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Experimental Study of Small Scale DC Direct MHD Thrusters.

Praveen Malali1 and Chad Luettel2

Old Dominion University, Norfolk, VA-23508

Ajay Bharadwaj3 and Aravind Ram4

Malali Research Labs, Bangalore, India.

and

Anirudh Hegde5 and KshithijPrakash6

Malali Research Labs, Bangalore, India.

NomenclatureF = Lorentz Force. Ain = Area of the entrance.Lc = Length of the conductor. Aex = Area of the exit.I = Current.B = Magnetic field.θ = Angle between electric and magnetic field.L = Length of the electrode.W = Width of the electrode or channel.ρ = Resistivity of the electrolyte.V = Voltage applied.T = Thrust force.Uin = Entrance Velocity.Uex = Exit Velocity.f = friction factor.Pen = Pressure at the entrance of the channel.Pex = Pressure at the exit of the channel.

1

.

m = Mass flow rate at the entrance.

=2

.

m Mass flow rate at the exit.

I.) Introduction

Magneto hydrodynamics (MHD) is a field concerned with the mutualinteraction of fluid flow and magnetic fields [1]. Even though the laws of fluid flow andmagnetism were well known as early as the 1870’s, MHD emerged as a field in the 1940’s.

The first experiments involving the study of interaction of fluid flow and amagnetic field was performed by Michael Faraday. The experiment involved the measurement ofcurrent produced from the flow of the river Thames in the earth’s magnetic field [2]. In the1940’s due to the pioneering works of Hans Alfven and others, the field of MHD gainedsignificant importance as they were largely used in the field of astro-physics.

1Graduate Student, Department of Mechanical Engineering, Old Dominion University, Norfolk, VA.2Graduate Student, Department of Mechanical Engineering, Old Dominion University, Norfolk, VA3,4Research Associates, Malali Research Labs, Bangalore, India.5,6Research Associates, Malali Research labs, Bangalore, India.

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Then, geo-physicists tried to explain the origin of earth’s magnetic field usingthe principles of MHD. Later, Plasma physicists, in 1950’s, used MHD as the interest in thermo-nuclear fusion generators increased. The work centered on the stability of plasmas in magneticfields. The engineering applications of MHD began in the 1960’s. Prior to this time period,notable works were done by scientists such as J.Hartmann, who is credited with the invention ofthe electro hydrodynamic pump in 1918. Since then, the engineering fields using MHDprinciples have increased. Some of them include Power generation, Micro fluidics [3],Propulsion and Metallurgy etc.

Research into MHD propulsion systems for marine vehicles started in the1960’s [4]. The initial patent is by W A Rice [5]. Since a MHD propulsion device would have nomoving parts, there was a belief that it would be highly suitable for submarines. However,experiments discovered that the trail left behind by such a system could be easily detected [6].Also, high magnetic field and electric currents were required to propel these submarines [6]. In1969 P A Doragh [7] suggested the use of super conducting magnets to provide high magneticfields. The idea of super conducting magnets had to wait due to the fact that that superconducting magnets were very expensive and not readily available. Then in early 1994 Takezawaet.al [8] reported that the ship, ‘Yamato’ was propelled using MHD thrusters in the Kobe harbor.The ship made use of superconducting magnets and attained a velocity of 15 km/hr. The MHDthrusters used made use of direct current (DC) and had a scale of the order of 3m.

This paper explores centi scale (10-2) MHD thrusters. The overall objective ofthis study is to experimentally investigate small (10-2) scale DC direct MHD thrusters. Inaddition, a small boat having length and breadth of 20 and 10cm was propelled by using one ofthe small scale DC direct MHD thrusters. The paper also intends to push forward the idea ofusing these thrusters to propel unmanned marine vehicles or remotely operated vehicles (ROV).Since there has been an exponential increase in underwater explorations for oil deposits andother energy resources these (MHD) propulsion systems can be used as alternatives to existingsystems of propulsion. With no moving parts they have very low wear and tear and are thusreliable.

II.) Theoretical analysis of MHD thrusters

The principle of MHD thruster is based on the Fleming’s left hand rule ofelectromagnetics. According to Fleming’s left hand rule, the Lorentz force acts on a currentcarrying conductor in presence of a magnetic field.

