Use of a homopolar generator in hydrogen production from water

0361~3199/85 $3,0(I ~ 0.0~1 Pergamon Press Ltd (~) 1985 International Association lot Hydrogen Energ~

l m J, Hydrogen Energy, Vol 10, N o 1. pp. 101-112. 1985. Printed in Great Britain

USE OF A H O M O P O L A R G E N E R A T O R IN H Y D R O G E N P R O D U C T I O N FROM W A T E R J. GHOROGHCHIAN a n d J, O ' M . BOCKRIS

Chemistry Department, Texas A&M University, College Station, TX 77843, U.S,A.

(Received 18 September 1984) Abstract--This paper examines the direct induction of a low voltage in a rotating electrode by outside magnets in hydrogen production• Possible gains include the absence of a generator, transformer and rectifier. Two configurations were experimentally examined. In the first (A), a disc was rotated at 2000-3000 rpm in a field around 0.9 T. The hydrogen-oxygen production was measured as a function of rotation speed. In a second (B), a permanent magnet was placed at each end of a propeller, which was made to rotate. The poles of the magnet passed over a series of conductors, themselves separated into groups. The pulsed potential induced in each group was applied directly to a conventional electrochemical cell, to produce H2 and 02. An economic gain in electrolysis by the use of homopolar generators seem difficult to realize using permanent high-strength magnets, but reduction in cost of equipment by around 50% appear likely using electromagnets.

1. I N T R O D U C T I O N Water electrolysis technology has been developed so that reliable electrolyzers are available which operate without excess pressure or under a pressure of 30 bar. Electrolyzers operate at low cell voltage (1.8-2.2 V) and high current d.c. This requires transformers and rectifiers; these involve not only capital expenditure but give rise to an overall loss of about 15% of electrical energy [1]. The goal in this paper is to report experiments in which a suitable d.c. is generated within the electrolysis cell. This could be done by means of a homopolar generator. It could result in a practical technology where primary sources of energy from hydro or other sources of mechanical energy (wind and waves) were available. There are two ways in which one could use a homopolar generator for hydrogen production. (1) A rotating disc is immersed inside an electrolyte. If sufficient voltage is generated between two regions of the disc by means of magnetic induction, electrolysis occurs. The generator and electrolyzer are in one unit. (2) A homopolar generator could produce appropriate electricity with which to drive an electrolyzer. The voltage could be in the form of straight d.c. or produced in pulses (see below). 2~ E X P E R I M E N T A L

2.1. Hornopolar generator and electrolyzer in situ (one unit) A stainless steel disc with 30.48 cm dia. and 0,31 cm thickness was mounted on a stainless steel shaft which was 3.81 cm in diameter and 6.35 cm long. The shaft ran inside a self-lubricated bearing. The disc was mounted vertically inside a Plexiglass container of dimensions of 35.5 x 35.5 x 3.175 cm. The electrolyte was 35% potassium hydroxide. The • 101

thickness of electrolyte layer was 1.27 and 0.635 cm in front and on the back of the disc, respectively. The machine components were mounted on an aluminum frame wall and the assembly was bolted to an aluminum frame base which was accommodated between the poles of the magnet. The schematic arrangement of the device is shown in Fig. 1. A V-3602 Varian Associates electromagnet was used, and would be replaceable by a permanent magnet in a potential commercial device. To accommodate the rotating disc in the field, the pole faces was made the same, as that of the rotor, so the magnetic field covered the whole surface of the disc. Magnetic-flux density was measured by a C E N C O Hall-effect gaussmeter, model 78562-002, and a reasonably uniform field was observed across the air gap. The disc was rotated via a pulley by means of a variable speed motor. The rate of rotation was measured by a Stewart-Warner tachometer. Potential measurements were carried out in the absence of an electrolyte, using brushes, located at different positions on the disc. Current passing through the disc was measured by short-circuiting the disc between the rim and the center, and measurement was carried out by a Bell current gun. Qualitative detection of hydrogen was achieved by taking the gas sample from the top of the container• After drying, the gas was injected into an automated multi-valved, multi-column gas chromatograph [2]. Since taking a gas sample from the cell was associated with difficulties resulting from the high state of agitation in the electrolyte, it was decided to analyze the evolved oxygen within the magnetolysis device• The measurement was based on the increase of oxygen in an initially deoxygenated solution. A n Orion oxygen analyzer was used [3]. The solution was deoxygenated by bubbling pure nitrogen for 12 h prior to the electrolysis. The oxygen

