MAGNETOHYDRODYNAMICS Vol. 00 (1964), No. 00, pp. 1–??

Design of Marine Vehicle Powered byMagnetohydrodynamic Thruster

C.-S. Chan1,2, J.-H. Cheng2, C.-H. Zeng3, J.-R. Huang4, Y.-H. Chen2,Y.-J. Chen3, T. T. Pham5, W.-H. Chao6, J.-T. Jeng5, T.-L. Liu2,4,

K.-C. Pan2,4,∗, Y.-H. Li2,3,†, C.-Y. Chen2,‡

1 Department of Mechanical Engineering, National Yunlin University of Science andTechnology, Taiwan, R.O.C.

2 Department of Mechanical Engineering, National Chiao Tung University, Taiwan,R.O.C.

3 Department of Mechanical and Aerospace Engineering, Chung Cheng Institute ofTechnology, National Defense University, Taiwan R.O.C.

4 Department of Power Vehicle and Systems Engineering, Chung Cheng Institute ofTechnology, National Defense University, Taiwan R.O.C.

5 Department of Mechanical Engineering, National Kaohsiung University of Science andTechnology, Taiwan, R.O.C.

6 Materials and Electro-Optics Research Division, National Chung-Shan Institute ofScience and Technology, Taiwan R.O.C.

∗Email: pankc@url.com.tw†Email: yanhom@ndu.edu.tw

‡Email:chingyao@mail.nctu.edu.tw

The present study outlines the design of a magnetohydrodynamic (MHD) thruster sys-tem, which is capable to power a 3-meter ship model cruising at a speed of V = 0.5m/s using the Lorentz force generated by the electric field and magnetic field in con-ductive seawater. Based on the computational fluid dynamics (CFD) simulation of amodified Delft 372 catamaran model, the thrust needed to achieve the targeted cruisingspeed is first estimated. To achieve the estimated magnitude of thrust, dimensions ofthruster modules are designed, based on numerical simulations of magnetic field, for bet-ter distributions of the strength and uniformity of the magnetic field. Additional CFDsimulations of the flows passing through the thruster module, coupled with magneticand electric fields, are conducted to realize the hydrodynamics. Consequently, severalconfigurations of thruster modules are manufactured and experimented. A particularconfiguration of shielded two-unit module is chosen to power the ship model. Finally,a complete system of MHD-1 marine vehicle, including a ship model, multiple MHDthruster modules and power suppliers, is assembled and tested. The system is showncapably to cruise closely to the targeted speed.

1. Introduction Magnetohydrodynamics (MHD) is a unique branch offluid dynamics concerning the dynamics and behavior of the conducting fluidsaffected by magnetic and electric fields. The typical conductive magnetofluidsinclude plasma, liquid metals, salt water and electrolytes. By using the Lorentzforce generated by perpendicularly placed magnetic field and electric current, theapplications of MHD had been interests of engineers since its initiation in 1940s [1],e.g. propulsion system [2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12], pump [13, 15, 16, 17],motor [18], heat transfer device [19], metal process [20] and generator [21]. Amongthem, the MHD propulsion applied in marine vehicles has been a long and activearea, since first proposed by Ref. [2] in 1960s, because of the conductive propertyof sea water to achieve propellerless power system. In the following developments,superconductor was applied to generate MHD propulsion [3, 4], since extremely

strong magnetic field is required to achieve better electrical efficiency, e.g., about40% efficiency at 5 Tesla [6]. However, the heavy weight as well as the complexityof superconductor prevented the practical uses of MHD propulsion. Neverthe-less, the study of MHD propulsion continues for several decades. In 1988, thecapability of MHD propulsion in a ship was successfully demonstrated [5], andlarge-scale vehicles were able to be powered by MHD thrusters, for instance theMHD-propelled Yamato 1 [9] and HEMS-1 [10] built in 1990s. It has been widelyreported that the progresses of developing MHD-propelled submarines are ongoingin recent years, e.g., news reported in Ref. [22]. Taking the advantages of the ad-vancement of key technologies of magnetism and design tools, such as permanentmagnets of neodymium iron boron, lithium battery and powerful numerical soft-ware, we intend to develop a small scale marine unmanned surface vehicle (USV)using permanent magnets. In addition, the designed marine MHD USV possessesthe potential ability of thrust vector control (TVC) by installing multiple thrusterunits. The MHD USV is expected to carry special tasks which stealth and ma-neuverability are crucial, even the electric efficiency might be extremely low. Thedetails of design procedures and tested results are reported in the present paper.