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Figure 1. Channel with the electrodes and the magnets

The direction of the Lorentz force (F) is as shown in the figure 1 above. Themagnitude of the force is given by the following equation.

θsinIBLF c= (1)

By definition, the Lorentz force is maximum when the direction of current andthe magnetic field are perpendicular to each other. A schematic of the MHD thruster is shown infigure 1. From the schematic, the channel houses a pair of electrodes which are used to passcurrent to the conductor. The required magnetic field is produced by a pair of permanentmagnets. In a MHD thruster the current carrying conductor is usually an electrolyte such asseawater. When electric current is made to pass through the electrolyte (saltwater), the Lorentzforce acts on the seawater, thereby pushing the sea water in that direction. Evidently the Lorentzforce is dependent on certain key parameters of the thruster which are listed below [9].

• Length of the electrode (L).• Width of the electrode (W).• Magnetic field strength (B).• Resistivity of the seawater (ρ).• Applied Voltage (V).

An equation for the Lorentz force (F) developed in the thruster as a function ofthe key parameters listed above is as follows [6] [9].

ρLWBV

F battery= (2)

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The above equation takes into account the global parameters which changeinside the channel of the thruster. However the above equation is sufficient in that it provides arelationship between the Lorentz force and the thruster parameters.

The propulsion (thrust) force (T) developed by the thruster is obtained as areaction to this Lorentz force [8]. However the thrust force (T) is always lesser than the Lorentzforce because of fluid friction losses, fluid losses at the inlet etc [8]. Thus it can be written as

lossesfFT )(∆−= (3)

where lossesf )(∆ represents fluid flow losses.

The thrust force produced by a MHD channel can be written as [10].

)()(1

.

2

.

exinambininexinex AAPAPPUmUmT −+−+−=

In the present case since Ain = Aex we have

ininexinex APPUmUmT )(1

.

2

.

−+−= (4)

Equating equations 3 and 4 we have

lossesininexinex fAPPUmUmF )()(1

.

2

.

∆+−+−=

Assuming the losses to be frictional the above equation can be written as

inindensity

Hininexinex A

U

D

LfAPPUmUmF

+−+−=

2)(

2

1

.

2

. ρ(5)

The above equation proves that any increase in the Lorentz force will increasethe thrust force. This has been proved by obtaining velocity measurements for certain variationsof the key parameters of the thruster. The results have been discussed in detail in the latersections.

III.) Parameter VariationFrom the theoretical analysis, it can be inferred that the flow velocity depends on four criticalparameters. They are as listed below.

1) Length of the thruster (L).2) Salinity.3) Applied voltage (V).4) Separation width (W).

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In the above list, the resistivity parameter has been replaced by salinity (salt concentration).Resistivity of a conducting fluid mainly depends on the salinity. Thus, salinity of the conductingfluid was varied in order to vary the resistivity of the conducting fluid (electrolyte). Theparameters and the variation in their values are listed in the following table.

Table 1: Parameters and their respective values at each level.Parameter Number of levels Values at each level

Length of the thruster 2 0.10 and 0.15 m

Salinity 4 32,39,46,and 53 kg/m^3

Applied Voltage 3 25, 30, and 35 V

Separation width 4 0.015,0.017,0.020, and 0.022 m

IV.) Experimental set-up

Figure 2. Schematic of the experimental set-up.

1). Overview block diagram.This section provides an overview of the experimental setup used to study MHD thrusters. Thesection consists of:

i.) Power source and auxiliary units.ii.) Reservoiriii.) Input voltage and current measuring instruments

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i.) Power source and auxiliary units.

The autotransformer and the rectifier-filter-regulator (RFR) circuit constitute the power sourcefor the experiment. The AC auto transformer used has a range of 0-260 volts. This AC is fed tothe RFR circuit which gives out regulated DC for the MHD thruster. The autotransformer and therectifier-filter circuit is shown in figure 3 (a) and (b) respectively.

(a) Autotransformer (b) RFR circuit

Figure 3. The auto transformer and RFR circuit.

ii.) Reservoir.

The reservoir consists of a plastic tub measuring 30cm x 6 cm x 12 cm (figure 4). The reservoiris filled with salt water of a known concentration prior to the start of the experiment. Thereservoir has a capacity of 0.00216 m3.

iii.) Input voltage and current measuring instruments.