J. GHOROGHCHIAN AND J. O'M. BOCKRIS

102

w

C D S B P W

p

MAGNETIC SOUTH POLE

MAGNETIC NORTH POLE

PLEXIGLASS CONTAINER STAINLESS STEEL DISK RUBBER SEAL SELFLUBRICATED BEARING PULLY ALUMINUM SUPPORT WALL

II II II

Fig. 1. Schematic diagram of an in situ homopolar generator and electrolyzer (one unit system).

remaining at the end of this period, and the increase of oxygen during electrolysis, was measured in situ. The measurements were made after 10 min runs, the time being restricted to prevent oxygen saturation of the electrolyte. After each run, the solution was deoxygenated before a new run was commenced with change of rotation rate. F r o m the concentration of oxygen, the current passing during electrolysis could be determined. For a given rotation rate and magnetic field, the potential induced was the same as that measured in air.

2.2. Pulse producing homopolar generator driving an electrolyzer The permanent magnets used were InCorl6 (Indiana General), with 2.5 cm dia. and 0.94 cm thickness. The magnetic circuit was closed by means of a soft U shape iron (Fig. 2). The magnets were held on the two branches of the U and the magnetic field across the air gap of 6.25 mm was measured to be 0.6T. Each U assembly was screwed to the ends of a propeller, 60 cm long (Fig. 2), which was mounted on a shaft and rotated via a pulley by a motor. The mechanical arrangement of the device was similar to the disc configuration discussed in Section 2.1.

A loop of Plexiglass (Fig. 3) was constructed which holds a series of strips of copper, attached to the inner and outer side of the loop. A schematic diagram of the device is shown in Fig. 4. The conductors were in groups of four, each consisting of a piece of copper, 2.0 cm across the Plexiglass loop and 0.6 cm in the direction of motion of the magnets. Such groups (of which 80 existed on the loop) were both on the inner and outer side of Plexiglass. Each copper strip within a group of four was connected in series and each set on the inner side was connected to the corresponding set on the outer side. For each set of such interconnected copper strips there existed a twin, 180 ° away on the other side of the loop. The two twins were connected in series, there being 20 sets of twins. This arrangement was made because it was desirable to get a relatively large voltage (2.5 V) at a relatively small rotation rate (1000 rpm). Thus, induction occurred transversely across each copper element so that with eight elements on the one side, and eight in the twin, at any instant when the magnets passed across the connected twins, 16 copper elements were in series. Hence, a relatively small potential difference (ca O.15 V), induced across each copper strip, made a relatively large potential pulse available. (Because of the rotating nature of the propeller the p.d.

Prol~ller Magnets

o o, I

I

l

Ioool

Magnets

l.l II

l

MagnetHolder

MagnetHolder,

Fig. 2. Schematic diagram of the propeller with magnet.

Jl l

USE OF HOMOPOLAR H: GENERATOR

Beann9 Houmn9

103

iuctoLroop

Loop

Holder Magnet

Fig. 3. Schematic diagram of Plexiglass loop.

was made available in a pulsed form.) To block the flow of current through conductors which were outside the magnetic field, a germanium diode, model G15R4 (from the G e r m a n i u m Power Devices Corporation) was connected to each twin set of copper electrodes. This device effectively stopped undesired circulating currents and thus confined the current to the electrolysis process. The instantaneous forward current was measured and the voltage drop in a given diode up to a range of 10 A was found to be less than 0.2 V. Pulse duration and amplitude were measured by means of a Hewlett-Packard oscilloscope and then

~artns Hcmsin9

Propeller

Suppor:

Loop

Fig. 4. Schematic diagram of pulse producing homopolar generator.

applied to an electrolysis cell. The cell was a beaker type and the electrodes used were of nickel gauze, 1 cm: surface area. The electrolyte used was 35% K O H , the electrode distance was 1 cm. 3. R E S U L T S 3.1. In situ electrolysis (one unit system) 3.1.1. Potential measurements. The potential difference between the rim and center of the rotating disc was measured in air as a function of the magnetic field and the rotational speed (Fig. 5). The maximum magnetic field was 0.86 T and at a speed of 2100 rpm the measured p.d. was about 2V. When the rotational speed was increased to 2700 rpm, the generated emf was 2.5 V, There is fair agreement between the measured potential and the calculated one (Table 1), Although enough potential should be available for water splitting, the distances (ca 7 cm) between regions of different polarity would be expected to give rise to a significant IR drop. Results of the radial potential distribution measurements made in air are shown in Fig. 6. Measurements of potential along a radius of the spinning disc were made at a speed of 2400 rpm and a field of 0,86 T. A cathodic area was identified by assuming arbitrarily that electrolysis of water occurred at a finite rate for areas of the disc from which there was a 2 V differential against that of the center; correspondingly, the anodic area was identified as that part, for which the potential was 2 V from that of the rim, cf. Fig. 7. 3.1.2. Potential-current relationship. The results of

104

J. G H O R O G H C H I A N A N D J. O'M. BOCKRIS 2.5

25

2.0

2.0

ro= 15.24

cm

Speed= 2 4 0 0 r . p . m . Field=8.6 K G

UJ

1.5 15

~

b

o

l

"6

r.p.m.