At the first stage of design, the major concern of the marine MHD USV ismainly the net propulsion, which involves the MHD thrust and hydrodynamicdrag, so that understanding of the magnetic, electric and flow fields are crucial.The governing equations of hydrodynamics incorporated with the Lorentz force inan incompressible Newtonian fluid are expressed as the augmented Navier-Stokesequations [18]

∇ · u = 0, (1)

ρ[∂u

∂t+ (u · ∇)u] = −∇p+ µ∇2u + FL. (2)

Here, t, u, p, µ and ρ denote time, velocity vector, pressure, viscosity and densityof the conductive fluid, respectively. FL represents the force density of the Lorentzforce, and takes the form of

FL = (J×B), (3)

where J and B are current density and magnetic field, respectively, and obtainedby the Maxwell equation and Ohm′s Law given as

∇ ·B = 0, (4)

J = σ[−∇ψ + (u×B)]. (5)

Here σ and ψ are the electric conductivity and electric potential, respectively. Fora sufficiently conductive medium, the electric charge is conserved, i.e., ∇ · J = 0,so that the electric potential equation is governed by

∇2ψ = ∇ · (u×B) (6)

These equations will be solved numerically to provide guidelines for better design.

2. Results and discussion

2

Figure 1: Geometry and dimension of the modified Delft 372 catamaran modeldesigned in the present study.

Figure 2: Flow field (a,c) and wave height (b,d) at t = 1 and 6 s ; (e) Temporalevolution of total drag obtained by numerical simulation of the ship model with acruising speed of V = 0.5 m/s.

3

Figure 3: (Left) Geometry and dimension of a single MHD thruster unit. Four con-figurations of thruster modules are considered: (a) single-unit module, (b) shieldedsingle-unit module, (c) two-unit module, and (d) shielded two-unit module.

2.1. Design of Ship Model The present study aims to power a scaled-downship model by the MHD thrusters with a cruising speed of V = 0.5 m/s. Thedimensions of ship model, named MHD-1 modified from the Delft 372 catama-ran model [23], is shown in Fig. 1. It had been well concluded that, resistanceon the surface ship is induced both by the viscous skin friction and the gravita-tional surface waves. To estimate the needed thrust, i.e., the total induced dragof the sailing ship model, numerical simulation is carried out to solve the full3-D unsteady Reynolds-Averaged-Navier-Stokes (RANS) equations. The compu-tational domain (30m × 6m × 2.5m) includes the seawater (or air) beneath (orabove) the surface. The viscosity and density of seawater and air are taken asµwater = 9.7×10−4 kg/m · s, ρwater = 1.023×103 kg/m3 and µair = 1.789×10−5

kg/m · s, ρair = 1.225 kg/m3, respectively. The turbulent effects are dealt withthe k− ε model. The ship model is designed to have a draught of 0.33 m beneaththe seawater surface with a displacement of 525 kg, and encounter a free streamvelocity of V = 0.5 m/s. Volume of Fluid (VOF) method is applied to capture thewaving surface of sea water. The set of equations are numerically solved by theANSYS Fluent [24], and results are shown in Fig. 2.

Figs. 2(a,c) and (b,d) show the velocity distribution on the middle cross-section from side and wave height on the surface from top, respectively, at t = 1s. When the ship model just starts to move from rest at t = 1 s, strong inducedwakes associated with significant heights of wave at bow and stern of the ship areclearly observed. The presence of strong wake and high wave results in significantresistance as shown at very early time in Fig. 2(e). As time proceeds, the wakeand wave on surface is continuously weakened, e.g., t = 6 s shown in Figs. 2(c)and (d). This strong transit phenomenon leads to significant fluctuation of thetotal resistance till t ≈ 40 s as also shown in Fig. 2(e), and eventually evolves toa nearly constant value about 7 N after t > 40. This nearly steady resistance of7 N serves as a reference value to design the MHD thrusters, whose total thrustshould be capable to overcome the resistance, and power the ship model for steadycruise.