Multimeters and ammeters of varied ranges have been made use of in the experimental study.Two multimeters with a voltmeter setting were used to measure the regulated voltage output andto measure the voltage across the electrodes during the experimentation process. Additionally, anammeter with a range of 0-20 A, was used to measure the circuit current between the electrodes.The measuring instruments along with the test bed and the thruster are shown in figure 4.

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Figure 4. Test bed along with the thruster and the measuring instruments.

2.) Channel.

Acrylic plastic sheets, 2 mm thick, were chosen for the construction of the channel (figure 5 ).Acrylic was chosen for its desired properties such as lightweight, strength, high chemicalresistance and transparency. Cyanoacrylate glue was used in the construction of the channels. Atotal of eight channels were constructed out of acrylic for the experiments. The channels weredivided into two sets based on their lengths. Each set had four channels having same length andheight but different separation widths. The dimensions of these channels are given below.

Table 2: Dimensions of the channels used.Channel Set Length (m) (L) Width (m) (W) Height (m) (H)

1 0.010 0.015, 0.017, 0.020,0.022

0.017

2 0.015 0.015, 0.017, 0.020,0.022

0.017

Figure 5. A complete channel.

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3.) Electrodes.

The electrodes were made out of brass material. Brass was chosen over other materials becauseof its relatively high resistance to corrosion and low electrical resistivity [11]. The surfaces of theelectrodes were buffed to ensure that a clean surface of brass comes in contact with theelectrolyte (seawater) during experimentation. A hand file was used to shape the electrodes toexact dimensions and then were either inserted or glued to the respective channels. A total of 8pairs of brass electrodes were made out of 1 mm thick brass sheets. The length and width ofthese electrodes are the same as the channel dimensions (Table 2). A pair of brass electrodes isshown in figure 6.

Figure 6. Completed Brass Electrodes.

4.) Electrical connections:

Special attention was given to electrical connections to the brass electrodes upon their insertioninto the respective channel. Prior to the insertion of the electrodes, small holes were drilled onopposing faces of the channel. These holes formed the contact points for the wires and the brasselectrodes. The electrodes were then glued on to these surfaces of the channel with the help of ametal adhesive (Araldite). Once the electrodes were held in place then copper wire, stripped ofinsulation, was inserted through the drilled holes and was made to come in contact with theelectrodes. Once the contact was established, a special silicon adhesive was melted and droppedover the contact point. The location of the adhesive sealed the contact point from the outsideenvironment. The electrical circuit was then checked for completeness using a multimeter. Thisprocedure ensured that there was no leakage of saltwater or current through the contact pointduring experimentation. A channel along with the electrodes and the electrical connections isshown in figure 7 (a) & (b).

(a) (b)Figure 7. Channel with electrical connections and electrodes.

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4.) Magnetic Field.

The magnetic field was applied to the thruster by using six NdFeB (Neodymium Ferrous Boron)magnets each having a dimension of 0.050m x 0.020m x 0.005m These magnets were used sincethey are the strongest known ferro magnets. A minor improvisation had to be done before thesemagnets could be used alongside the channel. Two strips of acrylic sheet of 0.02 m height and0.17 m length was cut. A thin layer of duct tape was applied to all the six magnets so as toprevent them from getting corroded once they were in the salt water. Then three magnets wereattached to each of these strips such that all three magnets on one strip had the same pole (saynorth) facing away from the strip. This was helpful during experimentation, since these stripscould be removed from one channel and could then be immediately fixed to another channel.

V.) Measurements.

Measurements of entities such as flow velocity and magnetic field distribution were performedusing the following procedures.

a.) Flow velocity measurements: The apparatus used to measure the average fluid flow velocityfrom the exit section of the thruster is shown in the schematic (fig. 8). It consists of a holdingstand and a syringe used for insertion of the dye. Potassium dichromate solution was used as adye. A small amount of the dye was injected at the entrance of the thruster once fluid motion wasobserved. Simultaneously a stop clock was started. The clock was stopped once orangecoloration was observed at the exit of the thruster and time was noted. The same procedure wasrepeated 10 to 15 times for a given setting of the key parameters. The ratio of the channel lengthto the average time taken by the dye to traverse that distance gives the average fluid flowvelocity. Prior to deciding upon this type of flow measurement procedure, a general survey wasmade to obtain a rough idea about the magnitude of the flow velocity. It was found that the flowvelocity will have a range of 0.2 m/s to 0.7 m/s [6]. Since these velocities are relatively low theabove mentioned system was used. The measurement system used is not error free and moreaccurate results can be obtained if one used flow measurement systems like the PIV etc.