0

't.0

iii

2700

A

2400

O

2100

1,0

1950

0.5

I

I

6

7 Field( K G )

I

8

9.0

Fig. 5. Potential difference between center and rim of disc as a function of magnetic field and rotational speed.

the current measurements in the absence of electrolyte are shown in Table 2. In the presence of an electrolyte as load, the current was diminished, as seen from Fig. 8 which shows relations of electrolytic current, rotational speed and potential difference induced across the disc. 3.2. Pulse

producing homopolar generator, driving an

electrolyzer Figure 9 shows the pulse amplitude vs the rotational speed both in the presence of the load (cell) and for an open circuit. It is shown (Fig. 10) that the pulse amplitude and pulse width (duration) have an inverse relationship. The variation of the current with potential is shown in Fig. 11. The formation of bubbles depend on

0.5

0

I 02

I 0.4

t 0.6

1950 2100 2400 2700 3000

o

1.0

r I'o

Fig. 6. Potential distribution in the magnetolyzer. Here r0 is the radius of the rotating disc and r is the radial distance at which the potential, relative to the center, was determined.

duty cycle: for the off/on ratio >10, no bubbles were observed. When the off/on ratio decreased to two or less, bubble formation became visible.

Table 1. Potential difference between the center and periphery of the disc at an applied magnetic field of 8.6 kG Rotational speed (rpm)

I 0.8

Calculated p.d. (volts)

Measured p.d. (volts)

Measured p.d. Calculated p.d.

2.02 2.18 2.49 2.80 3.11

1.78 1.95 2.25 2.50 2.75

0.88 0.89 0.90 0.89 0.88

105

USE OF HOMOPOLAR H2 GENERATOR :-

30 c m ~

/

3.0

-;

24 cm 11 cm

•-

Am

/o °

Load

x

NO

0

Wtt"

2.0

g @

"O ,-i ,,,.,

E n

1.0

Fig. 7 Schematic diagram of electrodes in the magnetolyzer. 0.0 250

500

750

1

0

1 50

R.p.m. of M a g n e t s

Fig. 9. Variation of pulse amplitude and rotational speed of magnets in the pulse producing generator.

Table 2. Current and potential measurements in air in a field of 8.6 kG Rotation speed (rpm)

Potential difference (V)

Cu~ent (A)

1950 2400 2550 2700

1.78 2.25 2.38 2.5

52 57 74 81

4. D I S C U S S I O N

4.1. One-unit system 4.1.1. Potential-current relation. W h e n a conducting disc rotates in a magnetic field, B, with a velocity, v, with v at right angle to the magnetic field, an electric field ( X ) will be induced in the disc from center to

2400

2300

~; t~

2.15

2200

,m

,=,, o.. 03

2100

1.95

2000

1900

I

I

40

80

I 120

CURRENT

1.75 160

MA

Fig. 8. Variation of current with speed and cell potential in one unit system.

J. GHOROGHCHIAN AND J. O'M. BOCKRIS

106

Hence

3.0

E = ½o)B(r~ - r?),

where E is the potential difference (volts) from the center to the edge of the disc, o) its angular velocity (radians s-~), B is the magnetic flux density (T), and r0 and r~ are the outer and inner radius of the disc (m), respectively. The magnetically induced 'cell potential' must be equal and opposite to the potential needed for the electrolysis of water. Thus

2.4

o

(3)

1.8

E '~ 1.2

Ere, + Yrl + l(R~ol.) = Eindueed,

L 0.6

0.0 0.00

I

I

0.25

0.S0

I

0.75 Pulse Duration (ms)

J ~.o0

~ ~.25

(4)

where E=, is the reversible cell potential for hydrogen and oxygen evolution at the appropriate temperature (80°C in the present case), Zr/is the sum of the activation overpotentials at the current densities used, while I R is the total integrated ohmic potential drop in the solution between cathodic and anodic areas. The overpotential may be written as: [4]

Fig. 10. Relationship between amplitude and duration of pulses.

r/+ = In ix+o - In i~+

(5)

17_ = - I n izJ + In i~_,

(6)

where periphery. According to the Faraday-Lenz law: X = V. B = t o r . B

RT

because the direction of X is radially outward along the disc. Therefore, the potential difference between the center and periphery of the disc is E =

X dr =

;to = ~

(1)

(7)

and the i's are the mean current densities on the cathodic and anodic areas as indicated. Since i. ;

(2)

torB dr.

