(SANITIZED)UNCLASSIFIED SOVIET BLOC PAPERS ON MAGNETOHYDRODYNAMIC ELECTRICAL POWER GENERATION(SANITIZED)

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00247A003400170001-4
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 71
• Document Creation Date: December 27, 2016
• Document Release Date: March 6, 2014
• Sequence Number: 1
• Publication Date: July 8, 1964
• Content Type: REPORT

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OW\ I -FI LJIVI
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ELECTRICAL POTENTIAL POTENTIAL VARIATION LAYERS NEAR ELECTRODES
G.A. Liubimov
Institute of Mechanics, Moscow State University, USSR
Certain problems of magnetic hydrodynamics have to deal with the flow
of gas contadting the surface of a conductor. If the surfaces are the electrodes,
with the flow confined between them, i.e., the surfaces through which there
occurs exchange of current between the gas and an "external" object, the
boundary condition is frequently specified as the current density on the
surface of the electrode hl/s = f(xz)/ or, which is the same, the potential
difference between the two electrodes. Such boundary conditions presuppose
that the current density on the interface specified or determined from the
given potential difference is ensured by the mechanisms of the current transfer
on the gas-electrode surface.
On the other hand, the current density on the surface of an electrode is
determined, as we know, .by the emission properties of the electrode material,
its temperature and the intensity of the electric field near the eledtrode
surface /1/. With small electric fields '-E'n the electrode surface; the'
current density can be determined by the ration
Jel = AT? exp [- g + 4;39
(i)
where ID is the work function of the electrode material and T--its temperature.
The relationship /1/ shows that the current density
on the surface of the electrode cannot, generally speaking,
be specified or determined from the solution of the problem
of current distribution in the gas. It has been shown in
a number of editions, for example in /2, 3/, that when the
boundary conditions are specified on the surface of the
electrode, account should be taken of the possibility of
.formation of narrow layers of the electric potential change
at the electrode. Such layers make the change in the
potential in the flow area different from the potential
STAT
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I . - 2 -
tial in the layer at the electrodes is determined from the
condition of uninterrupted current density on the surface
of the electrode and depends on the properties of the
electrode material and the physical processes which occur
near the surface of the electrode.
Since we know very little of the structure of the
electrode layer, we must allow for certain assumptions,
which can be specified more accurately or verified by
comparison with the experimental data, to solve our problems.
As the simplest resort we may replace the electrode
layers by the potential breaking surface /2/. For the next
approximation we may assume that the potential has a
linear distribution inside the layer, in which case
E
where d is the Debye length /3/.
From the assumption /2/ and the balance
charged particles on the electrode surface we
following ratio for determining the change in
tial in the electrode layer, depending on the
density
where
t(jet,h)
i-1-(1-ylE "It 1)
jevte?eN )
2 a 4
integral of probability.
If we regard the electrode layer as the
surface of the potential /2/ we shall obtain,
/3/ the following expressions
9
(2)
of the
obtain the
the poten-
current
(3)
I) is the
breaking
instead of
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3
?
4????,'
Je
e ? ,
Jz4-Jel-J
K T je
) _ e (fejt ( 4)
The volt-ampere characteristic for the gas interval,
to which the potential difference V is applied, and with
account taken 9f the layers at the electrodes, will have
the following form /4/ '
( 5)
The characteristic /5/ is actually nonlinear (if
we disregard the layers at the electrodes,the characteristic
will be linear: v rj). Obviously, from the standpoint of
their effect on the volt-ampere characteristic, the
electrode layers can be described by certain resistance
0 T4:1-
7.= --7--which depends on the current density.
The shape of the characteristic /5/ depends on the
structure of the layer at the electrodes. If we use the
assumptions in /4/ the characteristic has a.saturation
current area. With the assumptions in /3/ there is no current
saturation area. The experimental data obtained in /2/ show
that the characteristic has no current saturation area and,
at large concentrations of the seeding, the characteristic
has a large slope angle at greater currents.
The comparison of the experimental data with the
data calculated in /5/ demonstrates that the assumptions
in /3/ describe better the qualitative (and even quantitativA
aspects of the phenomenon in question than the assumptions
made in /4/. In this connection, the theory based on the
assumptions /2/-13/ appears to be in good agreement with
the experimental data when the temperature of the electrodes
is T 20000.
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?
4 ?
References
1. V.I.Gaponov. "Electronics", Fizmatgiz, 1960.
2. Z.Croitoru, A.Montardy. "Electrode Phenomena, Tensor
Conductivity and Electrode Heating in Seeded Argon."
IV Symp. Eng. asp. magnetohydrodyn., 1963.
3. G.A.Lyubimov. "Change in the Electric Potential at the
Channel Wall with an Ionised Gas Flowing in a Magnetic
Field". Applied Mechanics and Technical Physics, 1963, No. 5.
4. G.A.Lyubimov. Electrode Layers of the Potential Change
in Passing Weak Current Through an Ionised Gas, Applied
Mechanics and Technical Physics, 1963, No. 6.
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FORMATION OF SPACE' CHARGE SHEATHS AND FLOW OF AN ELECTRIC CURRENT IN A
PLASMA STREAM
INVESTIGATIONS OF IONIZATION CHARACTERISTICS OF PLASMA STREAMS IN AN
ELECTRIC FIELD
A.K. Musin
V.I. Lenin All-Union Electrical Institute, Moscow, USSR
1. A theory developed by Thompson and Wilson f1,e for a non-self-
sustained current in a gap is often used for studies of ionization properties
of plasmas. However, this theory is based on the assumption that processes
associated with electric current flow are stationary.It is inapplicable to
rapidly moving plasmas, plasmoids and flames. In this paper approximate
analysis of setting up processes of non-self-sustained current and sheaths
adjacent to the electrodes are given and basic setting up periods are defined.
Thompson-Wilson's theory describing a steady non-self-sustained current may be
regarded as a particular ease when t -400 (see also EV).
