Superconducting thermo-magnetic-mechanical energy conversion machine


 This paper presents a superconducting thermo-magnetic-mechanical (STMM) energy conversion process. This energy conversion concept revolves around of utilizing a cryogenic coolant, e.g., liquid nitrogen, as a thermal energy facilitator to cool down the superconductor to below the critical temperature. Then, utilizing the mixed state, i.e., Meissner effect and weak vertex - which leads to partially shielding the magnetic field - an external magnetic field is used to apply force on the superconductor and create motion. The concept proposed is demonstrated using thorough Multiphysics understanding i.e., thermal, magnetic, and mechanical. The proof of concept is completed by using a combination of analytical and numerical simulations and calculations, and measurements. Using this concept, a practical automotive drive has been theoretically designed and compared with a counterpart electric drive. The proposed technology has a potential to provide a step change for the sustainable cleaner cost-effective transportation.

weak vertex. Therefore, the superconductor will partially shield the external magnetic field thus resulting in a force applied on the superconductor which will move the superconductor resulting in motion.
Once the motion has happened, the superconductor temperature will be increased from the critical temperature, hence achieving the normal state by losing the superconducting state. This would result in the removal of the force that has been generated/applied by the external magnetic field due to the magnetic shielding. Hence, the superconductor can move back to the original position with the help of a mechanical arrangement.
The paper presents an illustration of the proposed energy conversion system and provides a detailed explanation of the process. Furthermore, a measurement has been conducted to experimentally measure the equivalent relative permeability of the superconductor under the superconducting state. Finally, a practical system that utilizes the STMM energy conversion system has been proposed and theoretically designed. This system shows a suitable performance, i.e., torque and speed, for a direct-drive marine propulsion application. The proposed system has the advantages of longer running time as compared to the conventional electric machine drive used in such application. This is because the consumption of the liquid nitrogen, i.e., energy facilitator, in the proposed system is around five times lower than the electric power in the conventional electric machine drive.

2-Flux expulsion (shielding) in superconductors
Below lower critical field Bc1 (full shielding) Based on the literature on Type II superconductors, a full shielding occurs below the lower critical field due to the exhibition of Meissner effect. The lower critical field of some Type II superconductors around the critical temperature of -196ºC can be as high as 0.05T 2 . Thus, at such field, a superconductor completely expulses the magnetic field independent of the size of the superconductor 3 , whether the superconductor field cooled or zero-field cooled 4 .
Above lower critical field Bc1 (partial shielding) A partial shielding can be achieved with an external field above the lower critical field. The magnitude of partial shielding would depend on the operating temperature along with factors mentioned herewith. The shielding then depends on the size of the superconductor and depending on whether the superconductor is field cooled or zero-field cooled 5 . This effect can be presented in the form of the equivalent.

3-Superconductor thermal states
The critical temperature of the superconductor is the threshold where the state changes from normal to superconducting. From the literature, the change in the resistance of the superconductor from the maximum value to zero occurs over a few degrees Celsius, e.g., from -175°C to -168°C a difference of 10°C.
It can also be interpreted as, the change in the magnetic susceptibility of a superconductor occurs over a few degrees Celsius when the superconductor is zero-field cooled. However, when the superconductor is field cooled, the magnetic susceptibility change occurs over a relatively wider range, e.g., from -190ºC to -210°C a difference of 20°C 6 . Fig. 1 presents an illustration of the superconducting state change with temperature.  Fig. 2 presents an illustration of the superconductor thermos-magnetic energy conversion process. A magnetic circuit consists of a permeant magnet, permeable material shaped C structures and a superconductor. In the normal state, the superconductor behaves like a reluctance gap with an equivalent relative permeability of one and therefore the magnetic field flows through the circuit, i.e., 'on state', shown in Fig. 2 (a). In the superconducting state, the equivalent relative permeability of the superconductor reduces to zero if the magnet field is below the lower critical. Hence, the reluctance of the superconductor becomes infinite and block the flux from passing, as shown in Fig. 2 (b). However, if the external magnetic field is above the lower critical field, the reluctance of the relative permeability of the superconductor is between 0 to 1, hence large reluctance. Depending on the level of the applied external field and temperature, the superconductor partially blocks the magnetic field leading to a reduced magnetic field passing through the circuit, as shown in Fig 2 (c).

5-Numerical and analytical design of superconductor-thermo-magneticmechanical energy conversion drive
To use the concept of superconductor-thermo-magnetic-mechanical in a practical system to generate mechanical power, a proposed system is shown in Fig 3. The proposed system consists of three main parts, 1) the rotating machine, 2) the thermal control reservoir and 3) the tank (energy storage). To mathematically evaluate the performance of the system, each part will be analysed separately.