RT

and 3.~ = a'~F

and i- = ~22'

(8)

where A1 and A2 are anodic and cathodic areas, respectively, then by substituting equation (5), (6) and (8) in equation (4), one obtains

150

[ l~+a, ]

E - Erev - / R

= In

[A~A~J -

ln[i°+)~"(i°'-)~"

(9)

Introducing L + Xc = g ~00

(10)

and, since the anode and cathode materials are the same, one may also write

g

( i o , + ) ~ ( i o - ) ~ ( A l ) ~ " ( a : ) ~ =I~.=,.

Equation (9) may be written as

O

"1 0

(11)

I = I0.=, exp

5O

E - E=v - I R

g

(12)

When E - E = v - I R was plotted against the log I, a slope of 0.19 resulted (see Fig. 12). In this calculation, the 1R term was numerically evaluated from the experimental I - V graph, using the Tafel equation as: .o

i

i

1o

i

21o

1

310

Cell Volllge

Fig. 11. Current-potential relationship of an electrolyzer driven by a pulse-producing homopolar generator.

E - E~

- I R = a + b log i.

(13)

Thus, taking experimental values of E - E ~ and the corresponding I values at two different points, R could be obtained from equation (13). It should be noted that

USE OF HOMOPOLAR H: GENERATOR 1.5

1.0 rr "7

w

_°..L------

,,,

°

___-------r--0.5

Slope = 019 0.0

-1 75

-1 .~50

-1.25

-1 bO

-o~s

-0~0

Log I ( A m p )

Fig. 12. Variation of the sum of activation overpotentials with current in a one unit system.

in the present experiment, no attempts were made to correct for any chemical reduction of oxygen by hydrogen, the two gases being allowed to mix and to contact the stainless steel disc. Thus, the measured c u r r e n t - which depends on the oxygen concentration--may have been higher than that arising from the measurements. The near identity of the calculated Tafel slope (0.19) with the expected (0.22) is an indication that this problem was not severe. 4.1.2. Current density and electrocatalysis. The maximum current actually obtained in experiments (at 2300rpm) is 0.14 A. The current density cannot be evaluated precisely because of lack of exact definition of the area, but taking a mean of the anode and cathode areas, it is about 1 m A cm -2. This is too small for an electrolysis device, but the difficulty can be overcome by the use of electrocatalysts. Thus, the difference in the overpotential on steel and that on platinum for O: is (/.2 V (Pt the lesser) [5] and this would be equivalent to an increase in current density of around 20 times. Such an increase in current density would give rise to an increase in IR drop. Utilizing a current density of 1 m A cm-:, and taking an average distance between the anodic and cathodic section as 7 cm, the value of the IR drop would be about 7 mV and thus a current density of about twenty times larger than this would give rise to the more significant value of 0.14 V. The increase in rotation rate necessary to compensate this can be calculated from equation (3). Utilizing E = 0.14 V, B = 0.86 T and r~ = 15 cm, the necessary increase in rpm is found to be 138. This, however, would give a current density of only about 2 0 m A c r o -2 and to attain 100 m A c m - : , one will have to increase the potential driving force to such an extent that the current density increases five times, Now, the actual (IR corrected) slope of the AV - log I line (see Fig. 12) is 0.19. Hence: 5 = O£

1 0 ~xv:019

AV = 0.13 V.

* Data for these substances at high temperature are not available.

107

However, a large increase of potential is necessary because of the added IR drop which an increase current density from 20 m A c m - : to 100 m A cm -2 would cause. This would be 0.14 × 5 = 0.7 V. Hence one would need a further increase of rotation rate equal to 0.13 + 0.7 = 0.83 V. Using the equation (3), this means a further increase in rotation rate of 690rpm, i.e. a total increase compared with that necessary for 1 m A cm-: (2300 rpm) of 138 + 690 or 828 rpm. Hence at a rotation speed of about 3100rpm, one should observe a current density of about 1 0 0 m A c r o - : . It is probable that with better catalysts (e.g. M o - C o for the cathode [6] and RuO2 for the anode),* higher current densities could be achieved. 4.1.3. Energy used in one unit system. The mechanical energy needed to drive a disc in a magnetic field, the disc being immersed in an aqueous solution, consists of two major contributions: (a) The work done in overcoming the magnetic torque. (b) The work done in overcoming the viscous drag between the disc and the solution. 4.1.3a, Evaluation of the magnetic torque. The force on the rotating disc of radius r and width z carrying a current density i in a magnetic field B (where i and B are mutually perpendicular) is given by F = i x B.