2. Let a uniform ionized gas stream flows with steady velocity 1
into a space between two plane electrodes to which a constant external voltage
Uoisappliedfseefig.g.During this process the total electric current
in external circuit remains constant. However, the current density will vary
along the direction of the plasma flow because space charge sheath S and
potential drops at the electrodes do not set up instantaneously. In a coordi-
nate system associated with the flow certain expressions appears to be dependant
on "equivalent" time t = Z/V. Equations of continuity and of field source
in moving coordinate system may be written as follow ;
-,- .* (1)
1)A,
60,e(fleE) - 061- er (2)
e0(74- ne) (3)
There n, ,n, oe -are concentrations and mobilties
of electrons and ions; E- is the electric field strength;
I- the ionization rate; cc- the effective recombination
coefficient; rE (42)- depending on a dominant recombination
process. If it is .assumed that the cathode and anode do not
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tion equilibrium occurs when no electric field is applied,
then the boundary conditions can be assumed to be:
xo
ilz/x = xo = /
X = 0 ; E(X) d X =-? Uo. (4)
0
nei = no ( / 0 ; r-
c
_ r
d_
tz c5)
= t.= 0
Solution of the expressions 1)-45) has been found in the
form of continuous functions which are plotted in fig.2-4.
3. After the application of an external voltage the
electrons move from the cathode and form a high current at
the anode. A positive charge sheath forms near the cathode.
As a result, an electric field at the cathode increases and
causes considerable increase of the ion current. Simultaneously
the thickness of the cathode sheath increases while electric
field in a plasma gap decreases. This leads to a decrease of
1
the electronic current to the anode. Soon the positive ion
concentration near the cathode begins to decrease due to the
'difference in drift velocities- of the ions in the cathode
region and in the plasma gap. The ion current value, having
approached the electronic current value and having passed
maximum , decreases together with that of electronic current.
'Whena2all the values approach their limits asymptotically.
Expressions for these limiting values coincide with formulas
of the Thompson-Wilson's theory for a steady process. Principal
form of the solution is given in fig. 4 and 5.
Electric field in the plasma gap /outside the space charge
sheaths, fig. 4/ is given by the expression:
Ea) E,!= = (en- 63cP :L )2
E),?;0
?(S ? i) 3n. 7v
-Efre07-36,: (a + oe) i4? (6)
2 /
L LC-6e .7eo 4+ 6e)
r r 73 2 6i. ac,
4. Setting up processes for the electric current and space
charge sheaths may be divided into three periods:
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3
???
4.1. Initial period (L te ) )
during which the electric field in plasma gap changes
insignificantly and a proportionality between the electric
current and the external voltage is approximately maintained.
Then the current-voltage characteristic takes the form
o t(2 e, 6, no -0- y)
(7)
Wherefrom the plasma conductivityYmay be determined
4.2. Intermediate Period (V.' .6 erz
when EY6)L.E)'and the ion concentration near cathode is
co)
0
no Presstuze.s and. ionization velocities being
_cm Isec A2 -3
sufficiently high vism sp-(7454.i/jr ):
the current-voltage characteristic has the form&7 eio4T6(415i141)
. yo eon? C.Z V 6i uo)r2
0 or ( 8 )
Wherefrom the concentration of charged particles // 0 in the plasma
may be determined.
In the opposite case of low-pressures and small electron
concentralions An-1g /012.5/7Mthe current -
St7 ( +1)
-voltage characteristic has the form (C. ==
612 T /
1()
f 264:201,1:
Veo n.)311/4
(g)
Wherefrom the concentration of the Charged particles tqz)
may be determined too.
4.3. Steady current period /77:44-s-cc/ is characterized
by the constancy of the electrode current density.
The current-voltage characteristic then has the form
-= Y020
26- ao
(t0)
and. does not depend directly on concentration of the charged
particles but allows to find the ionization rate Tin the
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5. Application of the described theory to the results
of Boucher's (47 (fig.) and Banta's 15.7 (fig.?) experiments
are given below as an illustration. These authors -have
investigated ionization properties of air flames at
combustion temperature T- 2 ? 1O3? ( natural gas -
air mixture) with additives Bael C41 and Kel (5). Experimental
points of current-voltage Characteristics are denoted by
circles with crosses. Electron concentrations tie were
determined from formula (9): continuous straight line denotes
the mean value of1/ e' squares correspond to experimental
'
points of the current-voltage characteristic. Corresponding
^3 0r/
temperature rrt:==42,11-00,/)'16/ Kis in good agreement
with measured temperature (fr- 2-1403?1 4. Ion concentration near cathoderat)may be both
greater or less than the charged particle concentration
no in a plasma gap.
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cot &OM
7 '4i,
5:0
At '
Function approximating a space dependence of
effective ionization rate Tz(X1.0=r-o?,e n ? in a
-
cathode region X6 (O,A.) and, in a plasma gap X6 a x0)
Form of the function. in the cathode region is determined
by value ge Due to the 'equality of ionization and
? recombination rates (ionization equilibrium) in the
plasma gap the value-T-1-(X, i) 0.
Principal form of a function approximating a
EA
dependence of an electric field strength in a plasma gap
upon equivalent time /v/),
.Relaxation time and decay
factor may be found. from the solution (see section 3).
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V. - 9 -
tip
,r77.5
Pig.5.
Principal form of dependences of electronicele and
? ion j. currents, and. cathode sheath thickneseAupon equivalent
.time /11/. . In initial setting up period .6 6 CO,
Lt.
an electronic curreutiefalls slowly and an ion currentirapidly
increases. Ohm's law is approximately satisfied because the
total. current remaines approximately proportional to external
voltage (see section 4.1.). In intermediate period L. 6 0.7-:E.
ion current passes maximums, its value approaches that of the
electronic current and rapidly decreases w-J.th the latter.
Ohm's law is not satisfied., ion and electronic currents depend
significantly upon electron concentration in the plasma gap
(see section 4.2).
hent''Cr (steady current period) then values ?e
and di
are equal to each other , approach their limiting value, and
are determined by the ionization rate (see section 4,3).
? Cathode region thickness changes monotonously, the most
rapid. growth occurs when (0,;), and asimptotically
approaches its limiting value .A 0. ?
