region, in the conduction pumps the values of the current
density and of the magnetic flux density can be independently
controlled. Thus, one can obtain the same value of the
pumping force for a higher value of the magnetic flux density
and a lower value of the current density, respectively for a
lower value of the Joule power. This aspect is very important
in case of molten salt electromagnetic pumping.
This section evaluates ac conduction pumps 50 Hz
supplied, and quasi-dc conduction pumps, for the same
reference value pe = 105 N/m2 of the electromagnetic pressure.
A. AC conduction pumps
The 2D geometry in Fig. 22 corresponds to the conduction
pump CP1, in which the ac magnetic field is created by two
identical electromagnet units alongside placed, each unit with
separate magnetic core, and one field coil around the yoke of
this core. The channel of the pump is placed in the lined
airgap of the two units, where the vector of the magnetic flux
density has vertical orientation.
The ac electric current in the molten salt inside the
pumping channel is normal oriented with respect the plane of
Fig. 22, and consequently, the vector of the pumping force
has horizontal orientation. The length of the pumping channel
in this direction is 1000 mm.
The inner thickness of the pumping channel is a = 40 mm
For the evaluation of the global quantities the 2D model
considers the value b = 300 mm for the inner width of the
pumping channel, respectively of the magnetic core
thickness. Consequently, the rated pumping force acting on
the molten salt is pe⋅a⋅b = 1200 N.
The thickness of the pump airgap is 130 mm. The width
of the magnetic core yoke is 600 mm and the horizontal
dimension of the two magnetic cores is 2420 mm. The height
of the magnetic cores is 1730 mm. The laminations of the
magnetic cores are characterized by the high saturation 2.4 T
and the initial relative permeability 4000.
The field coils cross-section 50 mm x 530 mm and the
mean rms value 6 A/mm2 of the current density over the coils
cross-section were considered. The rms value 2800 A of the
pumping current injected in the molten salt corresponds to
2800/40/1000 = 0.07 A/mm2 of the mean pumping current
density over the cross-section of this region. The shift phase
between the two ac currents, in the field coils, and in the
molten salt, both of 50 Hz, is zero.
Figs. 23 and 24 show the magnetic field lines and the chart
of the magnetic flux density. The charts of the magnetic flux
density, of the current density (peak value) and of the
electromagnetic force density in the molten salt inside the
pumping channel are presented in Fig. 25.
Fig. 23. Magnetic field lines - CP1 ac conduction pump.
Fig. 24. Magnetic flux density - CP1 ac conduction pump.
Fig. 25. Field quantities inside the channel of CP1 ac pump.
Fig. 22. CP1 conduction pump.
Fig. 18. Magnetic field lines.

The CP1 ac conduction pump generates the pumping force
1192.1 N. The Joule power in the molten salt is 256.93 kW.
Taking into account the copper resistivity 2.45⋅10-8 Ωm,
8 turns per coil and the value 0.6 of the stacking factor, the
Joule losses in the field coils are 46.75 kW. The total active
power is 303.68 kW and the reactive power is 29.9 MVAr.
If the two field coils of the CP1 ac pump are series
connected, the ac supply of the field coils is characterized by
the couple current/voltage 19875 A / 1510.4 V. For the two
coils parallel connected, the result is 39750 A / 755.2 V.
The ac supply of the channel is characterized by the couple
current/voltage 2800 A / 69.96 V.
The version CP2 of the ac conduction pump in Fig. 26,
consists in two electromagnet units placed one over the other.
Since the inner side of each of the two identical field coils
contains the magnetic pole of the corresponding pump unit,
the magnetic field generation is better than in the CP1 pump
version.
The global horizontal and vertical dimensions of the
magnetic cores assembly are the same as for CP1, the
dimensions of airgap and pumping channel are unchanged.
Each field coil has 4 turns, the cross-section dimensions are
50 mm x 265 mm. All other physical and computation data
are the same as for the CP1 version.
Figs. 27 and 28 show the magnetic field lines and the chart
of the magnetic flux density. The CP2 ac conduction pump,
50 Hz supplied, generates the pumping force 1240.6.1 N
and 262.23 kW of Joule power in the molten salt. The Joule
losses in the field coils are 23.27 kW.
B. DC conduction pumps
The ac 50 Hz conduction pumps present interest taking into
account the accessibility of this type of electric power supply.
The condition of minimum or zero value of the shift-phase
between the magnetic flux in the pump airgap and the
pumping current in the molten salt is not so easy to be
achieved. Another disadvantage is the high value of the
current in the field coils. The high level of the pump reactive
power imposes parallel compensation with capacitor banks.
In this context it is placed the interest for the study of a quasi-
dc supply, at the limit of the dc supply, of the previously
presented conduction pumps. A quasi-dc supply means a low
frequency ac supply.
The previously ac steady state finite element analyses are
replaced by magnetostatic analyses. The sources of the
magnetostatic field are now the dc current density 6 A/mm2 in
the field coils and 0.07 A/mm2 in the molten salt. The airgap
and channel dimensions rest the same, the physical properties
also. For the computation of voltage and current supply the
field coils of the CP1 dc pump have 56 turns/coil, instead of
8 turns in case of the ac 50 Hz supply, and the coils of the
CP2 dc pump have 20 turns/coil, instead of 4 turns for the ac
supply.
Figs. 29 and 30 show the magnetic field lines and the chart
of the magnetic flux density for the CP1 dc pump. This pump
generates the pumping force 1261.8 N and 196 kW Joule
power in the molten salt. The Joule losses in the field coils
are 46.75 kW.
If the two field coils of the CP1 dc conduction pump are
series connected, the supply of this electric circuit is
characterized by the couple current/voltage 2839 A/16.5 V.
The dc supply of the channel circuit is characterized by
the couple 2800 A / 70 V.
Figs. 31 and 32 show the magnetic field lines and the chart
of the magnetic flux density for the CP2 dc pump. This pump
generates the pumping force 1263.8 N and 196 kW Joule
Fig. 26. CP2 conduction pump.
Fig. 28. Magnetic flux density – CP2 ac conduction pump.
Fig. 27. Magnetic field lines – CP2 ac conduction pump.