(14)

The torque at a point on the disc at r from the center is

re, = Fr

(15)

and the total torque is given by the integration of the point torque over the entire volume

re~ = J Fr dV

(16)

or

f~'£2~fo~{ ] B r t d r d Z r d r~ = , \2w, Z / IB ~, = -~- (r~ - r?),

0

(17)

where I is the total current (A), B is the magnetic flux density (T), and r0, r, are the outer and inner radius (m), respectively, r,a is the electromagnetic torque (Nm). The electromagnetic torque for the present case (at 2300 rpm, the current being 0.14 A and the magnetic field 0.86 T) is 1.3 × 10 -3 Nm. The power required to overcome this torque would be

P = rw = 0.31 W.

(18)

This may be compared with the power needed to run a normal electrolyzer, at 2 V and 0.14 A, viz. 0.28 W. 4.1.3b. Evaluation of the viscous torque. The evaluation of the magnetic torque is easier than that of the viscous torque. The difficulty is that the experimental work reported here was carried out in a turbulent region, and purely theoretical treatments are not appli-

108

J. GHOROGHCHIAN AND J. O'M. BOCKRIS

cable. Daily and Nece [7] have shown that, for a rotating disc in a fluid, the torque r,, can be obtained from an equation containing an empirical coefficient:*

r,~ = ~C,,ptoZr 5,

(19)

where p is the fluid density and C,, is a parameter, the torque coefficient, which has been found experimentally, to be given by Cm = 0.0102 (g/r) tq° Re -t/5,

(20)

where g is the axial clearance between the disc and the wall of the container, and Re is the Reynolds number. Using equations (19) and (20) with appropriate conversion factors, the mechanical torque loss for the condition of 2300 rpm, r = 0.15 m and p = 103 kg m -3, the Reynolds number of 1.4 x 106, would be 1.18 Nm. The power required to overcome this torque at a rotation rate of 2300 rpm and for the other constants given, is ( P = r,,to) 284 W, which makes the production of hydrogen for a disc in contact with a liquid rotating in a magnetic field for an rpm range in the thousands and a magnetic field of around 1 T, unattractive. However, it will be shown that under other conditions, more attractive conditions in respect to energy use can be reached (Section 4.1.4). 4.1.3c. Power consumption. It is normal practice to express the power consumption for hydrogen production in terms of kilowatt hours of electricity per normal cubic meter of hydrogen. Since the number of moles of hydrogen produced by a current I a m p s in a time of t seconds is equal to It/nF, the current required to produce 1 m 3 of hydrogen in one hour is:

nF 3600

x

1 22.4 x 10 -3

of Fig. 1 would have a comparable energy consumption with that of electrolyzers it is expedient to calculate the total torque of the device from equations (17) and (19). noting the constancy condition as 2E Bto = --x- = 1.77 x 102. r~

In this equation, the cell potential is taken as 2 V and r0 = 0.15 m (cf. Section 2.1). The calculation has been for magnetic fields between 2 and 2 0 T and for corresponding rpm's between 845 and 84.5. Having obtained the total power, from (17) and (19), the power consumption for one cubic meter of hydrogen is calculated and shown in Fig. 13. It is seen from this figure that the conditions at which the magnetolysis device begins to consume less energy than a normal electrolyzer occur (for the dimensions of the

1000

(

100

E

= 2.393 x 103.

Solution

(21)

Thus, the energy consumption for an electrolyzer can be calculated as follows E x I = 2.393 x 103E W hm -3 = 2.3932 kwh m -3 H2.

(23)

0 Q.

S c o U

(22) o

Taking E (the cell potential) as 1.9 V, the power consumption for normal electrolyzers would be about 4.5 kWh m -3. Now let us discuss under what conditions the energy consumption of magnetolysis could be comparable to or less than that of normal electrolysis. As pointed out in previous sections, the power required to overcome the viscous torque is the major source of energy loss in the present device and under the conditions used. However, the situation may be changed if a sufficiently high magnetic field is used, because the disc might then be rotated at a Correspondingly lower rate. An increase of B by 10 times means a 10 times decrease in to and by utilizing this change in equation (19) it is seen that the mechanical torque is reduced by about 100 times. To find the condition at which the magnetolysis device * The parameter in this equation corresponds to the use of British units in the equation,

10

.............. ~

s

NOViscousTorque

1°

J 4

[ 8

I 12

I 16

I 20

Meg~tlc Field ( t e s l e ) I

I

I

845

338

I,

I

169

112

I

Corre~oondlng r,p.m.