4

Figure 4: (a) Magnetic lines and strength distribution of a plain single-unit moduleobtained by 2-D simulation. The flux lines are not shown in the iron shell wheremagnetization saturation occurs. Strength distribution obtained by 3-D simulationat the cross-section at (b) y = 0 mm and (c) y = ±25 mm.

Figure 5: (a) Magnetic lines and strength distribution of a shielded two-unit mod-ule obtained by 2-D simulation. The flux lines are not shown in the iron shellwhere magnetization saturation occurs. Strength distribution obtained by 3-Dsimulation at the cross-section at (b) y = 0 mm and (c) y = ±50 mm.

2.2. Design of Magnetohydrodynamic Thruster Module The thrust by Lorentzforce (TL) depends on the external magnetic field, so that strength and distribu-tion of the magnetic field are important for a better design of thruster module.After considering the weight of iron shell and available magnets, dimension of asingle thruster unit is proposed and shown in Fig. 3. A pair of permanent mag-nets of neodymium iron boron (NdFeB, N40) are placed at the bottom and top ofsoft-iron shell. It is noticed that, various thicknesses of the shell had been tested,and thicker shell always results in stronger magnetic strength inside the thrusteras expected. Nevertheless, considering the weight constraint, a 2-mm iron shellwas chosen to optimize the field-to-weight ratio of MHD thruster. Four config-urations of the thruster modules are considered as also shown in Fig. 3, such as(a) single-unit module, (b) single-unit module with additional shielding by NiFealloy, (c) two-unit module, and (d) two-unit module with additional shielding. De-tailed distributions of magnetic fields for these four configurations are simulatedby ANASYS Maxwell, and results are shown in Figs. 4, 5 and 6.

Fig. 4(a) shows the magnetic lines and strength distribution of the plain single-unit module by 2D simulation. The non-uniformity of the magnetic field can beclearly observed in which weaker strength locates at the central region (z = 0),

5

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.05

0.1

0.15

0.2

BZ (

T)

y (cm)

shielded 2−unit module 2−unit moduleshielded single−unit modulesingle−unit module2−unit module (sim)shielded 2−unit module (sim)

Figure 6: Measured field strength along the y-axis at the central cross-section(x=0 and z=0). Simulated results are also shown by solid lines.

especially at the edges (|x| > 25 mm). The full 3-D simulation shown in Figs. 4(b)and (c) also confirms the observation. The field distribution on the cross-section atthe central region, e.g., y = 0 mm as shown in Fig. 4(b), is between B = 0.1 ∼ 0.27T with an average of Bavg = 0.194 T. The field strength and uniformity deteriorateat the outer position of thruster module (|y| > 0). Shown in Fig. 4(c) the is fieldstrength at the cross-section of y = ±25 mm, where are the positions of 1/4 and3/4 length of the thruster unit (total 100 mm as shown in Fig. 3). The variation offield strength is enhanced with a weaker average of Bavg = 0.181 T. Also observedin Fig. 4(a) is the significant leakage of magnetic flux outside the shell becauseof magnetization saturation in the iron-shells. These results lead to two majordrawbacks: (1) dramatic reduce of magnetic strength away from the magnets, and(2) significant leakage of magnetic flux.

Based on the results shown in Fig. 4, a shielded two-unit module is considered,i.e., configuration shown in Fig. 3(d). By connecting the two units in series, regionwith dramatic drop of strength at the edges may be minimized. In addition,magnetic leakage could also be improved with outer NiFe alloy shielding. Thesimulating results of the shielded two-unit module are shown in Fig. 5. The averagefield strengths on the cross-sections at center (y = 0 mm) and 1/4 (or 3/4) length(y = ±50 mm) are raised to Bavg = 0.21 T and 0.205 T, respectively, which areimproved significantly.

Sample modules of these four configurations are manufactured, and their cor-respondent field strengths along the central axis (x = 0 and z = 0) are measuredby Gauss meter as shown in Fig. 6. In general, the measured strengths are in goodagreements with the simulations. As suggested by the simulations, the strength

6

Figure 7: Designs of (a) single-unit MHD thruster installed with a pair of alu-minum electrodes perpendicularly to the magnets, and (b) a completed two-unitthruster module. The aluminum plates fully cover the inner sides of iron shell.The arrows show the input/output of electric current I.

is stronger with shielding. In addition, the two-unit modules can elongate theregion of nearly uniform strength, so that diminishes the weaker edging effect. Asa result, the shielded two-unit module is expected for better performance to powerthe ship model.