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,
A ce,
Qi
Q7
QS
as
414
QI
- 10 -
590
141_,
n, !Om
C,,.,
se
I.5
re'Qs
i5Oal
Results of the treatment of Boucher's 147 experiments
(air flame with additive NaC1). Continuous curves (parabolas)
theoretical; they are plotted for ne ne
(continuous
horizontal line) and 44,4 ,z st (lower dashed line).
The upper dashed line gest corresponds to value
obtained by the Author Iki when current was assumed to be
constant.
are
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4,
A
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Fig.7.
Results of the treatment of Banta's 6.1 experiments
( air flame with KC1 additive). Continuous curves are
calculated. for /7e=7/7e and 4ic . A value 4:4=
(the upper dashed line), obtained by the author [5,
when current was assumed to be constant, approaches value
eiz-re
, obtained taking account of the electric current
setting up processes.
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,,-,,
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ELECTRON EMISSION IN MED GENERATORS
D. Halisz, Ch. Szendy dnd Ch. P. Kovacs
Institute for Energy Research, Budapest, Hungary.
\
Nomenclature
C5 gas conductivity, mhos/meter
number of free electrons/0
electron mobility, d sec-1 volts
V work function, eV,
j,
gas temperature, degrees Kelvin
/
charge density, coulomb/1u3
r, R radius of the sphere, m
w.
q
velocity, meters/second
Boltzmann constant, 1,38 x 10-23 joules/deg K
electronic Charge, 1-0-6-4e10-19 coulombs
electric field strength, volts/meter
1
4.51* 9.109
codlombs
in volt
current density, amperes/d
electron mass, g
In the MED-generator the working fluid should be made to
some extent /2-100.thos/m/ conductive. As the conductivity
may be expressed by .
6 = n, q b_ mhos/m /1/
this can be attained if we provide .for n free electrons.
According to the present practice free electrons may be
produced by- means: of thermal ionization in equilibrium. This
process. requires a very high temperature. The test showed,
that the above conductivity values may be attained at a tem-
perature of 2500.,3100?K1)r seeding 1 perdent of potassium
to: the gab.
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The ionization potential of some materials:
K - 4,33V
Cm 3,90 V
The work function of these and other materials:
095 - 20 eV
Cs 0,7 - 198 eV
CaP 0,7 eV
BaO 1,0 eV
By comparing these numerical values it is obvious that the
conditions of producing free electrons, as regards the re-
quired temperature, are much easier to obtain than by means
of thermal ionization in the equilibrium state.
Thus, it seems worth investigating what temperature condi-
tions occur in both cases. We assume that the selected ma-
terial, with a relatively low work function /e.g. 1 eV/ and
resisting to the operating temperature during a period of
1/10 to 1/100 sec, is pulvexized and injected into the gas. [1]
2. Among the injected particles let us consider a sphere with
a radius ro 9 a work functionV 9 temperature ToK9
j
floating in a gas. Now, let us determine how many electrons
viii be emitted until the equilibrium' state is attained, and
in that state what will be the distribution of charges.
3. In the steady state conditon assuming only the intermole-
cular heat motion, the conditions for equilibrium may be
determined by the following
a/ the sum of the forces acting on an electron in any point
at distance of r is equal to zero, or
b/ the resultant of the velocities of electrons passing
through the surface of a sphere of radius r /assuming
spherical symmetry/ is equal to zero. It should be
noted that only radial velocities are considered.
The electron acquires velocity because of two reasons:
a/ the attraction of the sphere of radius ro becoming
positive by the emission of .electrons;
b/ the phenomenon of diffusion due to different charge-
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"4.
- 3 -
Other possible effects are neglected.
Placing the origo of the coordinate-system into the centre
of the sphere, the velocity caused by the electric field
will be
w1 = - b E m/sec
the velocity due of diffusion is
/2/
W2
= k T b_ LC- m/ sec /3/
dr
In the state of equilibrium the sum of both velocities
is equal to zero, that is
E =
kT 1
dr
volt/m /4/
The system should also satisfy the Poisson's :law
?dE 2 E ja_
dr r
a
The potential of the electric field can be expressed as
dV
=
.E - dr
Therefore from /4/
? /Vo-V/1
50 exp
kT
where V, - are the values on the surface of radius ro
/0
Substituting it in the /5/, it can be written as
dV
1 d.
r`?
= r2
dr - o exp lp
r kT /V0 - V/}
/6/
This differential equation can be solved by means of ana-
logue computer.
4.. If the temperature of the sphere of radius ro is T?K,
the working function is Vi /volts/, than in the immediate
vicinity of that sphere mr the electron density in vacuum
m k. T/ r12.1.11
exp 1- /7/
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o =
-4
iT - coulomb/cm3 /8/
1 12 kT
2 m
where w is the emission velocity of electrons.
5. The investigated space As the inside of a sphere of radius R
where the sum of all charges is zero. Consequently, the
field strength in radius R is also zero, Thus,
E ,dVj_
' dr 'R
/9/
This can be taken as the first initial condition of the
differential equation /6/. The second condition is dealt
with the charge density of electrons on the surface of
radius r which is given by /8/.
6. In course of our investigation only one emitting spherical
body /radius ro/ has been dealt with so far, tacitly neglect-
ing the influence betweenthiemitting bodies being present
In a great number. As we shall see in the following, with
regard to the average ionization interesting us mostly in
the present investigation this neglection is permissible.
Around each of the uniformly distributed spherical bodies
of radius ro 9 injected into the gas we imagine a concentric
sphere of radius R . All these spheres fill Out the whOle
space when arranged in the most congested manner. As is
well-known, this condition is satisfied by the hexagonal
arrangement when each sphere is at 12 points in contact
with the surrounding spheres and the porosity, i.e. volume
of space not within the spheres is 26 per cent. The phenomena
are, however, definitively influenced by the events in the
nearest vicinity of the solid body and the distance of both'
bodies from each other is generally 50 times as great as
the value of ro 0 On the boundary surfaces with a radius
R the variables can be assumed as having identical values.
