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Eddy Current Reduction in an Annular Linear Induction Pump Ryan M. Sullenberger∗ NASA - Marshall Space Flight Center, Huntsville, Alabama, 35812

The predicted performance of an alternate magnetic stator material for use in induction pumps is presented. Magnetic field modeling of a liquid metal Annular Linear Induction Pump (ALIP) is used to compare the performance of stators comprised of iron and Fluxtrol. The ALIP being modeled will be incorporated into a sodium potassium (NaK) loop designed to simulate conditions in a nuclear reactor proposed as a power source for a lunar surface base. Based on the conductivity disparity between Fluxtrol and iron, it is hypothesized that the ALIP magnetic circuit can be fabricated as a monolithic piece of Fluxtrol, rather than using iron separated by laminate layers which are employed to reduce eddy currents. The NaK loop’s operating conditions call for a temperature in excess of 880 K, and these temperatures could cause delamination over time. Fluxtrol is a highly magnetically permeable material yet possesses an electrical conductivity many orders of magnitude lower than iron, which leads to minimal eddy current formation in the stators and consequently lower electromagnetic losses and a higher pump efficiency.

Nomenclature 𝐵 𝐵𝑟 𝐵𝑧 𝐷𝑚 𝐻 𝐼 𝑙 𝑃 𝑤 𝜇0 𝜇 𝜌 𝜎 𝜏

Flux density Radial component of flux density Longitudinal component of flux density Magnetic diffusivity Permeability of free space Electric current Magnetic penetration length Magnetic permeability Stator leg width Permeability of free space Magnetic permeability Z component of flux density Conductivity Reciprocal of frequency (period)

I.

Introduction

he National Aeronautics and Space Administration (NASA) has plans to return to the Moon by the T year 2020. When this happens, there will be need for a dependable, reliable energy source to provide power for a manned base. The use of solar power requires not only large arrays to harness sunlight, but also batteries to store power for the lunar night (which lasts 14 Earth days). Research and development at Marshall Space Flight Center (MSFC) is geared toward developing a nuclear-based lunar surface power system. A nuclear power reactor can provide power at anytime, capable of operating through the lunar night ∗ Summer Intern, Propulsion Research and Technology Applications Branch, Propulsion Systems Department, Student member AIAA.

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or in permanently shaded regions such as craters. A nuclear system of the type being considered could be used on both the lunar surface and the surface of Mars. Recent efforts at MSFC have lead towards the development of a safe, simulated nuclear power reactor that is equipped with resistive heater elements instead of live nuclear components that accurately depict the operating conditions of a fully functioning reactor. The fission surface power reactor simulator is referred to as the Fission Surface Power - Primary Test Circuit (FSP-PTC). Heat is extracted from the reactor using the liquid metal sodium potassium (NaK-78). The NaK flows through a loop by first encountering a linear induction pump, flow meter, the resistive heater elements to extract heat, and a heat exchanger before completing the loop.

II.

Liquid Metal Pumps

Liquid metal pumps can be built with zero moving parts, and they take advantage of the fact that liquid metals are capable of conducting electric currents.1, 2 In general, NaK flows through a channel that contains a magnetic field (B) and electrical current (I), both perpendicular to the flow and to each other, exerting a Lorentz body force on the NaK.1 The simplest form of a liquid metal pump is a conduction pump whose schematic can be found in Figure 1a, where electrodes provide a constant current, and permanent magnets or electromagnets provide the magnetic field.

Figure 1. Components of a Liquid Metal Pump. (a) shows the simplest schematic for what would be a DC conduction pump and (b) is the schematics for an annular linear induction pump.