The rotating machine
At first, to understand the concept to generate mechanical power, an illustration of the force generated on a superconductor is presented. Using the layout presented in Fig.   4 where the flux source produces a flux below 0.1T (the lower critical field), thus, superconductor relative permeability is set to zero. The force acting on the superconductor does not change with the increase in the thickness of the superconductor. Using finite element analysis (FEA), the layout presented in Fig. 4 has been rigorously analysed. In the study, the superconductor thickness changed from 1mm to 10mm with an interval of 2mm. The force versus the distance of the superconductor to the source is calculated and presented in Fig. 5. With the variation of the thickness of the superconductor no change is observed. Therefore, theoretically, the force produced is independent of the thickness of the superconductor. On the other hand, above the lower critical field, the change in the external magnetic field leads to different flux vertices and therefore varying the equivalent relative permeability of the superconductor accordingly. The same layout in Fig. 4 has been used to study the effect of the equivalent relative permeability on the exerted force. A magnetic field of the magnetic field source has been increased to 0.5T and a superconductor relative permeability of 0.2 has been used 7 . Fig. 6 presents the force versus the distance of the superconductor with a relative permeability of 0.2.
It is worth noting that modelling superconductor in FEA requires taking into account the effect of the London equation and using a formulation such as T-A 8 .
However, equivalent relative permeability can also be used to simulate the superconductor in FEA with good accuracy 7, 9-13 . A rotating machine topology can be made by utilizing the exerted force on the superconductor. Fig. 7 (a) presents a proposed rotating topology utilizing the concept.
The topology consists of a ring of superconductor made of 45 degrees segments, and a permanent magnet set to produce magnetic flux with a ferromagnetic material to enhance the magnetic circuit. Fig. 7 (a) presents the FEA setting for the rotating topology. The outer diameter of the topology is 45mm, the axial length is 25mm and the airgap between the superconductor ring and magnets is 0.5mm. As illustrated in Fig. 7 (a), the superconductor segments above the X-axis are set to a normal state, i.e., relative permeability of 1, and the segments below the X-axis are set to superconducting state with a relative permeability lower than 1. The rotor, shown in Fig. 7 (a) is set to rotate a cycle of 45 degrees. Different relative permeability values of the superconductor were analysed, in order to predict the influence on the torque production. Table 1 presents the average torque of the different investigated cases of relative permeability, and Fig. 7 (b) presents magnetic flux lines and magnetic flux density in the rotating machine.  The thermal control reservoir The thermal reservoir is the section where the temperature of the superconductor is cyclically changed above and below the critical temperature to maintain the rotation. It consists of a liquid nitrogen reservoir covering half the superconductor ring -which is the cool-down section -and a heat dissipation mechanism, which is the heat up section. Initially, the temperature of the superconductor is reduced from room temperature (20ºC) to the liquid nitrogen boiling temperature of -196ºC. Subsequently, the thermal cycle consists of increasing the temperature by the difference required to change the superconductor from the superconducting state to normal state, e.g., from -196ºC to -166ºC (30ºC) for YBCO superconductors. This cycle consists of two states: 'heat up' and 'cool down'. The first is when the superconductor temperature is raised from below to above critical temperature ('heat up'), i.e., from -196ºC to -166ºC. The second stage is when the temperature is reduced from above to below the critical temperature 'cool down', i.e., from -166ºC to -196ºC. Fig. 9 presents an illustration of the cool-down condition.   On the other hand, the 'heat up' condition can be made by natural convection of the superconductor to the environment. However, to reduce the time for the heat up, four different mechanism were investigated. Fig. 10 presents an illustration of the different mechanism: (a) is the natural convection method, (b) a heat dissipation surface near the superconductor with a small airgap, (c) a heat dissipation surface with direct contact with weak contact conductance and (d) a heat dissipation spinning mechanism with direct contact with high contact conductance. Table 3   The calculation shows that for a thin layer of 2mm superconductor exposed to liquid nitrogen, the cooled-down time is 0.1s, and the same layer heat-up using the mechanism, However, the cooling down temperature is the cut-off limit for the system. Therefore, the 2mm superconductor can have a maximum change time of 0.1s, hence a 300rpm.

The tank
In the proposed system, the coolant, e.g., the liquid nitrogen, acts as the energy facilitator. The container that reserves the liquid nitrogen is the fuel tank for the system.
This consists of a thermal dewar (flask) to store the liquid nitrogen and insulated pipes to contact the tank to the thermal control reservoir. The thermal dewar and thermal pipes have very high thermal insulation i.e., 0.00104 evaporation rate of millilitres per second.
Therefore, the evaporation of the liquid nitrogen through the thermal dewar and thermal pipes will be neglected. As a result, the liquid nitrogen will mostly be consumed by the contact with the superconductor surface. To estimate the consumption time of a finite amount of liquid nitrogen in contact with the superconductor surface, the following equation can be used: Evaporation rate= (change in temperate/liquid surface resistance)/enthalpy Liquid surface resistance= liquid surface area/liquid conductivity Therefore, to maintain the operation for a longer period of time, the temperature difference and the surface area of superconductor needs to be as small as possible. Using the above equations, Table 4 presents the evaporation time of 50 litres of liquid nitrogen at different temperature differences and different superconductor surface areas.