Figure 8. Apparatus for measuring the flow velocity.

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b.) Magnetic field distribution: The magnetic field strength between a pair of magnets isdependent on the distance of separation between the magnets. Nd-Fe-B magnets of thepermanent type were used to produce the magnetic field in the thrusters. The magnetic fieldstrength values were measured at equidistant discrete points along the separation distance byusing a Gauss meter. A plot of the magnetic field strength (mT) vs. discrete set of points for eachof the separation distance (W) has been given in the figure 9(a). Also, a plot of the averagemagnetic field in (mT) vs. separation width (w) is given in figure 9(b).

Figure 9: Plots showing the magnetic field distributions along the separation widths.

VI.) Observations

• Variation of current:

The current in the MHD thruster showed variations during the experiments. It was observed thatthe moment voltage was applied across the electrodes of the thruster, the current increased from0 and attained a peak and after 5 to 6 seconds the magnitude of the current decreased to aconstant value and remained at that value for the rest of the experiment. For any combination ofthe key parameters the peak value of current remained in the range of 10 A -13 A and theconstant value of current in the range of 5 A to 8 A. The variations in current caused the appliedvoltage itself to fluctuate. But these fluctuations were restricted to within 3 V and wereimmediately stabilized once the current attained the constant or steady state value.

The initial raise in current values can be attributed to the low resistance of the salt water(electrolyte). Also, the face of the electrodes does not have any deposition on them at the start ofthe experiment. The value of current comes down later owing to the chemical reactions that takeplace in the process of electrolysis.

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• Formation of bubbles:

The MHD thruster is chemically very active. Because of the passage of current into the salt waterthe process of electrolysis occurs [12]. The occurrence of the bubbles is due to gases liberated inthe process of electrolysis and other chemical reactions which occur near the electrodes. Thereactions at the respective electrodes are as shown.

At Anode:

−+

−−

++→

+→

eHOH

eClCl

4402

22

22

2

At Cathode:

222 HeH →+ −+

The above reactions release H2, O2 and Cl2 as gases. This results in the formation of the bubbles.The concentration of these bubbles is more at the exit of the thruster as shown in figure .

Figure 10. Bubbles at the exit of the thruster.

• Deposits on Electrodes:

After each trial, both the electrodes were found to have chemical deposits on them. This was aresult of the immense chemical activity that took place inside a MHD thruster. The main

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compounds that were formed were Copper Chloride (CuCl2) and Copper Oxide (CuO). Thereactions leading to the formation of these compounds are given below.

OHCuClHClCuO

CuOOCu

22

2

2

22

+→+→+

Copper oxide (CuO) was formed mainly at the anode. This is because oxygen is liberatedat the anode. CuO is a black solid. Copper chloride is blue-green in color because of the moisturefrom the salt water. Other than the above reactions, copper plating on the cathode was alsoobserved. Usually it was in small amounts when compared to the Copper chloride and Copperoxide.

The above listed deposits were removed after every trial. This was done by using a highlydiluted solution of hydrochloric acid (HCl). Upon applying HCl to the electrodes they werethoroughly scrubbed and were then washed with water. This ensured complete removal of thedeposits from the electrodes. This was done to prevent changes in the resistance of theelectrodes.

VII.) Results and Discussion

Velocity Vs. Channel length

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16

Channel Length (cm)

Vel

oci

ty(c

m/s

)

1.5 cm width

1.7 cm width

2.0 cm width

2.2 cm width

Velocity vs. Channel length

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20

Channel length (cm)

Vel

oci

ty(c

m/s

)

32 kg/m^3

39 kg/m^3

46 kg/m^3

53 kg/m^3

(a) (b)

Velocity vs. Channel length

0

5

10

15

20

25

30

0 5 10 15 20Channel length (cm)

Vel

oci

ty(c

m/s

)

25 V

30 V

35 V

Velocity vs. Width

0

10

20

30

40

50

60

0 0.5 1 1.5 2 2.5Width (cm)