The FSP-PTC NaK loop receives its ΔP from an Annular Linear Induction Pump (ALIP). An ALIP consists of an annular channel for the NaK to flow with a magnetically permeable core most usually composed of Cobalt. There exists several sets of wires wrapped around the channel as coils, and a magnetically permeable material which we will call the stators between the coils to complete the magnetic circuit. An isometric cutaway exposing the internals of an ALIP can be found in Figure 3. As a time varying electrical current passes through the coils, a magnetic field is produced that travels through the conducting fluid. An electrical current within the NaK is induced by this traveling magnetic field, and results in a Lorentz force acting upon the NaK in the direction of flow.2–5 The magnetic fields and induced currents can be referenced in Figures 1 and 2. An ALIP is well suited for the NaK loop due to its capability of handling larger flow rates at typically higher efficiencies than that of an equivalent conduction pump.1 The material used for the stators play a significant role in a pump’s efficiency

III.

Performance Loss Mechanisms

An ALIP, just like any other pump, experiences several unavoidable loss mechanisms. The coils wrapped around the duct experience resistance heating (also known as 𝐼 2 𝑅 power loss), and the same goes for the conducting fluid within the channel. Eddy currents are developed in the iron stators that encompass the coils due to the time varying magnetic fields.1 No real work is performed by the eddy currents in the stators.

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Figure 2. Induced Magnetic Fields and Currents in an Annular Linear Induction Pump (from [1]).

Figure 3. Cutaway of an ALIP.

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III.A.

Iron Laminate Stators

One way to help eliminate the eddy currents is to use a stator composed of an iron laminate. An iron laminate will provide an excellent way of keeping the permeability high while also lowering the electrical conductivity to essentially zero at the same time. With zero electrical conductivity the eddy currents in the stator would be eliminated, increasing the overall efficiency of the pump. Using an iron laminate stator is not the best idea for an ALIP. For one thing, it would be costly to manufacture, but the main concern would be the extreme heat the stator would be exposed to, severely elevating the risk of delimitation over a period of time.1 III.B.

Fluxtrol Stators

Fluxtrol is a candidate for a material to use as stators instead of an iron laminate in the ALIP at MSFC. The unique material is able to possess excellent thermal properties while at the same time being easy to machine with great mechanical properties. Fluxtrol’s large resistivity is strongly desirable, as eddy currents will have a more difficult time forming. Despite the high resistivity, Fluxtrol is an excellent permeable material, perfectly capable of conducting magnetic fluxes. In all extensive purposes, Fluxtrol behaves in the same way an iron laminate would magnetically, but does not pose a risk of delamination and is cheaper and easier to manufacture. For a complete list of material properties, reference Table 1. Table 1. Fluxtrol material properties.

Density (g/cm3) Operating Freq. Range (kHz) Maximum Permeability Temperature Resistance (K) Resistivity (kOhm*cm)

IV. IV.A.

Fluxtrol A 6.6 1-50 120 573 0.5

Electromagnetic Simulation

Simulation Setup

The simulations that were performed of an ALIP were done in a finite element analysis (FEA) software package called QuickField. QuickField is phenomenal for performing any type of electromagnetic field simulations. The flux densities and eddy currents resulting from the use of iron, fluxtrol, and an iron laminate were recorded and compared. Due to the design of the ALIP as can be seen in Figure 3, an axisymmetric simulation was appropriate. The axisymmetric model with magnetic flux lines can be seen in Figure 4. The ALIP that is currently being used at MSFC contains iron stators and a cobalt core. The flow channel is 15.575” long and 2.375” in diameter. The cobalt core is also 15.575” in length, and has a diameter of 1.750”. For the simulations, the conductivity and relative permeability for the different materials needed to be known. Fluxtrol, iron, and cobalt all possess a non-linear B-H curve. A B-H curve relates the magnetic flux intensity (H) to the magnetic flux density (B) using the relationship: B=𝜇⋅H

(1)

Figure 4. Quickfield axisymmetric model of an annular linear induction pump showing the magnetic field lines.