Simulations of the current density J are also carried out to verify the betterperformance of the two-unit module. The designs of thruster unit is shown inFig. 7(a). To ensure good electrical insulation, the surfaces of NdFeB magnetsand iron shell are all coated with varnish. The electrodes, which are arranged onlateral sides of the seawater channel, are also electrically insulated with varnishat the input and output ends. The spaces between the electrodes and the lateralsides of iron shell are filled with polyvinyl chloride (PVC) foam to further improveelectrical insulation. The electrodes are made of flat aluminum sheets with theinput-and-output current leads extended outside the seawater channel. We hadfound that, at the current as high as 120 A, only negligible amount of aluminumanode dissolved in electrolysis of salt water within an hour.

The difference of electric potential applied on these two electrodes is ψE = 64Volt in the simulations associated with the electrolytic conductivity of sea waterσ = 5 S/m. For an ideal situation, the magnitude of electric potential would behalf the difference of applied potential on the central section, i.e., ψ = 32 Voltat x = 0. Nevertheless, the magnitudes of electric potential across the centralsection for single-unit and two-unit module, respectively shown in the Figs. 8(a)and (b), are general less than 32 Volt. The electric potential at middle region oftwo-unit module is closer to the ideal magnitude, while the electric potential of thewhole single-unit module is significantly smaller. The correspondent distributionsof current density are demonstrated in Figs. 8(c) and (d), respectively. Noted

7

Figure 8: Simulations of MHD thruster modules at the central cross-section (x = 0)for ψE = 64 Volt: (a) electric potential for single-unit module; (b) electric potentialfor two-unit module; (c) current density inside single-unit module; (d) currentdensity inside two-unit module. The two rectangular blocks in (a) and (b) are theside views of permanent magnets. Noted: (c) and (d) shares the same colorscale.

that only the region inside thruster is shown. Consistent with the distributionsof electric potential, the current density is apparent much stronger in the middleregion of two-unit module. Since the Lorentz force is directly proportional to thecurrent density, these results support the better design of two-unit module.

Based on the results obtained in the simulations of magnetic field and electriccurrent density, the two-unit module is chosen as the complete design shown inFig. 7(b). To overcome the strong repulsive force between the magnet modules,the NdFeB magnets are fastened to the iron shell by fiber-reinforced plastic (FRP)plates and bolts. Then, the two units are bolted together to form a two-unitmodule, of which the front and back ends of thruster are covered by FRP platesto fix the position of magnets. The input/output current leads are bent to the endsurfaces of thruster.

2.3. Flow Simulation of MHD Thruster Module Numerical simulations ofthe flow field incorporated with the Lorentz force through the thruster module arealso carried out by the ANSYS Fluent to determine the performance of thrustermodule of different configurations. Geometries and dimensions similar with thethruster module shown in Fig. 3 and 7 are used. Furthermore, based on themeasured field strength obtained in Fig. 6, a uniformed field strength of Bz = 0.2 Tis assumed. By the simplification, only the Ohm′s Law is coupled with the Navier-Stokes equations but the Maxwell equation. The potential difference applied onthe electrodes is ψE = 64 Volt, and yields average current strength I ≈ 25.9A and 57.7 A within the thruster chamber for single-unit and two-unit module,respectively. Fig. 9(a) shows the induced flow by the Lorentz force to a stationary

8

Figure 9: Flow simulations of MHD thruster modules at the central cross-section(x = 0): (a) single-unit with V = 0 m/s and Bz = 0.2 T and ψE = 64 Volt; (b)two-unit module with V = 0 m/s, Bz = 0.2 T and ψE = 64 Volt; (c) single-unitmodule with V = 0.5 m/s, Bz = 0 T; (d) two-unit module with V = 0.5 m/s andBz = 0 T; (e) single-unit module with V = 0.5 m/s, Bz = 0.2 T and ψE = 64Volt; (f) two-unit module with V = 0.5 m/s, Bz = 0.2 T and ψE = 64 Volt. Thetwo rectangular blocks are the side views of permanent magnets.

single-unit thruster, i.e., no cruising speed V = 0. Driven by the Lorentz force,apparent flow is generated inside the thruster chamber, in which the maximumflow speed is about 3.5 m/s. Noted that the negative sign shown in colorbar offigure indicates the fluid flows from left to right. A mass flow rate of Q = 2.4 kg/sis pumped to pass through the thruster in the present condition. The induced flowis significantly enhanced for the two-unit module as shown in Fig. 9(b), in whichthe maximum speed is increased to about 5 m/s. As a result, the mass flux isfurther raised to Q = 3.4 kg/s for a two-unit module. These results indicate thatthe present design is capable to pump significant amount of seawater through thechamber of thruster.