Therefore we do not commit a great error if we imagine the
phenomenon to proceed between .the surfaces. of the two con-
centric spheres of radius ra and R..
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7. From a high-temperature sphere of radius ro
n =
2(-
? 4 r 11e, dr
electrons were emitted.
Ao/
? However, the number of molecules existing in the spherical
body must be much greater than that of the emitted electrons
consequently the diameter of the sphere cannot be decreased
below a certain limit.
Through the emission of the electrons the sphere gets posi-
tively charged. Consequently the emitted electrons have not
only to perform the work function from the molecular band
but also to overcome the potential difference between the
surfaces of ro and R
8. As to give an idea of the quantitative conditions let us
investigate the following example
T = 1,3.103
Fo . 2,46.107
R = 107m
VJ
= 1 eV
5o
5
4.10 coulumb/m3
1,1.10-1 n?/volt sec
Seeded with 2 per-cent BaO.
The 4/6/ is solved by Solatron analogue computer, so
the specific charge at radius R
qR . 20 coulomb/m3
The Pig shows the specific charge and the field strength
in fdnction of the radius. So it can be seen, that the
required conductivity is obtained.
Even this value with certain modifications considerably
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9. On the basis of the above consideration it seems possible
to operate the MHD generator in a range of temperatures
which the structural materials known at present can with-
stand.
References:
1 Mc Grath, I.A.? Siddal Thring M.W.
Advances in Magnetohydrodymamics? Pergamon Press 1963.
Oxford, London, New York, Paris.
2 Mc Intyre, Robert I.
Extendes Space-Charge Theory in Low-Pressure Thermoionic
Converters, Journal of Applied Physics, vol. 33.
Aug. 1962.
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106
107.
105
103
,
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blikl
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CI-AT
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THE EXPERIMENTAL DIRECT CURRENT .MHD GENERATOR OF THE OPEN CYCLE
W.S. Brzozowski, J. Dul, E. Fuksiewicz, M. Miko6 & R. Wang
Laboratory of Plasma Physics & Technology, Institut of.
Nuclear Research, Swierk near Warsaw, Poland
1. Introduction.
STAT
The research project on the direct conversion of thermal into
electrical energy using magneto ? hydrodynamic generators was
first initiated in the fall of 1960 and experimental work
commenced in 1961. The purpose has been to study energy
conVersion processes in MHD ? generators and to establish
their practical feasibility. After the first experiment with
small power generators, performed during the 1961 and 1962
/ 1,2,3 /1 decisionywas taken to build a greater experimentil
unit mi order to get more reliable data and to attain runs of
considerable duration.
2. Open cycle direct current magnetohydrodynamic generator.
During 1963 a bigger rig was designed for thermal input power
of approx. 1 MW. The general lay?out of the, stand is clearly
visible from the Fig.1. The facility is in the course of the
final stage of assembly and it is hoped to be able, during the
year to come, to evaluate some of the practical problems
associated with larger scale experiments.
On completion of the programme, in 196$, it should be possible
to provide a realistic assessment of the feasibility and
utility of MHD electrical power generation for the future power'
station using oil as fuel.
In order to come as near as possible to the future practical
cycle a kerosene combustion chamber was chosen charged by
preheated air in a 'prototype heat exchanger.
During the course of erecting of the principal items of 1 MW
rig / electromagnet of 20.000 Gauss, air.preheater, air
compressors) fuel supply installation etc./) in 1963) a program-
me of the preliminary investigations was carried out on
amnllmy.
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3. Combustion chambers.
TWo combustion chambers have been built, one for 100 7 300 kW
and another for 1000 kW thermal power input. Description of
both designs is given in the paper, and their main features are
discussed.
Small combustion chamber, 100 ? 300 kW
A small rig consisting of a combustion chamber for a thermal
power input of 100 kW.? 300 kW, oxygen, nitrogen, air and fuel
supplies was built and operated successfully during 1963. Its
principal object was to study the behaviour of walls and electro?
des outside the M?H?D generator itself.
This facility is shown in Fig.2.
Kerosene was burnt in the flame of hot nitrogen and oxygen, fed
separately through the plasma torch of 50 kW power. The "simulated"
air has thus been preheated. up to 1500?C. Additional air has also
been fed by four fuel .spray nozzles of air ? assisted design.
Construction for high ? temperature operation
The internal parts of the combustion chamber must either be
capable of resisting the very high gas temperature of the combus?
tion zone or be thoroughly cooled by air or water. We have chosen
a mixed design with a ceramic flame tube made of "Refrax", with
water circulating in copper tubes encircling the flame tube with
an intermediate layer of "Carbofrax" cement.
The combustion chamber shown in Fig.. 2 ) is 154 mm long, and of
56 mm diameter.
The maximum wall temperature was kept with in a range of 1700?C.
This rather simple design proved to be very cheap in Manufacturing
and in maintenance, sufficiently reliable, and long ? lived.
No trouble with differential thermil expansion was encountered,
and no breakage observed.
The plasma torch was placed in the centre of a
copper header. Four fuel nozzles were situated
around the axis of the plasma torch outlet.
Seeding was introduced trough one nozzle as an
water.? cooled
circumferentially
alcohol solution
of KOH. Complete stability of combustion was observed over the
normal range of operating conditions, it is from 12 ? 25 kg of
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3
During the normal operation, switching: off the plasma torch used
to cause some instabilities, and this mode of operation had to
be avoided. Special magnetic valves were embodied in the rig in
order to. close automatically the fuel flow to the nozzles in case
of plasma torch failure.
When the seed flow was used, we experienced some trouble in that
a rather great amount Of slag flowed out of the outlet nozzle of
the chamber.
Deposits of slag sticking to the flame tube and generator walls
caused rapid corrosion of the oxide materials with subsequent
spalling and cracking.
In order to get rid of that trouble, a special secondary chamber'
had to be designed with a slag tap in the bottornof it.. The langer
path of the out - going gases with 'several bends should guarantee
that most of the slag would remain in the chamber.
Performance characteristics af small combustion chamber.