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For all other material properties, see Table IV.A. In order to successfully model a laminated stator, a conductivity of 1E-10 S/m was used to simulate nearly infinite resistance to eddy current formation. The modeled ALIP contains 12 coils, grouped into segments of three, each group containing a different phase of AC current. The first group of coils is the reference point for the next two groups whose phases are off by 120 and 240. The final group of coils remains at the same phase as the first group, or off by 360. An AC frequency of 60 Hz was used, and each coil possesses a current of 100A, for a total of 1200A for the entire ALIP coil configuration. Table 2. Material Properties

Iron Iron Laminate Fluxtrol NaK Air

Conductivity (S/m) 10405800 1.00E-10 0.2 7E6 0

Relative Permeability (u/u 0) 1 1

Each of the following current density flood plots were taken at the same instantaneous moment in time. The difference between iron and both Fluxtrol and an iron laminate can be clearly seen. The iron stators contain a current density quite large in magnitude, whereas Fluxtrol and the iron laminate show essentially zero eddy current formation. The magnitude of current densities in each material was measured in the far left stator “leg”, where it is known that the Eddy currents are in one direction only. Joule heating was also measured in the left stator leg. These quantitative results can be found in Table 3. Table 3. Blabhalbddfaah

Fluxtrol Iron Iron Laminate

IV.B.

Eddy Current (Stator Leg) 1.5931e-7 A 8.1017 A 8.954e-17 A

Joule Heating (Stator Leg) 5.086e-11 W 0.0028079 W 3.259e-20 W

Flux Density

Not only is the reduction of eddy currents important, but so is the magnitude of flux density the different materials can deliver to the NaK. The radial flux density 𝐵𝑟 , longitudinal flux density 𝐵𝑧 , and the magnitude 𝐵 were exported from QuickField at 1 inch radius from the centerline of the pump (directly in the NaK channel) for all three materials, normalized between -1 and 1, and superimposed on top of each other for comparison. See Figures ?? for details. IV.C.

Eddy Current Mapping

Eddy currents in the stators were mapped for all three materials at a 1.5 inch radius from the centerline (𝑟 = 0) of the pump. The results for Fluxtrol can be found in Figure 9 and results for iron and the iron laminate can be found in Figures XXXX and XXXX respectively. Although the graph for the eddy currents in iron stators displays a similar sinusodial shape as the Fluxtrol and iron laminate graphs, there is a clear difference as can be explained with the magnetic diffusion equation that can be written as: √ 𝜏 𝑙= (2) 𝜎⋅𝜇 where 𝜎⋅𝜇 = 𝐷𝑚 is the magnetic diffusivity, 𝜎 is the conductivity, 𝜏 is the period of the AC waveform, and 𝑙 is the magnetic penetration depth. Conductivity is the term that largely effects the different penetration depths for the different materials, because they all have relatively the same permeability, but their conductivities vary the most. The penetration depth for iron is much smaller than the width of one of the stator “legs” (𝑙 << 𝑤) whereas the penetration depths for the iron laminate and fluxtrol are much larger (𝑙 >> 𝑤). These characteristics of the different materials lead to a smooth sinusodial distribution of eddy currents in the 5 of 9 American Institute of Aeronautics and Astronautics

Figure 5. Induced current density flood plots. a) conventional iron stators; b) Fluxtrol stators; c) iron laminate stators.

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1 .2 1 .0 0 .8 0 .6 0 .4

0 .0

B

r

(T )

0 .2

-0 .2 -0 .4 -0 .6

F lu x tr o l Iro n L a m in a te

-0 .8 -1 .0 -1 .2 0

5

1 0

1 5

2 0

2 5

3 0

2 5

3 0

z ( in )

Figure 6. Flux Density. 𝐵𝑟

1 .2 1 .0 0 .8 0 .6 0 .4

0 .0

B

z

(T )

0 .2

-0 .2 -0 .4 -0 .6

F lu x tr o l Iro n L a m in a te

-0 .8 -1 .0 -1 .2 0

5

1 0

1 5

2 0

z ( in )

