MHD pumps: Annular Linear Induction Pump (ALIP)

MHD pumps: Annular Linear Induction Pump (ALIP)

Linards Goldšteins - Institute of Physics of University of Latvia([email protected])

Emmanuel Lo Pinto - CEA Cadarache ([email protected])

14/04/2021 2021 - March 31

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Summary1. Basics of MHD pumping

2. Some applications of MHD pumping

3. Types of MHD pumps

4. Elements of design of an ALIP

5. Equivalent circuit model

6. Ideal ALIP model

7. Role of the slip magnetic Reynolds number in ALIP

8. Stalling instability in ALIP

9. MHD instability in ALIP

10. Experimental and numerical studies on TESLA-EMP loop (IPUL)

11. Experimental and numerical studies on PEMDYN loop (CEA)

Linards Goldšteins / Emmanuel Lo Pinto MHD pumps: Annular Linear Induction Pump (ALIP)

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1. Basics of MHD pumpingExample of a conducting fluid in a channel

• EM force on an elementary volume of fluid:

𝑓𝐸𝑀 = 𝑗𝑦𝐵𝑧𝑢𝑥

• Total EM force in the channel:

𝐹𝐸𝑀 =ම

𝑉

𝑗𝑦 𝑥, 𝑦, 𝑧 𝐵𝑧(𝑥, 𝑦, 𝑧)𝜕𝑥𝜕𝑦𝜕𝑧

• Developed pressure:𝑝𝐸𝑀 = 𝐹𝐸𝑀/𝑆


Lorentz force

𝑓𝐸𝑀 = Ԧ𝑗 × 𝐵

Navier-Stokes momentum equation

𝜌𝜕 Ԧ𝑣

𝜕𝑡+ Ԧ𝑣. 𝛻 Ԧ𝑣 = −𝛻𝑝 + 𝜇∆ Ԧ𝑣 + 𝑓𝐸𝑀

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2. Some applications of MHD pumping

Linards Goldšteins / Emmanuel Lo Pinto MHD pumps: Annular Linear Induction Pumps (ALIP)

Nuclear industry

Alkali & non-alkali metal production

Space industry

Computer hardware

Concentrated Solar Power

JHR reactor CALIPSO device prototype pump

LM-10 pump for CPU cooling

SNAP 10 pump for space reactor

• Conducting fluids

• Reliability / service time is key• no sealing required

• no moving parts in direct contact with fluid

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MHD pumps

Conduction pumps

DC conduction

AC conduction

Induction pumps

Moving inductor

Static inductor

• Current directly supplied to the fluid• Magnetic field from permanent magnets

(DC type pump) or electromagnet

• Travelling magnetic waveo Moving permanent magnetso Arrangement of coils (static)

• Current induced in the fluid channel thanks to the time-varying magnetic flux (Lenz’s law)

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DC conduction pump• Common operating range:

o Low flowrate (0 – 10 m3/h)

o Low pressure rise (0 – 1 bar)

• Assets:o Simple design & optimisation o Cheap productiono No moving part

• Drawbacks:o Very high current requiredo DC power supply needed

3 l/min, 0.05 bar (UNIST)

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Permanent magnet pump (radial air gap type)


• Assets:o Higher efficiency (compared to other EM pumps)o Relatively cheap production (use of commercial motor)o Relatively small size (for high developed pressure)o Simple construction (no coils…)

• Drawbacks:o Rotating magnetic diskso Flow channel has a complex geometry

• Common operating range:o Low to medium flow rate (up to 102 l/s)o Low to high developed pressure

(0 – 10 bars & more)

(IPUL design)

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Annular Linear Induction Pump (ALIP)

• Common operating range:o Medium to high flowrate (up to 103 m3/h)o Low to high developed pressure (0 – 10 bars)

• Assets:o No finite width effect o Very high mechanical resistanceo No moving parts

• Drawbacks:o More expensive than other EM pumpso High developed pressure means higher

currents or longer pump

Drawing of ALIP design with external inductor

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Origin: asynchronous motor

Magnetic circuit

rotor

Liquid metal

PolyphaseinductorConducting

side bar

ferromagnetic

Conducting side bar

Intermediate step: flat linear induction pump

Symmetry axis

Ferromagnetic corePolyphase inductor

Annular liquid metal channel

Final step: the ALIP

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3

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FERROMAGNETIC YOKE

FERROMAGNETIC CORE

Longitudinal cross section

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Detail of transverse cross section