Fig. 13. Power consumption as a function of rotation speed and magnetic field for one unit system.

109

USE OF HOMOPOLAR H2 GENERATOR cell reported here) when the rpm value falls below 120 and the magnetic field rises above 15 T. Such a result directs attention towards the optimal cost situation. 4.1.4. Cost situation of in situ magnetolysis. As the magnetic field gets stronger, the cost of the magnet goes up but the cost of rotating the device drops. Figure 14 shows the total cost as a function of magnetic field and rotational speed (for producing 2 V under the same geometrical condition as those used in the examples given above). The minimum capital cost is at a magnetic field of 0.5 T, where the rotational speed is about 3500 rpm. However, the power consumption under this condition is higher than that of normal electrolyzers (Fig. 13) due to the energy needed to overcome the viscous torque. Better results would arise in a device in which the solution is contained in a cassette which would rotate at the same rate as the disc [8]. In the limit, viscous drag will then be zero and the power consumption is spent predominantly in overcoming magnetic torque. The relation between power consumption and rotation speed (or magnetic field strength) under these conditions is shown in Fig. 13. The cost of 1 m 3 of hydrogen is Capital cost x amortization rate of return m 3 h -1 x 8"760 + power cost m -3

(24)

100.000

for the condition of Fig. 14 and zero viscous drag. The capital cost can be obtained from Fig, 14 (as the minimum value). The current value used is 14 A, on the basis that a 100 times increase in current would occur using electrocatalysts. The value 4.25 in the following equation is a kWh m -3 value from Fig. 13. Thus, using the value of the minimum capital cost from Fig. 14, one obtains for the cost of 1 m 3of hydrogen

($):

4000 x 0.15 + 4.25 C = 5.8 + 4.25 C, 14 -x 8760 2393 where C is the cost of electricity per kWh, in dollars (=0.04). Thus, the capital cost dominates. For electrolysis, the cost of 1 M B T U is [9] 2.29 EC' + 3,

(25)

where E is in volts, C' is cents per k w h and $3 represents principally amortization rate of 15%. This gives $13.99 per M B T U , or $0.14 per cubic meter of hydrogen. Thus, the magnetolysis device (one unit), as foreseen here, needs a reduction in capital costs of about 80 times. A reduction of this order cou]d only occur where series production of high strength magnets begun. 4.1.5. Other configurations. Two other configurations in the development of a magnetolysis generator will now be discussed. 4.1.5a. Drum shaped. A possible configuration which was shown in the original Bockris and Gutmann [1] article is shown in Fig. 15. In this configuration the generated emf can be calculated as follows

E = toBrl,

where 1 is the axial length (meter) and r is the radius of the drum (meter), The symbols to, B and E have the same meaning as before, Let us assume a drum with a length of 10 cm and radius 5 c m , rotated in a magnetic field of 1T. By applying equation (26), one finds that a potential of 2 V would be generated between the two ends of the drum by a rotation rate of 4000 rpm. Thus one may find the energy needed in this case by utilizing equation (19) for viscous torque and calculating electromagnetic torque

v o

U

(26)

10,00(

U

~,oot0 I 11L

~ 2000 ll70

5o~oo 40100 Rotation Rate (r.p.m.) k 0.50

, 0.33 I

8o'oo

10,000

N] s]

S

N

.÷÷÷÷

÷.÷÷÷ Rotating Drums

0.20

Magnetic Field (te$1a)

Fig. 14. Capital cost as a function of rotation speed and magnetic field.

J

,,.

Electrolyte

Fig. 15. Drum shaped homopolar generator and electrolyzer in situ.

J. GHOROGHCHIAN AND J. O'M. BOCKRIS

110

as

(29) would give re~ = 1Brl.