power in the molten salt. The Joule losses in the field coils
are 23.37 kW. If the two coils of this dc pump are series
connected, the electric supply of the field coils circuit is
characterized by the couple 2839.3 A / 8.23 V. The channel
electric supply is characterized by the couple 2800 A / 70 V.
V. CONCLUSIONS
The 2D finite element analyses of the electromagnetic
pumping of molten salts - conductive liquids with resistivity
much higher than the molten metals, for different operating
principles, offer important findings.
Some variants of the induction pumps of traveling
magnetic field type, with multi-phase electric supply, whose
main advantage consists in the non-contact generation of the
pumping current and pumping force inside a nonconductive
pumping channel, can offer technical solutions for 50 Hz or
for higher frequency supply.
The conduction pumps with 50 Hz supply can represent an
attractive solution, but the best efficiency of molten salts
electromagnetic pumping can be obtained with quasi - direct
current conduction pumps.
The superconductive generation of magnetic fields with
high values of the magnetic flux density in the pumping
channel is a solution to increase the efficiency of conduction
pumps. The same electromagnetic pressure can be obtained
for a lower value of the current density in the molten salt
inside the pumping channel, which means lower Joule losses
associated with the molten salts electromagnetic pumping.
REFERENCES
[1] V. Ghetta, J. Fouletier and P.Taxil, “Sels fondus à hautes
températures” (2009) PPUR – ISBN 978-2-88074-832-6.
[2] H. Hasuikea, Y. Yoshizawab, A. Suzukic and Y. Tamaurac, “ Study on
design of molten salt solar receivers for beam-down solar
concentrator “, Solar Energy, Volume 80, Issue 10, October 2006,
Pages 1255-1262.
[3] S. Morota, K. Imaichi, M. Nakato & S. Takezawa (1991) An outline of
the R&D project on supra conducting MHD Ship propulsion
Proceedings MHDS91, pp53-68.
[4] http://www.gen-4.org/ PDFs/GIF_2008_Annual_Report.pdf
[5] http://en.wikipedia.org/wiki/Molten_salt_reactor.
[6] V. Fireteanu , “Electromagnetic pumping of liquid metals” (in
Romanian language), Technical Press , Bucharest, 1986.
[7] J. W. Gaban, P. T. Pileggi. And A. H. Powell, “Primary loop
electromagnetic pump design”, NASA Contractor Report, June 1970.
[8] SEUNG-HWAN SEONG, SEONG-O KIM, “Analyses of annular
linear induction pump characteristics using a time-harmonic finite
difference analysis“, Nuclear engineering and technology International
Journal of the Korean Nuclear Society.
Fig. 29. Magnetic field lines – CP1 dc conduction pump.
Fig. 30. Magnetic flux density - CP1 dc conduction pump.
Fig. 31. Magnetic field lines – CP2 dc conduction pump.
Fig. 32. Magnetic flux density – CP2 dc conduction pump.

BIOGRAPHIES
Jacqueline Etay was born on February
1956 in Firminy in central France. She
majored in mechanical engineering at the
Institut Polytechnique de Grenoble in 1979
and in 1982 obtained a PhD in Sciences at
the same Institute. She conducts research on
material processes using magnetic fields in
the EPM group (www.cnrs.epm.fr) of the
SIMAP laboratory (http://simap.grenoble-inp.fr/). She is
appointed as Senior Researcher at the CNRS (National Center
for Scientific Research).
Virgiliu Fireteanu was born in Runcu-
Dambovita, Romania on November 7,
1947. He graduated in 1970 the former
Polytechnic Institute of Bucharest,
Electrotechnical Faculty, where he
continued to work until now, in
different higher education positions, until
full professor of POLITEHNICA University of Bucharest,
from 1994. His first important step in research experience
was the PhD thesis related electromagnetic pumping of liquid
metals, presented in 1980. His special fields of interest
include finite element analysis in electrical engineering,
mainly connected with electro-mechanic and electro-thermal
energy conversion.
In the lasts 15 years he animates the activity in higher
education, research and development of the EPM_NM
Laboratory (Electromagnetic Processing of Materials and
Numerical Models, http://www.amotion.pub.ro/~epm ).
Yves Fautrelle was born in Lons-le-
Saunier, France on December 13, 1947. He
was graduated in 1970 from the Grenoble
Polytechnic Institute (France), Mechanical
Engineering department. He is now full
professor at Grenoble Polytechnic Institute
(France), since 1988. His special field of
interest is related to Magneto-Hydro-Dynamics applied to
Materials Processing. He published 272 publications (85 in
per-reviewed journals). He is heading the Electromagnetic
Processing of Materials group in the SIMAP
laboratory (http://www.epm.cnrs.fr/) and Director of the
Rhone-Alpes cluster on Energies (http://www.cluster-
energies.fr/).
Cristian Roman was born in Braila,
Romania, on March 24, 1986. He graduated
in 2009 POLITEHNICA University,
Electrical Engineering Faculty.
He is currently working on his PhD studies on
electromagnetic pumping of molten salts in
EPM_NM Laboratory (Electromagnetic Processing of
Materials and Numerical Models,
http://www.amotion.pub.ro/~epm).