Transverse cross section

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4. Elements of design of an ALIP• Generation of a “sinusoidal” travelling wave

3 phases & 2 slot/pole/phase case


Wavelength 𝜆 = 2𝜋/𝑘

Pole pitch 𝜏 = 𝜆/2

Ԧ𝑗 = 𝑗0𝑒𝑗(𝜔𝑡−𝑘𝑧−𝜓)𝑢𝜙

𝑖1 𝑡 = 𝐼0 cos 𝜔𝑡

𝑖2 𝑡 = 𝐼0 cos 𝜔𝑡 −2𝜋

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𝑖3 𝑡 = 𝐼0 cos 𝜔𝑡 −4𝜋

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• ALIP (external inductor) seen as an Single-sided Linear Induction Machine (SLIM)

• Short primary: inductor

• Long secondary: liquid metal


Back iron

Liquid metal(secondary sheet)

Primary core with windings

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• SLIM equivalent circuit for one phase referred to primary phaseo V1 : input voltage / I1 : input current

o R1 : resistance of primary winding

o X1 : stator leakage reactance

o Xm : magnetization reactance

o X’2 : secondary leakage reactance referred to primary side (X’2 ≈ 0 for liquid secondary sheet)

o R’2 : liquid metal annulus resistance referred to primary side

o 𝑠 =𝑣𝑠−𝑣𝑓

𝑣𝑠: slip

o 𝑣𝑠 = 𝜆𝑓 = 2𝜏𝑓 : magnetic field velocity

o vf : liquid metal velocity

o Iron losses neglected

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• Expression of circuit parameters (3-phase ALIP): R1

𝑅1 = 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 ×𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟

𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟≈ 𝑟𝐶𝑢

𝑊1𝜋𝐷00,6𝑤ℎ

𝑊1/(2𝑝𝑞)

= 𝑟𝐶𝑢2𝑝𝑞𝜋𝐷0𝑊1

2

0,6𝑤ℎ

o rCu : electrical resistivity of conductor (ex. copper)o W1 : number of coil turns per phaseo D0 : average diameter of a coil turno p : number of pole pairso q : number of slot/pole/phaseo w : slot widtho h : slot deptho Hypothesis : 60% of the coil cross section is made of conductor


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• Expression of circuit parameters (3-phase ALIP): X1

o W1 : number of coil turns per phase

o D0 : average diameter of one turn of coil

o p : number of pole pairs

o q : number of slot/pole/phase

o w : slot width

o h : slot depth

o d : slot depression depth

o Hypothesis: rectangular slots of constant width


w

h

d

𝑋1 = 2𝜋𝑓𝐿1 ≈2𝜋𝑓 2𝜇0𝑊1

2𝜋𝐷0ℎ − 𝑑3𝑤

+𝑑𝑤

𝑝𝑞

coil

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• Expression of circuit parameters (3-phase ALIP): R’2 & Xm


• rlm : electrical resistivity of liquid metal

• W1 : number of coil turns per phase

• Dc : average diameter of liquid metal annulus

• p : number of pole pairs

• τ : pole pitch

• ge : effective air gap (𝑔𝑒 = 𝐾𝑐 × 𝑔)

• g : air gap

• Kc : Carter’s coefficient

• dc : annulus thickness

• Hypothesis: single layer winding, 1 phase/slot (winding factor kw ≈ 1)

𝑅′2 ≈ 𝑟𝑙𝑚6𝜋𝐷𝑐𝑊1

2

𝑝𝜏𝑑𝑐

𝑋𝑚 = 2𝜋𝑓𝐿𝑚 ≈ 2𝜋𝑓6𝜇0𝜋𝐷𝑐 𝜏𝑊1

2

𝜋2𝑝𝑔𝑒

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• Computation of pressure rise (3-phase ALIP):

Useful output power: 𝑃𝑈 = 3𝑅2′ 1−𝑠

𝑠𝐼2𝑟𝑚𝑠′ 2 = (Δ𝑃𝐸𝑀𝑄)