Let the current assumed be that used in the experiment described above (for disc configuration), i.e. 0.14A. Then with (19) and (27) one may find the torque and using equation (18), the power becomes known. From equation (21) one may calculate the rate of production of hydrogen and then the power consumption. With the parameters stated above one finds 128 kWh m -3 and this may b e compared with 4.5 kWh m -3 for normal electrolysis. Hence, the configuration assumed does not give encouraging results. The power consumption for the drum configuration can be correspondingly reduced, by a method similar to that suggested for the disc, namely, one may assume it possible to bring about a situation in which the drum is enclosed by an outer cylinder rotating at the same rate so that the viscous drag between drum and solution would be reduced towards zero. Assuming the extreme case, one may calculate the energy needed for the drum configuration in terms of electromagnetic torque only. Utilizing, then, equation (27), and following the mode of calculation outlined above, one obtains 4.78 kWh m -3 H2. This value compares, then, very favorably with the value for the classical electrolyzer (4.5 kWh m-l). However, there does not seem to be any particular advantage in the drum over the disc configuration. 4.1.5b. Straight f l o w . It would be possible to pump the electrolyte between the two electrodes and have a magnetic field perpendicular to the direction of motion of the fluid. An emf would be induced between the two electrodes. Suppose the cell has a rectangular channel with dimensions of 2 x 20 x 100cm. Let distance between the electrodes l = 2 cm, distance between the poles of magnet b = 20 cm, therefore the cross-sectional area of the channel would be 40 cm 2, and let the electrode length L (in the direction of flow) be 100cm. Then, for a magnetic field B = 10 T, electrolyte velocity, V, required to generate 2 V, can be calculated as follows: E = VBl.

(28)

From this V = 1 0 m s -l.

Electrolyte is moved at a speed V against a hydraulic pressure p at a volume rate Q = blv across the magnetic field (l is the electrode distance and b is the distance between the poles of the magnet). The force required may be written as [10] F = B I I = blp.

P = pQ

where P is power (watts), i current density Am m-: and Q flow rate m3s -~ and L is the length of electrode (meters). The power required to pump the electrolyte is (from 31) 10 x 103 x 0.04 = 400 W. Assuming a current density of 100 mA cm-:, with the geometry and magnetic field stated above, then, the energy needed for production of 1 m 3 of hydrogen per hour is obtained from (21), according to which 2.393 x 103 A is required to produce I m 3 in 1 h. The current used here 0.1 x 2000 = 200 A, would produce 0.083 m 3 Ha h -t. As this current corresponds to the use of 400W, the energy to produce 1 m3h -~ of H2 would be 400/0.08 -- 4.8 kWh which is comparable to normal electrolyzers, but no transformer or rectifier required. 4.2. Pulse p r o d u c i n g h o m o p o l a r generator driving an electrolyzer

4.2.1. I n d u c t i o n o f potential. For a single conductor of length L, in a constant magnetic field B, where the relative velocity of the magnet to the conductor is U. the induced potential is given by

(30)

and substituting p from (29) into (30) and rearranging

(32)

E = UBL.

In the device discussed in section (3.2), the rotating magnet contacts a succession of conductors in series. In Fig. 16, one quarter of the conductors is shown affected by the magnetic field on one sweep. Thus, four conductors are in series on each side of the loop (eight on both sides) and the propeller containing a magnet at each end which doubles this number to 16. If, in general, n conductors are affected by the magnets at each pass, the maximum potential induced is Emax = n U B L

(33)

(assuming a uniform magnetic field) and the average

Z

E.~ = n U B L

(34)

E,v = 2 ~oRBL = n2 x 2~N60R B L ,

(35)

per pass. Hence,

2 ¢m

(29)

Thus the power P to pump the electrolyte between the poles of the magnets, assuming no viscous drag, would be

(31)

P = BiQL,

(27)

., H. ~6 err7

Fig. 16. Conductor arrangement in pulse-producing homopolar generator.

111

USE OF HOMOPOLAR H2 GENERATOR where R is the radius of the propeller and N its rotation rate in rpm. As the two magnets (each at the end of the propeller) pass the successive sets of conductors, the potential produced will thus come in triangular pulses the average magnitude of which should be given by equation (35). 4.2.2. Time in which current passes per pulse. The time for one rotation is given by 2~r to

2zr 2rrN/60

60 N '

\

(36)

Iss

e~

where N is the rpm. At N = 1000, r = 0.06 s. The length of one set of conductors was 2 cm and the loop radius 30.5 cm. Hence, the time during which the magnets are passing over the conductor to results as to

2.0 x 0.06 = 0.6 x 10 -3 s. 2x x 30.5

t (sec)

Fig. 17. Sequence of pulses in the homopolar generator.

Therefore, a mean potential of E,, = n (2~/60) N R B L = 3 V

17 one can write n

should be produced for 0.6 ms, the experimental potential observed is 2,6 V. The deviation from the calculated 3 V is doubtless due to the inhomogeneity of the magnetic field. The build up of the potential to a current density of i is given [4, 11] by r = 4CR = 4C 0r/ 6i

(37)

or

r =

4C R T I . o~F i

(38)

Taking the C, double layer capacitance as 50 ~tF cm-:, a = 1/2, then 1.02 x 10-5s r---

i

For an i of 0.07 A cm-: (see Fig. 11), r - 0.14 ms. Thus the pulse lasted about 5 times the switch on time, i.e, the double layer charging time. 4.2.3. Pulse electrolysis. It is well known that the rate of reaction in electrochemical cells decreases with time. This rate can be increased momentarily by a current or potential pulse [12] but decay again sets in. The ratio of pulse current, ip, to the steady-state current, i,,, can be calculated. Thus, the current due to a potentiostatic pulse can be written as: i~ = /max e -kt

•

1 ff.