The flow field associated with a thruster module cruising at V = 0.5 m/swithout/with the presence of magnetic field, i.e., Bz = 0/0.2 T, are shown inFig. 9(c)-(f). While the mass flow rates of single-unit and two-unit modules remainnearly unchanged at Q = 4.6 kg/s for Bz = 0, the mass flow rate is increasedsignificantly from Q = 5.1 kg/s for the single-unit to Q = 6.0 kg/s for two-unit module with the presence of magnetic field of Bz = 0.2 T. It is noticed theincrements of mass flow rate compared with the correspondent module withoutmagnetic field, i.e., ∆Q = Q(Bz@0.2T ) − Q(Bz@0), are ∆Q = 0.5 and 1.4 kg/sfor single-unit and two-unit module, respectively. The more significant incrementof ∆Q for the two-unit module confirms its better performance.

2.4. Experiments of Magnetohydrodynamic Thruster Module After de-tailed theoretical analysis and experimental measures, MHD thruster modules areassembled and tested. The designs of a shielded two-unit module is followed, asa sample unit of MHD thruster demonstrated in Fig. 10(a). First, to verify the

9

Figure 10: (a) A sample manufactured MHD thruster unit. Experimental testsof MHD thruster hanged on a sliding track: (b) a two-unit module and (c) twosingle-unit modules.

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

1.5

2

2.5

I (A)

TL (

N)

One−unit Module

Two−unit Module

TL = 0.012*I

Figure 11: Thrust (TL) vs current (I).

10

Figure 12: (a) The modified Delft 372 catamaran model MHD-1, and (b) with 5MHD thruster modules installed beneath.

better performance of the two-unit module than the single-unit configuration sug-gested by the theoretical result, experiments in a water tank are conducted. Fora fair assessment, a two-unit module is directly compared with two single-unitmodules. These modules are powered by a Lithium-Polymer (LiPo) battery. Theactual applied current is measured at I = 49.6 A. The thruster modules, fully sub-merged in the seawater, are hanging on a sliding tract with negligible friction. TheLorentz force drives the thruster module moving forward once the electric currentis applied. Two sensors are installed at sides of tank to calculate the average speedof the modules. Figs. 10(b) and (c) show the tests of the two configurations. Thephotos are taken at the times when the modules reach the first sensor (t = 0 s)near the left side of the tank, and when the modules reach the second sensor onthe right side. For both cases, apparent jet flows are generated to drive the modulemove toward the right direction. The slightly faster arrival of the two-unit modulesupports the better performance suggested by the theoretical analysis. Neverthe-less, the speed is just about V ≈ 0.1 m/s, which is much less than the expectedcruising speed. This is mainly because of the limitation of testing length, so thatno sufficient time allowed for the module to fully accelerate. The other factor isthe much lower current provided. In the ship model tests, the planned current willbe as high as to I = 120 A.

Because of the insufficient time allowed for tests, the MHD thrust, excludingthe induced drag of a moving thruster module, is measured by a pull dynamome-ter. Experiments under different electric current strengths are performed, and theresults are shown in Fig. 11. We like to point out that, the condition with ex-tremely high current I = 190.2 A is achieved by adding salts to raise conductivity.A nearly linear correlation is followed, such that

TL ≈ 0.012I. (7)

The nearly linear TL−I relation is consistent with the theoretical expression ofLorentz force for a fix area. For the particular case of I = 118.6 A and TL = 1.69 N,which is close to the planned operating condition for cruising speed of V = 0.5 m/s,the applied electric potential in salty water with 35.7 ppt of salinity is measured atψE = 46.4 Volt. The electric efficiency ηE of the MHD thruster module is obtainedby ηE = TLV /IψE ≈ 0.000154. The extremely small efficiency is consistent withthe prediction in Ref. [6].