6-Equivalent permeability measurements
To measure the equivalent relative permeability of the superconductor, a measurements set-up was created, as shown in Fig. 11 (a). The experimental set-up consists of a YBCO-123 disk, a NdFeB magnet to produce the external magnetic field, and a gauss-meter to measure the level of the magnetic field, as shown in Fig. 11 (c). The experiment is conducted in field cooled state, i.e., the superconductor cooled in the presence of the external field, as shown in Fig. 11 (d). The magnetic field passing through the superconductor has been measured when the superconductor is in normal state and is in superconducting state. Fig. 11 (b) presents an FEA simulation of the experiment. The FEA simulation is used to calculate the equivalent relative permeability of the YBCO-123 that matches the experimental values. In normal state, a 60mT magnetic field is measured and the same value has been predicted in the FEA simulation when the superconductor relative permeability is 1. In superconducting state, a 40mT magnetic field is measured and the FEA simulation predicted the same value when the relative permeability of the superconductor is 0.2.

7-Validation of liquid nitrogen evaporation time
Using the thermally insulated cup presented in Fig. 11 (6

8-Practical STMM drive
Since analysis shows that the concept of STMM can produce relatively high torque and low speed, a practical drive targeting application with similar requirements will be theoretically designed. Direct-drive propulsion systems are characterized by their low speed and high torque to meet the power requirement. In marine applications, i.e., ship propulsion, the engine or electric motors used for propulsion normally rotate between 50 to 500rpm. An electric drive system proposed for marine application with speed of 50rpm and torque of around 840Nm has been used as a benchmark 14 . Table 5 lists the performance, size and weight of the whole drive including the electric motor, inverter and batteries. The electric motor drive provides the full required power at 50rpm and 20 battery cells provide 1 hour of total operation time. The total weight of the system is 187.6kg and the total volume is 0.129m 3 . Table 6 presents the performance of the system.   12 presents a proposed STMM drive which will achieve the performance criteria in Table 6. The drive consists of rotating the superconductor ring sandwiched between two magnet cores modules. Half of the ring is located in a liquid nitrogen container and the second half is partly sandwiched between free-to-spin wheels connected to thermal dissipater. Thermal insulation is located in the middle, between the two halves, to eliminate unnecessary heating of the liquid nitrogen. To estimate the performance, the drive rotating machine is analysed using magnetic FEA. The thermal mechanism is analysed using thermal FEA, and the consumption of liquid nitrogen is calculated using the equations in section 5.
The rotating machine consists of NdFeB magnets with a magnetic field of 1.2T, ferromagnetic core with B-H curve, and a YBCO superconductor ring. FEA modelling is used to calculate the torque in the same setting, as presented in section 5. The equivalent relative permeability of the YBCO superconductor under an external field produced by NdFeB magnets is 0.2 9 . Therefore, in the FEA model, the relative permeability of the YBCO in superconducting has been set to 0.2. Fig. 13 presents the FEA layout and results.
Maximum torque of 905Nm and average torque of 860Nm has been predicted.

9-Conclusion
The STMM energy conversion concept has been illustrated and explained in this paper. The concept consists of utilizing the magnetic flux expulsion (shielding) of the superconductor that occurs at a small temperature difference when the superconducting state changes from normal to superconductor. The superconducting thermo-magneticmechanical concept can be utilized to generate electrical power by using a magnetic circuit with winding; mechanical power, by creating a linear motion or rotation, or both.
The superconductor coolant, i.e., energy facilitator, and the storage of such coolant, i.e., thermal dewar, is the energy storage of the system. A theoretical design of the system using numerical and analytical methods demonstrated a promising performance of the system. The proposed practical STMM drive for marine propulsion has a comparable performance to its counterpart electrical drive system, with the advantage of longer duration of operation. The proposed STMM drive can use different coolant, i.e., energy facilitator, with lower boiling temperature such as liquid helium or liquid hydrogen. Using a lower boiling temperature coolant increases the magnetic flux shielding capability of the superconductor and therefore increases the torque production. Similarly, the temperature gradient between the critical temperature and liquid temperature considered in this study is large and therefore higher rotation is expected. This makes such drive suitable operatable by different coolant.

Experimental methods
To realize the equivalent relative permeability of the YBCO-123, a commercial disk (22mmX2mm) has been used. A NdFeB (grade N42) commercial magnets (10X5X2) has been used. A cryogenic thermal insulation cup has been used to conduct the temperature change by liquid nitrogen. Temperature reading has been conducted using Type T, -200ºC -+350ºC, thermocouple and thermometer type MM2020, -200ºC -+1372ºC. The magnetic field has been measured using gauss meter grade WT10A.