/mean = "~

/max

e_k, '

(39)

where r is the pulse duration and 1/k a time constant Cs-t). If we have a succession of n pulses as shown in Fig.

, /max

0~'-~-- (1 - e -k`) + (n)i,, (40)

t/ or

ip _ ----1+ /~

im~x (1

e-k').

(41)

kzi,, "

Taking the value of i,,ax as 0.07 (Fig. 11), is, under the same conditions was found experimentally to be 0.038 A cm-:; the value of k was taken from the experimental results of H o b b e r et al. [13] to be 1.55 x 1 0 3 S - 1 . Thus, the ratio of iput~ to is~eadystatefor the present experiment would be 2.07, which is in agreement with the literature value of about 2 [14, 15]. Thus, by pulse electrolysis, the rate of production of hydrogen on a nickel screen would be around twice as much as the rate in steady state, one reason in favor of the device suggested. CONCLUSIONS (1) Co-rotation of a cassette-holding solution would make it possible to reduce the energy needs of the use of a homopolar generator, in situ, and make them equal to those of classical electrolyzers. (2) The external homopolar generation of low voltage d.c. has advantages in respect to electrochemical machines, e.g. the current can be pulsed without supplementary instrumentation. (3) Economic advantages could occur in the capital cost of an electrolysis device using an ex situ homopolar generator (no a.c. generator, transformer and rectifier). If such gains are to be realized using high-strength permanent magnets, their cost (per unit volume) would have to fall around 80 times those of research magnets.

112

J. G H O R O G H C H I A N AND J. O'M. BOCKRIS

Acknowledgements--The work reported was initiated by Dr Hampton Robinson, Jr in the course of the pursuit of his interest in the production of a clean fuel. It was continued in the Hydrogen Energy Research Center and in this respect the authors have to thank continued support from Dr Hampton Robinson. the National Science Foundation, and the corporate supporters of the Hydrogen Energy Center, namely, ARCO, Chapparal Minerals, Koppers, SOHIO, and Teledyne. The authors are grateful to discussions with Dr T. Nejat Veziroglu, Dr A. Gibson, Dr M. Ehsani and Mr J. Black of Texas A&M University.

REFERENCES 1. J. O'M. Bockris and F. Gutmann, Appl. Phys. Commun. 1, 2 (1981). 2. C. V. Philip, J. A. Bullin and R. G. Anthony, J. Chromat. Sci. 17, 523 (1979). 3. J. O'M. Bockris, Electrochemistry of Cleaner Environment, p. 184. Plenum Press (1972). 4, J. O'M. Bockris and A. K. N. Reddy, Modern Electrochemistry, p. 1195. Plenum Press (1970).

5. B. V. Tilak, P. W. T. Lu, J. E. Colman and S. Srinivasan in Comprehensive Treatise of Electrochemistry, Vol. 2. p. 30 (Bockris, Conway, Yeager and White, eds). Plenum Press (1981). 6. A, J. Appleby and G. Crepy, Proc, Syrup. Ind. Water Electrolysis (S, Srinivasan, F. J. Salzano and A. R. Landgrebe, eds). p. 150. Electrocbem. Soc,, Princeton, New Jersey (1978). 7. J. W. Daily and R. E. Nece, J. Basic Engng, 217, March (1960). 8. N. T. Veziro~lu, Private communication (1983). 9. J. O'M. Bockris, Energy Options, p. 324, John Wiley (1980). 10. M. G, Say and E. O. Taylor, Direct Current Machines, p, 29, John Wiley (1980). 11. J. C1. Pnippe, N. Ibl. J. Appl. Electrochemistry 10, 779 (1980). 12. J. O'M. Bockris, B. J. Piersma, E, Gileadi and B. D. Cahan, J. Electroanal. chem. 7. 487 (1964). 13. B. S. Hobbs, P. R. Vassie, A. C. C. Tseung, Symposium on Electrochemical Engineering (J. D. Thornton. ed.), Vol. 1, p. 1123 (1971). 14. S. M. Jusem and A. C. C. Tseung, J. Electrochem. Soc. 126, 1353 (1979). 15. A. C. C. Tseung and P. R. Vassie, Electrochim. Acta 21, 315 (1976).