Fuel flaw
12 - 25. Kg/hr
Nitrogen flow to plasma torch
10
- 12
11
Oxygen flow to plasma torch and chamber
60
- 75
Air to chamber and to plasma torch?,-----
35
? 50
11
Combustion intensity
Efficiency /including
Max.temp.of. gases
Max.velocity of gases
Seeding flow
plasma torch/
0,3 0,5 kW/cm3
0,79 0)88
2200?C .-. 2300?0
290 400 m/sec.
5 - 20 Kg/hr
/ 5 percent KOH in
alcohol /
Combustion chamber of 1000 kW thermal power.
The bigger combustion chamber has been designed for operation with
preheated air and kerosene, No additional oxygen enrichment is to
be used. Water coaling is limited only to metal parts of the
header and central fuel nozzle.
A flame tube also made of uRefrax", is cooled by air. This combus-
tion chamber has undergone preliminary investigations at another
laboratory.
They included about; 100 hours of operation at low power and medium
temperature. At present the chamber is being prepared to run on
full power for a long time. In Fig. 3. we may see the cross - sectiam
of the bigger chamber..
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4. Heat exchanger.
The heat exchanger is designed for a maximum inlet gas tempe?
rature of approx. 1800?C ? 2000?C, it should preheat air to
1100?C.
It is a prototype unit, and if its operation proves successful
it will be further developed and multiplied.
DesiQl conditions are as follows:
Inlet air temperature
Outlet air temperature
Air flow
Inlet air pressure
Air pressure drop
Inlet gas temperature
Inlet gas pressure
Outlet gas temperature
20?C
1000?C ? 1100?C
100 ? 150 Kehr
1,5 ? 2,0 ata
600.mm H20
1800?C ? 2000?C
1,05 ata
approx. 1600?C
Construction.
The inner tube of the heat exchanger is made of super refraotory
tube possesdng high resistance to thermal shock, and with?
standing high.operating temperature as high as 1800?C.
This silicon ? nitride bonded silicon carbide tube has excep?
tionally high thermal.conductivity at high temperature ;
/ approx. 113 BTEr.inch or 14 Kcal
hr.ft21?Y m.hr.?C
at 1600?C /.
In order to increase the coefficient of heat transfer from the
hot gases to the walls of the tube, special swirlers and
turbulence generators have been placed in the inlet portion
of the "Refrax" tube. They are made of pure stabilized
zirconia bricks.
After the first eXperiments, special corebusters with internal
air cooling will be inserted in side the tube. The cooling'
air will be returned to the main air flow of the recuperator.
Air .enters the recuperator in. the counter ? flow direction,
It follows a helical path formed by Nimonio L.? shaped sheet
tape wound around the "Refrax" tube.
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4
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One of the terminal walls of the recuperator is machined to
form a flexible membrane which allows thermal movement between
the tube and the outer shell; it secures, too, positive air ?
tight seal.
5. Electromagnet
An electromagnet for approx. 1.9 webers/m2 has been designed
and constructed.
Its main features are as follows:
pole faces
maximum air gap
power consumption
525 mm x 120 mm
132 mm
50 kW ? 60 kW
The eneral view of the magnet is presented in Fig. 6
In Pigs. 7 & 8 is shown the schematic diegram of powersupply and
cooling system.
Fig. 9 presents magnetic induction versus current for diffe?
rent air gaps.
Core
A core has been fabriCated from rolled sheets of approx. .
1.5" 2" thickness. They have been machined and bolted together.
in three main parts.
The sheets are made of low carbon pure magnetic iron of the
following components:.
C ? 0,04%; Mn ? 0,014%; P ? 0,015%; S ? 0,023%; Cu ? 0,054%;
Fe ? balance / "Armco En./.
Cross ? section of the magnet core is 2000 cm2, its weight
being 4200 Kg.
Coils.
The Coils of the magnet have been wound from high conductivity
/ hollow core / copper tubes of 12 mm diameter and 4,5 mm hole
diameter.
They are internally cooled by distilled water, thus providing
maximum heat transfer effticiency. The coils have been insulated
with glass fibre tissue of good dielectric properties and
further impregnated with epoxy resin, This. procedure not only
adds to their electrical properties but also provides excellent
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-6-
mechanical strenght.
Electrical resistance of both coils is 0212a; weight of one
coil is 420 kg.'
Power is supplied by four silicon diode rectifiers of the type
commonly used for welding purposes.
The maximum constant power is approx. 60 kW.
A heat exchanger included in the closed cooling loop dissipates
heat to water from the mains.
Carriage.
The whole magnet is mounted on a rail carriage so that it can
be rolled along, the rails in the laboratory room-.
6. Experiments with insulating walls.
A small rig has been constructed in order to test materials
suitable for wall:Ansulation in the conditions similar to
those taking place in MID?generators.
The facility used in our experiments is shown in Pig 10.
The hot gases passthrough the test section,
In this configuration the wall temperature can easily be
measured by an optical pyrometer / through holes in sidewalls /.
Some measurements have also been taken with high ? temperature
thermopiles.
The test section is constructed of two steel sidewalls and
two ceramic / or cermetallic / elements / top and bottom /.
The steel sidewalls are water ? cooled internally.
All measuring points required for heat flux calculation are
provided. The above mentioned four parts are bolted together
to form a rectangular housing lined with refractory slates.
Different materials were tested; as for example:
? linings moulded of Si? + 50% A1203
? bricks made of different grades of zirconia and magnesia
? bricks made of thoria
? slates made of ffRefrax" and of "Refrax" coated with A1203
with plasma spray gun.
Heat flux to the walls was estimated to range from 14 W/cm2
to 71 W/cm2. The highest value was obtained for Refrax, the
smallest for SIC + A1203 cement.
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-7?.
7. Electrodes
Graphite electrodes.
Experiments which were carried out at our Institute
in the autumn of 1961 and during 1962 began with the use of
graphite as high - temperature material for electrodes.
They lasted for several minutes and enabled us to make the
simple MED - generators work and to obtain the output
voltage and power as a function of the current.