Pressure from EM force: Δ𝑃𝐸𝑀 = 3 𝐶𝐼1𝑟𝑚𝑠2

Q

𝑅′2 1−𝑠

𝑠𝑅2′ 2

𝑋𝑚2 𝑠2

+1

Finite length effect coefficient: 𝐶 =2𝑝−1

2𝑝+1

Pressure loss (fluid viscosity): Δ𝑃𝑙𝑜𝑠𝑠 =1

2𝜌𝜆 2𝑑𝑐

2𝑝𝜏𝑣𝑓2

Available pressure: Δ𝑃 = Δ𝑃𝐸𝑀 − Δ𝑃𝑙𝑜𝑠𝑠


60 l/min, 1.3 bar ALIP (KAERI)

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6. Ideal ALIP model


1. Consider two, infinitely long perfect ferromagnetic cylinders

2. Sheet layer of external linear current density is spread on surface of external cylinder

3. Cylindrical layer of liquid metal with conductivity 𝜎, height 𝑑ℎ and mean radius 𝑅 is moving axially with velocity 𝑣 in the annular nonmagnetic gap with height 𝑑𝑚

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6. Ideal ALIP model


ቚ𝐵𝑧𝑟=𝑟𝑜

= 𝜇0𝐼𝑙𝑖𝑛From Amperes law follows boundary condition:

𝜕2 𝑟𝐵𝑟𝜕𝑟2

+𝜕2𝐵𝑟𝜕𝑧2

− 𝜇0𝜎𝑑ℎ𝑑𝑚

𝜕𝐵𝑟𝜕𝑡

+ 𝑣𝜕𝐵𝑟𝜕𝑧

= 0

Induction equation (r component) to solve in the gap:

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6. Ideal ALIP model


𝜕2 𝑟𝐵𝑟𝜕𝑟2

+𝜕2𝐵𝑟𝜕𝑧2




= 0

Let us height-average induction equation (otherwise solve for vector potential 𝐴 ):

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𝑑𝑚∙ ቤ𝜕 𝑟𝐵𝑟𝜕𝑟

𝑟=𝑟𝑖

𝑟=𝑟𝑜

+𝜕2𝐵𝑟𝜕𝑧2



+ 𝑣𝑧𝜕𝐵𝑟𝜕𝑧

= 0

𝜕 𝑟𝐵𝑟𝜕𝑟

= −𝜕𝐵𝑧𝜕𝑧

Using divergence of 𝐵 and boundary conditions, height-averaged form is obtained:

𝜕2𝐵𝑟𝜕𝑧2




= 𝑖𝛼𝜇02𝐴

𝑑𝑚

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6. Ideal ALIP model


Looking for solution in form:

𝜕2𝐵𝑟𝜕𝑧2




= 𝑖𝛼𝜇02𝐴

𝑑𝑚

𝐵𝑟 = 𝐵 ∙ 𝑒𝑖 𝛼𝑧−𝜔𝑡

𝐵 =𝐵0

𝑖 + 𝑅𝑚𝑠

Complex amplitude of magnetic field is obtained:

Where external field has been introduced:

𝐵0 =𝜇0 2𝐴

𝑑𝑚𝛼

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6. Ideal ALIP model


𝐵 =𝐵0

𝑖 + 𝑅𝑚𝑠

Slip magnetic Reynolds number:

𝑅𝑚𝑠 = 𝑅𝑚 ∙ 𝑠

𝑅𝑚 =𝜇0𝜎𝑣𝐵𝛼

𝑑ℎ𝑑𝑚

Magnetic Reynolds number:

Slip:𝑠 = 1 −

𝑣

𝑣𝐵

Velocity of magnetic field:

𝑣𝐵 =𝜔

𝛼= 2𝜏𝑓

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6. Ideal ALIP model


Height averaged induced current density follow from Amperes law:

ҧ𝒋 = 𝑗 ∙ 𝑒𝑖 𝛼𝑧−𝜔𝑡 𝒆𝝋 =1

𝜇0∙𝜕𝐵𝑟𝜕𝑧

−𝐼𝑙𝑖𝑛𝑑𝑚

𝒆𝝋 = −𝑅𝑚𝑠

𝑖 + 𝑅𝑚𝑠∙2𝐴

𝑑𝑚∙ 𝑒𝑖 𝛼𝑧−𝜔𝑡 𝒆𝝋

Quasi-stationary developed pressure can be found using complex amplitudes:

∆𝑝 = 𝑅𝑒𝑗𝐵∗

2∙𝑉

𝑆∙𝒆𝝋 × 𝒆𝒓

𝒆𝒛

∆𝑝 =𝜎𝐵0

2𝑣𝐵𝐿

2∙

𝑠

1 + 𝑅𝑚𝑠2

It leads to a relatively simple formula widely used in EMP design:

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What is slip magnetic Reynolds number?