11

Figure 13: Cruising MHD-1 ship model (from right to left) powered by MHDthrusters at t = t0 (c), t ≈ t0 + 6 s (b) and t ≈ t0 + 9 s (a).

2.5. Test of ship model Based on the designs presented above, a MHD-1ship model is manufactured and multiple MHD thrusters are installed as shownin Fig. 12. To successfully power the MHD-1 ship model with a cruising speed ofV = 0.5 m/s whose drag is about 7 N according to the CFD estimation, at least5 shielded two-unit modules are required in the operating condition of electriccurrent I ≈ 120 A, based on the previous testing results. To verify the capabilityof the MHD thrusters, we employed 4-6 two-unit modules in different operatingconditions with various strength of electric current, depending on the capacityof power sources. Generally, the range of cruising speed is measured at betweenV = 0.25 ∼ 0.5 m/s. A representative test is shown in Fig. 13, in which 6 MHDmodules (red objects beneath the ship model) are working at I ≈ 110 A. The fourmodules in the front and middle are powered by batteries, while the electricityfor the rear two is supplied by a diesel generator. The total water displacementis about 450 kg. Strong jet flows are observed in Fig. 13 to provide propulsivethrust. The cruising speed is closed to the targeted V ≈ 0.5 m/s, which supportsthe capability of the present design. Further improvements are in progresses,including weight reduction and streamlined thrusters. The weight reduction willbe achieved by replacing the heavy generator by more efficient batteries. 3D-printed cowlings will also be attached on the front sides of thruster modules toreduce the induced drag.

3. Concluding remarks The present study applies the MHD propulsionto design a propellerless marine vehicle driven by the Lorentz force generatedby the coupling effect of magnetic field and electric field in conductive seawater.The flow field of a cruising Delft 372 catamaran model is first simulated to obtainnecessary thrust. To acquire the better configuration of the MHD thruster module,numerical simulations of the magnetic field and current density are also carriedout for stronger strength and more uniform distribution. In addition, simulationsof flow passing through the thruster chamber are also performed to support theappropriateness of designated configuration of MHD thrust modules. Based on thetheoretical analysis and experimental measures, the designated thruster modulesare manufactured and tested. The sample MHD thruster module is verified toeffectively move forward by the Lorentz force. The gross thrust (TL) generated bythe present design of MHD thruster module is nearly proportional to the electriccurrent (I), such that TL ≈ 0.012I. The results suggest the ship model can beeffectively propel to motion by installing sufficient number of thruster modules.At last, the MHD-1 ship model installed with multiple MHD thruster moduleswas manufactured and tested. The testing results confirm the goal can be closelyreached by the present design.

To conclude the study, we like to point out that, the present manuscript

12

merely shows the feasibility of MHD vehicle by applying currently available perma-nent magnets and batteries. There are much more optimizations can be achievedfor better propulsive efficiency, such as better magnet arrangement to increasesthrust. In addition, reduction the hydrodynamic drag can be achieved by lighterweight, streamlined thruster module or integration of the thruster module withthe ship etc. These works are in progresses to improve the performance of theMHD propulsion.

AcknowledgementSupport by National Chung-Shan Institute of Science and Technology, TaiwanR.O.C. (Grant XV08095P498PE-CS) is gratefully acknowledged

REFERENCES

1. H. Alfven . Existence of electromagnetic-hydrodynamic waves. Nature. , vol. 150(1942), pp. 405–406.

2. W. Rice. Propulsion system. U.S. Patent , vol. 2997 (1961), No. 2,997,013.

3. J. Friauf. Electromagnetic ship propulsion. Journal of the American Society forNaval Engineers , vol. 73 (1961), pp. 139–142.

4. O. Phillips. Electromagnetic ship propulsion. Journal of ship research , vol. 43(1962), pp. 43–51.

5. D. Mitchell, D. Gubser. Magnetohydrodynamic ship propulsion with supercon-ducting magnets. Journal of Superconductivity , vol. 14 (1988), pp. 349–364.

6. E.D. Doss, H.K. Geyer . The Need For Superconducting Magnets For MHDSeawater Propulsion . Proceedings of the 25th Intersociety Energy Conversion En-gineering Conference , (1990).