In order to increase the useful life of electrodes, we used
to pump methane or acetylene through pores of graphite
/ at a pressure of approx. 1.5 ata /.
This prodedure increased the useful life of the electrodes
to 10 + 15 minutes.
In some tests formation of a pyrolytic carbon layer upon
the exposed surfaces of the electrodes was observed.
There was experienced some trouble caused in connection
with carbon formation inside the pores of the graphite.
The pores jammed, and gas flow stopped.
A new experiment using the pyrolytic graphite electrodes of
considerable thickness / 5 ? 10 mm / is to be carried out
at a later stage.
The new electrodes are equipped with special holes for
feeding methane to the exposed surfaoes of the electrodes.
It is hoped that this is likely to decrease the oxidation
rate of the electrodes.
We have tried several other materials for the electrodes
as for example:
- graphite electrodes coated pyrolytically with silicon
4 carbide
- pure silicon carbide and silicon carbide + silicon nitride
No satisfactory solution has been found.
Zirconium oxide electrodes.
A new research programme has also been started in order
to estimate the applicability of zirconium oxide for perma-
nent electrodes.
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-8 -
Small specimens of 20 mm diameter and 20 mm height made of
different grades of zirconia were pressed and sintered to be
tested.
Platinum - rhodium wire as electrical connection has also
been introduced into the sample, according to the schematic
view in Fig. 11.
The specimens were tested in the air in the resistance furnaoe
especially designed at temperatures up to 1700?C.
Some results are presented in Fig. 12.
There is some evidence, however, that zirconia may show poor
resistance to the corrosive action of the potassium seeding
present in the combustion gases.
Botides.
The third approach to the problem of permanent electrodes is
the application Of some metal borides.
Hot - pressed specimens made of titanium diboride, titanium
diboride + aluminium oxide etc. have been prepared for tests.
This work has just started and.. no results have yet been
accumulated.
8. Small M-H-D generator duct.
An assembly diagram of the device is shown in Fig. 14
and a photograph in Fig. 15.
The generator consists of three major component parts:
an inlet nozzle, the M-H-D segmented electrode duct and a
diffuser.
The generator itse f has a total of 8 indpendent transverse
electrode pairs of the Faraday type.
Two electrodes of the Hall type have also been embodied in
order to observe the potential difference produced at opposite
ends of the duct.
The inner duct of the generator is made of thick magnesia tube
Its inner diameter is approx. 1", outer diam.approx. 2".
Thermal insulation is provided by magnesia and alumina cement
in subsequent layers.
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9
The sidewalls of the housing are cooled by two water jackets
situated between-the magnet pole faces and the generator box.
This small unit is constructed mainly for study of the perfor?
mance of various types of generators / Faraday or Hall type /.
Special sets of variable resistances allow fast readings to be
made during operation of the unit.
The bigger unit of a rectangular cross ? section is now being
prepared for operation at a later stage. Its design will be
based upon the results of our preliminary investigations.
References.
1.-W.S.Brzozowski:."Results of the First Experiments with
Small?power Magnetohydrodynamic Generators".
Bulletin de L'Academie Polonaise des Sciences,
Serie des Sciences Techniques; Vb.IX; No. 10-1961.
2. P.J.Nowacki? W.S.Brzozowski, Z.Celiriski: "Experimental
MED?generator Usin?bmbustion, Gases
/Gas Burner/ as Heat Source".
Bulletin de L'Academie Polonaise des Sciences, Serie des
Sciences Techniques; Vol.X.No.5-1962
3. W.S.Brzozowski, Z.Celiriski: "Plasma Generators, Plasmotrons,
Arc Plasma Tbrches, Arc Heaters".
Bulletin de L'Academie Polonaise des Sciences, Serie des
Sciences Techniques; Vol.X; No 5 - 1962.
4. S.Suckewer, Z.Celiriski" Measurement of Plasma Velocity in the
MI D Generator Duct / in Russian I.
Nukleonika, 1964; Nr.IV..
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- 11 -
Fig. 3
. A .???
?IIIMA.N.WilL\ Iliki
. 9. IIlkil
II"
II IN /
ill="1,544.1
MOM
Pi lirfirlikk 7 il," Zaislomor
.?,4?7-?,,,,....
A 3
- k ti i MIIIIIIIM 11110q.`11 .6 . 1.1111111.1 a !
I if g IMIlljiyelliAllip SIMI MN 1
l' 4 ? . "Ai . .
HEAT-EXCHANGER
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-10- Fig. 1
GENERAL ARRANGEMENT OF 111-H-B GENERRTOR ASSEMBLY
SWIRL ER
C01778, CHRITIBER NOZZLE ELECTROMRGNET3 COILS GENERATOR DIFFUSER HERE EXGFIRNGER
COnFRESSIO
FUEL RIR
war Or COM
WOES 1600T
SMALL COMBUSTION CHRMBER 1-300k1111 WITH PLASMA TORCH
KEROSENE
NITROGEN
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4.,..,2,4375t1CletlINVI,ALAtIOr43,1,71.11t ..,4,,womemams,,,Nme4
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WO -NITROGEN PLIIS177/9 TORCH ?"?30kW
200-OBSERYRTI0N 1JJIN0011/
300-ONE OF THE SET OF FUEL SPRRY NOZZL
400-COMBUSTION CHNSER HERDER ?
500-IUALL DESIGN ANO COOLING
600-1UATER-COOLEO GLAND
700-NOZZLE
WRIER
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ca.
(.7%
- 12 -
Pig. 5
Air ttmp.