Slip magnetic Reynolds number:

𝑅𝑚𝑠 = 𝑅𝑚 ∙ 𝑠

Magnetic Reynolds number:

Slip:

𝑅𝑚 =𝜇0𝜎𝑣𝐵𝛼

𝑑ℎ𝑑𝑚

𝑠 = 1 −𝑣

𝑣𝐵

Velocity of magnetic field:

𝑣𝐵 =𝜔

𝛼= 2𝜏𝑓

What does it characterize???

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One definition can be : ratio of magnetic field convection and diffusion.

What does it characterize?

In context of ALIP: ratio of induced and full magnetic fields.

𝑅𝑚𝑠 =𝜇0𝜎(𝑣𝐵 − 𝑣)𝜏

𝜋

𝑑ℎ𝑑𝑚

Electrical conductivity Relative motion of magnetic field

Characteristic size (pole length)

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𝒗𝑩 = 𝟐𝝉𝒇

𝒗𝒎

Distribution of height averaged external magnetic field in ALIP

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∆𝑝 =𝜎𝐵0

2𝑣𝐵𝐿

2∙

𝑠

1 + 𝑅𝑚𝑠2 ~

𝑅𝑚𝑠

1 + 𝑅𝑚𝑠2

Developed EM pressure in Ideal ALIP is function of 𝑅𝑚𝑠 :

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,5 1 1,5 2 2,5

p'

Rms

Rms -> 0

Rms - > inf

Rms/(1+Rms^2)

Maximum EM pressure/force

High Flowrate Low Flowrate

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Induced and full field as function of 𝑅𝑚𝑠. Phase of induced field as function of 𝑅𝑚𝑠.

Demagnetization - Lenz Law – Skin effect – Magnetic field expulsion

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∆𝑝 =𝜎𝐵0

2𝑣𝐵𝐿

2∙

𝑠

1 + 𝑅𝑚𝑠2 ~

𝑅𝑚𝑠

1 + 𝑅𝑚𝑠2

Developed EM pressure in Ideal ALIP is function of 𝑅𝑚𝑠 :

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,5 1 1,5 2 2,5

p'

Rms

Rms -> 0

Rms - > inf

Rms/(1+Rms^2)

Stable Unstable

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Operating point of ALIP is defined by pressure – flowrate characteristics of pump and hydraulic load (loop).

∆𝑝

𝑄

∆𝑝𝐸𝑀∆𝑝𝐿

∆𝑝

𝑅𝑚𝑠

1

∆𝑝𝐿

∆𝑝𝐸𝑀

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In experimentally reported

behaviour of a large ALIP for SFR by

Ota et al. three principal operating

areas were identified and

summarized:

1. Stable, homogeneous flow.

Nominal operation regime.

2. Transient, instability. Operation

is impossible in this area.

3. MHD instability. Inhomogeneous

flow, large fluctuation of flowrate

and pressure. Undesirable

operation regime.

Stable

Unstable

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Stalling condition:

𝜕 ∆𝑝𝐸𝑀𝜕𝑄

>𝜕 ∆𝑝𝐿𝜕𝑄

∆𝑝

𝑄

∆𝑝𝐸𝑀

∆𝑝𝐿∆𝑝𝐿

No stalling!

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Valve opening

Valve closing

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Stalling in context of ALIP isuncontrolled transient from stableregion (1) to unstable (3).

Why stalling and transition tounstable region (3) is undesirable?

Region (3) is characterizedby MHD instability.Behaviour of ALIP is verydifferent. E.g. steady flowassumption falls apart.