Vel

oci

ty(c

m/s

)

32 kg/m 3̂

39 kg/m 3̂

46 kg/m 3̂

53 kg/m 3̂

(c) (d)

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Velocity vs. Voltage

0

5

10

15

20

25

30

35

40

0 10 20 30 40Voltage (V)

Vel

oci

ty(c

m/s

)

32 kg/m 3̂

39 kg/m 3̂

46 kg/m 3̂

53 kg/m 3̂

Velocity vs. width

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5Width (cm)

Vel

oci

ty(c

m/s

)

25 V

30 V

35 V

(e) (f)

Figure 11. Variation of the fluid velocity with the critical parameters.

From the above plots, it is evident that the fluid velocity increases with the increase in the valueof the critical parameters. Figure (7a) shows the variation of flow velocity with the length of thethruster. The reason for increase in the fluid velocity can be attributed to the increase in thevolume of conducting fluid, under the influence of the applied voltage. As a result, the velocityof the fluid increases when the channel length is increased from 10 cm to 15 cm.

Figure (7e) shows the variation of fluid velocity with applied voltage. Increase in the appliedvoltage to the thruster increases the force of attraction between the ions and their respectiveelectrodes. As a result the ions move at a faster rate with every increase in the applied voltage.Due to this faster rate of motion the magnitude of the Lorentz force acting on these ionsincreases and hence the fluid velocity increases.

Figure (7d) shows the variation of fluid velocity with the salinity. As stated earlier (parametervariation), salinity in a fluid and the resistivity of that fluid are directly related. With the increasein the salinity, the number of ions available at a given time increases. As a result, the number ofions transferring their momentum to the water molecules increases. The transfer of momentumcauses an increase in the fluid velocity at the exit.

Figure (7f) shows the variation of the fluid velocity with channel width. The reason for thisincrease is due to the raise in the volume of conducting fluid under the influence of the appliedvoltage. However, there is a limit on the extent to which the channel width can be increased. Thislimit arises due to the inverse relationship between the magnetic field strength and the channelwidth (separation distance) (refer fig. 9b). Therefore a large increase in the channel width willnot guarantee an increase in the fluid velocity. This condition can be overcome by havingstronger magnets.

From the above plots and from the thrust force calculations it was found that the thrust forceattained a maximum for a particular set of values of the critical parameters. The values are aslisted below.

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i.) Applied Voltage = 35 V.ii.) Channel Width = 2.2 x 10-2 m.iii.) Channel length = 15 x 10-2 m.iv.) Salinity = 53 kg/m3.

In the final section of the experimental study a simple boat was constructed out of Low DensityPolyethylene. The boat was then attached with a thruster having the dimensions for which thethrust force was found to be maximum (fig. 12a). The boat was then placed in a tub (fig. 12b)containing salt water for which the thrust force was maximum. The boat was then supplied withan applied voltage of 35 Volts. The boat was successfully propelled and achieved a top speed of4.375 cm/s.

(a) (b)Figure 12: The boat with the thruster (a) and the boat in the tub being propelled (b).

VIII.) Areas of further research

MHD is a field that is rapidly advancing with technology. Areas of further research includechanges in conductivity with temperature variation, evaluating different electrode materials, andvariation of magnetic fields and DC voltage differentials. Additionally, changes in the geometryof the channel including nozzle designs need to be further evaluated. The effect of bubbles on thethrust force needs further evaluation.

IX.) ConclusionThe small scale applications of MHD propulsion systems looks promising from the aboveexperiments. The experiments also prove that at small scales there is sufficient amount of thrustforce to propel small-sized floating or submerged objects. The thrust force was found to bemaximum for a particular set of values of the critical parameters. The tests reveal the effect ofeach parameter on the fluid flow velocity at the exit and the thrust force of the thruster thusproving that changes in critical parameters influencing the Lorentz force produces a change inthe thrust force and the fluid flow velocity. The above experiments were carried out with anintention to analyze the effect of majority of parameters. However, there are areas in whichfurther experimentation can be carried out. Notably, the effect of temperature on the thrust forceand coupling of the critical parameters.

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Acknowledgements

The authors wish to thank Prof. Sushil Chaturvedi, Sri M N Dattatry, Medina Taylor and Sri VathsaAithal for their constant support and encouragement through out the project.

References.

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