MO IMUM
'W
MMEMEM.MMEMINIMM MUM MEMIIIIIMMMUMMI
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-13-
Fig. 7
SCHEIIIITE &ROOM OF POWER SUPPLY OF THE ELECTROOMMET
Cods
Fig. '8
SCHEIIIRTIC DAUM OF MINS SY5TEO7 OF THE
ELECTROMAGNET
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electrical conductivity measurements
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electrical conductivity measuremzet
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Declassified in Part -Sanitized Copy Approved for Release 2014/03/06: CIA-RDP80-00247A003400170001--4 AT
. ON THE PROBLEM OF OPTIMISATION OF MHD GENERATORS
Gubarev, B.Y. Shumyatsky & V.V. Brejev
Institute of High Temperatures, Moscow, USSR
The prospects for the development of any new method of energy transfor-
mation, including the magnetaydrodynamio method, are determined in the final
analysis by the technical and economic indices, i.e., by the cost of one
kilowatt of generated electric power. For certain specific purposes the weight
and size are the most important'parameters. Therefore, the study of the prin-
cipal physical processes of energy transformation in M.H.D. generators and the
elaboration of the principal problems of technology should be supplemented with
the work to select the rational geometry' of the Channel, flow rates and load con-
ditions which will ensure the optimum Characteristics of the unit. The approach
to the selection of the optimum parameters of a M.H.D. generator depends
obviously on the purpose the unit is intended to serve and should take into
account the effect produced by the generator Characteristics on the parameters
of the unit as a whole. On the other band, the optimum parameters of a M.H.D.
generator depend both on the principal:Pardirs of the cycle and the Choice
of the thermal design of the unit. Therefore, the problem of optimisation
cannot be presented today in a general form:
However, a number of important practical results can be
obtained from the simplified initial premises.
The problems of optimisation of certain types of MED
generators were the subject of study in /1-6/. The optimi-
sation was conducted with the aim of obtaining the minimum
weight and size of the MHD generator and included two as-
pects:
STAT
1. Selection of the coefficient of .electric load in
a MED generator at which the length and volume of the
generator are reduced to the minimum.
2. .Optimisation of the flow rates in a MBD generator
channel which ensure the minimum volume and length of the
? generator channel at the given coefficient of electric load.
It has been shown in /6/ that with the given coeffi-
rtiort.E. nf ailesn+voin lnnA irt +Inn noon n? n trnwelnlila onnAlin44
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- c
vity the minimum volume of the generator will be ensured
if the flow rate in the channel corresponds to the maximum
value of the product 6u2 ( --gas conductivity, u--flow
rate). The minimum length of the generator will be attained
if the flow rate in the channel is selected from the con-
dition of the maximum ---- where f is the gas density.
As follows from /1/ and /34 the optimum value of electric
load is not determined. unambiguously. Thus, if we consider
the parameters of the flow at the generator channel input
as specified /1/9 then the optimum value of Kopt
Conversely, if the parameters are specified at the output
of the generator channel, then Kopt 0.5.
The common shortcoming of these investigations lies
in the fact that the optimisation was performed without
account being taken of the power required to ,drive the com-
pressor and excite the magnetic field. Besides, the calcu-
lations disregarded the effect of the friction and heat
losses on the generator ch,aracteristics, It should also be
noted that the problems of optimisation of the MHD generator
parameters, at which the maximum internal efficiency of
the process or the maximum power of the unit are attained,
have not been investigated until present time.
1.1. The useful power of the unit with a MHD generator
can be determined as follows:
Nu = N 4- t4
m s.t.. ? 44
where Nm?power of the MHD generator;
Ns.t.u?Ng.t.0 --power of steam and gas turbine units,
respectively.
8N0?power required to drive the compressors in
the MHD generator unit;
Nei?power lost to excite the magnetic field;
N1-Power needed by the plant services.
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For the given thermal design of the plant it can be
assumed to a first approximation that the power, the weight
and size factors and technical and economic indices of
steam and gas turbine units are determined only from the
flow of the working substance through the channel of the
MHD generator and do not depend on its characteristics.
The needs of the plant services are disregarded. In this
case we can write
aN? NWe,e4P (1.1a)
where P is the constant at the given flow of the working
substance through the channel of the MHD generator (m
const) and at the specified temperature T02. Consequently,
with the assumptions made above)the specific output of
energy Esp -Nu is determined only by the cycle of the
MHD generator proper (Fig. 1). It can be shown that the
weight and size factors and the'technical and economic
indices, as well as the efficiency of the plant as a whole,
will be determined in this case only by the parameters and
characteristics of the MHD generator proper, i.e., the
optimisation of the characteristics of the combined unit
as a whole may oak be reduced to the optimisation of the
simplest scheme of the unit with the MHD generator (Fig. 1).
Then, discarding the constant P9 we shall obtain:
NJ' -m - N ?
(1.2)
1.2. The power produced in the MAD generator can be
determined as follows (Fig. 1):
po(roi?Toz)?Oui
(1.3)
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4
where C0--average heat capacity of gas within the range
p
of the working temperatures of the MHD generator;
c),.=2.074.11)41x --heat transfer to the generator walls;
0
gtet:04,6,11? --heat flux into the wall;
ot --heat transfer coefficient;
ATuju1T?--114 --temperature drive;
h and S. --width and height of the channel (Fig. 2);
L --length of the generator channel.
The power required to drive the compressor can be
found from the following relationship (Fig. 1):
Y-1
( 1.4)
where C1--average heat capacity within the range of the
P
working temperatures of the compressor;
9e?compressor efficiency.
The power spent to excite the magnetic field is determined
from the following ratio
G.
(1.5)
where j--accepted current density in the electric maret
? winding;
2?conductivity of copper;
ye?specific weight of copper;
? G0--weight of the copper winding.
The weight of the copper winding in the simplest case of
a a-shaped magnetic system with steel at the constant
magnetic gap is found as follows:
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Declassified in
where
0, --2KY,S1) ??? K?sycL.
j
a
12 I: --width of the winding;
K--coefficient which accounts for the weight of
the end-face sections of the winding, the
number of amperelGrns to overcome steel re-
sistance, etc.
After substituting Ge in (1.5) we shall obtain
La.
(1.5a)
1.3. Utilising (1.3), (1.4) and (1.5a) we shall ob-
tain the following expression for the useful power of the
unit with a MHD generator:
k?,-mdro
Y-4
mer41-4'cL(F0'1,)
7;4 ? (-14)
-1 -
9, Pal
The task of optimisation of the MHD generator parameters
can be presented in the following way:
1. Let us divide termwise the right side of (1.6) by
L g. e which is the length of the generator channel, and
equate the derivative of the expression obtained by any
of the characteristics of the parameters to zero. This
will give us the optimum value of the parameter at which
g,
the specific power 3-1"717- is at its maximum. The variatio-
nal problem of optimisation may be presented in principle
? by a number of parameters.