Figure 7. Flux Density. 𝐵𝑧

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1 .2

F lu x tr o l Iro n L a m in a te

1 .0 0 .8 0 .6 0 .4

B (T )

0 .2 0 .0 -0 .2 -0 .4 -0 .6 -0 .8 -1 .0 -1 .2 0

5

1 0

1 5

2 0

2 5

3 0

z ( in )

Figure 8. Flux Density. 𝐵

0 .0 0 0 8

0 .0 0 0 6

iE d d y ( A /m

2

)

0 .0 0 0 4

0 .0 0 0 2

0 .0 0 0 0

-0 .0 0 0 2

-0 .0 0 0 4

-0 .0 0 0 6 6

8

1 0

1 2

1 4

1 6

1 8

2 0

2 2

Z ( in )

Figure 9. Eddy currents in Fluxtrol. (1.5 in radius)

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2 4

4 .0 0 E -0 1 3 3 .0 0 E -0 1 3 2 .0 0 E -0 1 3

iE d d y ( A /m

2

)

1 .0 0 E -0 1 3 0 .0 0 E + 0 0 0 -1 .0 0 E -0 1 3 -2 .0 0 E -0 1 3 -3 .0 0 E -0 1 3 -4 .0 0 E -0 1 3 6

8

1 0

1 2

1 4

1 6

1 8

2 0

2 2

2 4

Z ( in )

Figure 10. Eddy currents in iron laminate. (1.5 in radius)

3 0 0 0 0

2 0 0 0 0

iE d d y ( A /m

2

)

1 0 0 0 0

0

-1 0 0 0 0

-2 0 0 0 0

-3 0 0 0 0 6

8

1 0

1 2

1 4

1 6

1 8

2 0

2 2

Z ( in )

Figure 11. Eddy currents in iron. (1.5 in radius)

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2 4

iron laminate and Fluxtrol stators, as opposed to the iron where you see the eddy current concentrations “fall-off” at a certain depth into the stator legs.

V.

Concluding Remarks

The immense reduction of eddy currents in the stators of an annular linear induction pump by using a material known as Fluxtrol instead of iron has been presented. The reduction of eddy currents in the pump means less power is lost and a higher pump efficiency is possible. Fluxtrol stators were also compared to a stator comprised of an iron laminate, which would effectively eliminate eddy currents altogether. Fluxtrol compared well to the iron laminate, reducing the magnitude of eddy currents in the stators by a factor of 5E7 (as compared to iron), whereas the iron laminate reduced the eddy currents by a factor of 9E16.

Appendix An appendix, if needed, should appear before the acknowledgments. Use the ’starred’ version of the \section commands to avoid section numbering.

Acknowledgments I would like to thank Dr. Kurt A. Polzin and Jon B. Pearson from Marshall Space Flight Center whose techical support and guidance made this experience possible. I would also like to thank Dr. Azer P. Yalin and Dr. John D. Williams from Colorado State University who have shared the knowledge necessary to help me grow as a professional. Finally, I would like to thank Tina Haymaker and Mona Miller, and anyone else who has made this internship a reality.

References 1 Polzin, K. A., “Liquid Metal Pump Technologies for Nuclear Surface Power,” In Proceedings of the Space Nuclear Conference 2007, pp. 363-369, Boston, MA, June 24-28, 2007. Paper 2002. 2 Baker, R.S.; and Tessier, M.J.: Handbook of Electromagnetic Pump Technology, Elsevier Science Publishing, New York, 1987. 3 Blake, L.R.: “Conduction and Induction Pumps for Liquid Metals,” Proceedings of the IEE, 104A, Paper No. 2111 U, p49, July 1956. 4 Childs, B.M.: “Electromagnetic Pumps and Flow Meters for Fast-Reactor Development,” GEC Journal of Science and Technology, Vol. 40, No. 1, p 10, 1973. 5 Watt, D.A.: “The Design of Electromagnetic Pumps for Liquid Metals,” Proceedings of IEE, No. 2763 U, December 1958.

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