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Linards Goldšteins / Emmanuel Lo Pinto

A: vz fz or vz fz

Stable velocity profile

B: vz fz or vz fz

Instable velocity profile

Stable

1. Cut!

2. Unfold!

Periodic boundariesφ

zφ

zr

INLET

OUTLET

B A

𝑅𝑚𝑠 =𝜇0𝜎 𝑣𝐵 − 𝑣𝑧 𝑑ℎ

𝛼𝑑𝑚≈ 1

∆𝑟 ≪ 𝑅

OUTIN

OUTIN

MHD pumps: Annular Linear Induction Pumps (ALIP)

Unstable

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Linards Goldšteins / Emmanuel Lo Pinto

Gailītis et al. (1975)MHD instability threshold

𝑅𝑚𝑠 > 1 +𝑚𝜏

𝜋𝑅

2

Kirillov et al. (1980)

Ota et al. (2004)

Araseki et al. (2004)

Experimental evidence

Araseki et al. (2004)2D φ-z model of ALIP

Sta

ble

1. Amplifications of

azimuthal

unhomogenities

4. Strongly vortical

flow

2. Low frequency

pressure pulsations

3. Vibrations

5. Decrease of

efficiency

OUT

IN

IN

MHD pumps: Annular Linear Induction Pumps (ALIP)

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Experimental pump

FLIP-2

FLIP-1

Integral measurements:

• Flowrate

• Temperature

• Current

• Voltage

• Pressure

+ Pressure pulsations

Technological pump

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144 point magnetic field measurements fixed on inductor (grid y-z: 50 x 60 mm)

Bx

Bx

Bx

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Controlled parameters:

• Applied current I to FLIP (N)

• Flowrate Q in the loop (Rms)

Operating regimes:

𝑁 = 0.67𝑅𝑚𝑠 = 4.8…3.43

𝐼 = 220 [𝐴]𝑄 = 0…42 [𝐿/𝑠] = 0…151 [𝑚^3/ℎ]

Power supply of f = 50 Hz was used.

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EXP:

|Bx|, [T]



NUM:

vz, [m/s]

NUM:

|Bx|, [T]

• Development of M –

shaped flow profile

• Steady distribution of

|Bx|

𝑅𝑚𝑠 = 3.43𝑄 = 40 𝐿/𝑠

• Qualitative agreementspatial resolution: 50 x 60 [mm]

temporal: 0,05 [s]

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EXP:

|Bx|, [T]

• Agreement maintained



NUM:

vz, [m/s]

NUM:

|Bx|, [T]

• Pronounced M-

shaped flow profile.

• Negative velocity in

centre of outlet

• Small oscillation of

|Bx| in the outlet

𝑅𝑚𝑠 = 3.82𝑄 = 30 𝐿/𝑠

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EXP:

|Bx|, [T]



NUM:

vz, [m/s]

NUM:

|Bx|, [T]

𝑅𝑚𝑠 = 4.15𝑄 = 20 𝐿/𝑠

• Oscillations confirmed

experimentally

• Transition to vortical flow

• Periodic oscillations of

vz and |Bx|

• Strong recirculation in

centre

• Loss of symmetry

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EXP:

|Bx|, [T]• Qualitative agreement

maintained



NUM:

vz, [m/s]

NUM:

|Bx|, [T]

• Flow strongly vortical

all-over the channel

• Irregular oscillations of

vz and |Bx|

𝑅𝑚𝑠 = 4.47𝑄 = 10 𝐿/𝑠

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11. Experimental and numerical studies on PEMDYN loop (CEA)


PEM specification

Fluid Liquid sodium

Flowrate 0 - 1500 m3/h

Temperature 115 - 200°C

Input current 0 – 550 A

Supply frequency 5 – 20 Hz

Max power input 325 kW

Phases 3

Pole pairs 3

Slots/pole/phase 2

Stator length 2 m

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11. Experimental and numerical studies on PEMDYN loop (CEA)• Accuracy of numerical models in support of pump design: performance curves

Discrete inductor model

Current sheet model


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11. Experimental and numerical studies on PEMDYN loop (CEA)• Accuracy of numerical models in support of pump design: DSF amplitude estimate


Time (s) Frequency (Hz)

Time (s) Frequency (Hz)

Rms > 4

Rms < 1

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Useful resources

• General EM pumps design guidelines and feedback• Baker & Tessier – Handbook of electromagnetic pump technology

• Induction machines design• Nasar & Boldea – The induction machines design handbook (2nd Edition)

• MHD instabilities• E. Martin Lopez - Study of MHD instabilities in high flowrate induction

electromagnetic pumps of annular linear design (PhD thesis)

• L. Goldšteins – Experimental and numerical analysis of behavior of electromagnetic annular linear induction pump


Thank you for your attention!

Any questions?

14/04/2021 2021 - March 31

MHD pumps: Annular Linear Induction Pump (ALIP)

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Transcript of MHD pumps: Annular Linear Induction Pump (ALIP)