7. J. Thibault, A. Alemany, A. Pilaud. Some aspects of seawater MHD Thrusters. Proceedings of MHDS91 , (1991), pp. 211–218.

8. D. Swallom, I. Sadovnik, J. Gibbs, D. Choid. Magnetohydrodynamic submarinepropulsion system performance analysis results. Proceedings of MHDS91 , (1991),pp. 277–289.

9. Y. Sasakawa, S. Takezawa, Y. Sugawara, Y. Kyotani. The superconductingMHD-propelled ship YAMATO-1. Proceedings of the 4th International Conferenceand Exhibition: World Congress on Superconductivity , vol. 1 (1995), pp. 167–176.

10. L. G. Yan, Z. K. Wang, C. L. Xue, Z. Y. Gao, B. Z. Zhao. Development of thesuperconducting magnet system for HEMS-1 MHD model ship. IEEE Transactionson Applied Superconductivity , vol. 10 (2000), pp. 955–958.

11. D. Cebron, S. Viroulet, J. Vidal, J.-P. Masson, P. Viroulet. Experimentaland theoretical study of magnetohydrodynamic ship models. PLoS ONE , (2016),no. 12(6), e0178599.

12. T. Weier, V. Shatrov, G. Gerbeth . Flow control and propulsion in poor con-ductors. In Magnetohydrodynamics: Historical Evolution and Trends, S. Molokov,R. Moreau, H.K. Moffatt (Eds.), Springer, Dordrecht , (2007), pp. 295–312.

13. J. Jang, , S. Lee. Theoretical and experimental study of MHD (magnetohydrody-namic) micropump. Sensors and Actuators A: Physical , vol. 80 (2000), pp. 84–89.

14. O. M. Al-Habahbeh, M. Al-Saqq, M. Safi, T. Abo Khater. Review of mag-netohydrodynamic pump applications . Alexandria Engineering Journal , (2016),no. 55, pp. 1347–1358.

15. V. Dolgikh, A. Pavlinov. Experimental investigation of an MHD-pump modelwith inclined partitions. Magnetohydrodynamics, vol. 53 (2017), no.3, pp. 511–514.

16. V. Dolgikh, A. Pavlinov. Design optimization of the MHD pump with inclinedpartitions. Magnetohydrodynamics, vol. 55 (2019), no.1/2, pp. 39–46.

13

17. V. N. Timofeev, M. Yu. Khatsayuk, I. V. Kizhaev. Mathematical simulationof electromagnetic and hydrodynamic processes in the MHD pump. Magnetohydro-dynamics, vol. 55 (2019), no. 3, pp. 337–346.

18. M. Haghparast, M. Pahlavani, D. Azizi. Numerical investigation of the effectsof magnetic field and fluid electrical conductivity on the performance of marine mag-netohydrodynamic motors. IET Electric Power Applications, vol. 12 (2018), no. 8,pp. 1207–1214.

19. I. A. Belyaev, L. G. Genin, Y. I. Listratov, I. A. Melnikov, N. G. Razu-vanov, V. G. Sviridov, E. V. Sviridov. Features of MHD heat transfer in simplechannels. Magnetohydrodynamics, vol. 54 (2018), no. 3, pp. 245–260.

20. V. Timofeev, M. Khatsayuk, S. Timofeev. Analysis of the transverse end effectin the MHD stirrer for molten metals. Magnetohydrodynamics, vol. 53 (2017), no. 3,pp. 521–536.

21. S. Carcangiu, R. Forcinetti, A. Montisci. Simulink model of an iductive MHDgenerator. Magnetohydrodynamics, vol. 53 (2017), no. 2, pp. 255–266.

22. A. Hollings. China Successfully Tests Near-Silent Submarine Propulsion Tech-nology. https://sofrep.com/news/china-successfully-tests-near-silent-submarine-propulsion-technology/ , Nov. 1 (2017).

23. R. Broglia, B. Jacob, S. Zaghi, F. Stern, A. Olivieri. Experimental investiga-tion of interference effects for high-speed catamarans. Ocean Engineering , vol. 76(2014), pp. 75–85.

24. ANSYS, Inc.. ANSYS Fluent Theory Guide . ANSYS, Inc., Southpointe (2017)

14