? 2. Let us divide termwise the right side of (1.6)
by the useful volume of the generator channel
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-6-.
'( 1 .7)
and, equating the respective derivatives to zero, find the
optimum values of the sought-for parameters at which K =
Nu
---- is at its maximum.
3. Let us divide termwise the right side of (1.6)
by the mass flow rate of gas in the generator channel and,
equating the derivatives to zero, determine the optimum
value of any of the parameters which corresponds to the
maximum value of the useful energy obtained from one kg
of the mass.
The first two presentations of the optimisation prob-
lem are related to the weight and size factors of the unit
with a MHD generator.x It should: be noted that the optimi-
sation both by the length and the volume of the generator
does not determine the optimum value by the weight and size
factors of the unit with sufficient accuracy. However, it
is extremely difficult to indicate a more accurate method
of optimisation of the weight and size factors, which would
permit an elementary analysis.
The optimisation of the parameters of the MHD genera-
tor in the third presentation of the problem in the case
of the specified value of ATit="1:4-11.1 corresponds to
the optimum value of the unit efficiency. If the power
X This assertion is true if the weight of the MHD gene-
rator with a magnetic system considerably exceeds the weight
of the other elements of the unit or when the variations of
any of the parameters do not affect their weight and size
factors.
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spent to create a magnetic field and the heat transfer to
the generator walls are negligibly small, such optimisa-
? tion can be reduced to finding the maximum of the internal
efficiency of the energy transformation process in the
generator.
It should be stressed that in the case of more comp-
lete'presentation of the problem of determining the maximum
of the unit efficiency we shall require variation of the
parameters at the output of the MHD generator channel and,
in a general case, the value P in (1.1a) cannot be assu-
med constant. The solution of such a problem, and of the
? problem of determining the optimum value by the technical
and economic indices of the electric power plant as a whole.)
is rather difficult in the form accessible for analysis
and requires a large number of variational calculations.
The general approach to the problem of optimisation
of the parameters of the'MHD generator was discussed above.
To solve this problem we:muxt.establish the relationships
between the parameters of the flow in the MHD generator
channel, its load characteristics and geometrical dimen-
sions. The main difficulties of optimisation accrue from
the complex and multi-valued nature of these relationships.
Therefore, the variational problem must in a general case
be presented with many degrees of freedom. In our further
exposition we shall confine ourselves to establishing
these relationships on the basis of the quasi-one-dimensional
theory and, making certain assumptions, shall reveal the
qualitative aspect of the problem of optimisation of the
principal operating characteristics of MI-ID generators. In
conclusion we shall give some results of the calculations
? performed on a type M-20 computer.
2.1. Accepting certain assumptions, the flow of gas in
the MBD generator channel can be described by the following
system of equations:
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1. Continuity equation
fLJ= = cesf.
. 2. Momentum equation
P12.
-/
23)
3. Energy equation
dT 4- sli.44tA = [KO -14),I.t?' 0.1Sin + 0.+IN)ii1rw
4. Equation of state
P =1RT
The following notation is used here:
---coefficient of friction;
= --equivalent diameter of the channel;
S-44.1
R--gas constant;
gr---- --coefficient of electric load;
t.te,
E--electric field intensity;
(2.1)
(2.2)
(2.4)
1.41
T-Ti? --total temperature of gas flow.
0 Up
The change in the conductivity of gas 2, depending
on the thermodynamic parameters of the flow can be rep-
resented to a first approximation as follows
elz
= e., T e r
(2.5)
(2.5a)
The heat transfer coefficient OZ will be determined
from the known formulas
N
(2.6)
. 0 . 023 ge pt.
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where the criteria
0015 iL4bes
Nu
C Ao r - IA
t , f
are determined by the usual methods.
A
The system of equations (2.1) (2.6) is not
complete and to solve our problem we must establish additio-
nal relationships for certain parameters which enter into
the system. In our further exposition the following para-
meters will be assumed constant along the channel length
for the sake of simplicity:
n, B, k, AT = To - Tw, ae= Ein = 0.5
Then we have
J.
ou .11 cons+
2.
4x
&e'
hid d'Nme drez?{tc(f-x) Le? yw+Coz ? AT:4141x
Zi LA
(2.7a)
(2.7b)
(2.7c)
2.2. Let us consider the limiting cycle of the unit
with-a MHD generator when the temperature drop used in
the generator AT0 0. Then the power of the MHD generator
will be
1.0.4e*
14(4-1C-) ympAt 6.1- PIT aT,,, x
P 2/,
(2.8)
The pressure drop over the length of the generator
&To
4u1,'
-14) )6, 1- Col. 4,7r
2.rm ?41
is determined as follows
A.p.pi_pxzE(4 x)Auaz Pt41 -211-4 Ax
)i
(2.9)
(2.10)
and after appropriate transformations, assuming that the
pressure loss between the channel and the compressor is
equal to zero, we shall obtain the following expression
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- 1U ?
for the compressor power:
.dp T4 K (i 4 li!A442) Y-4 ((4_1()e.124. _I] (2.11)
9, Po
Thus, after substituting (2.8) and (2.11) in (1.2)
we shall obtain
I-I .
al 1, 3 21-. \I b...
444:4,61-10_ .? 4. g .. ,......., + ... I ." ^
I' ) C. P. N4 6G Mo 2f u
where
ax (2.12)
Po + 1-1L(4-)44g2+ 4-1P142? 3'LZ4
"
2.3. It follows from (2.12) that with the given para-
meters of the flow at the input of the MHD generator chan-
nel, with the length 41x, the useful power of the unit
depends on the rate of flow u, the coefficient of electric
load and also on the characteristics of the magnetic system
field induction B, copper conductivity and the current
density in the winding. The optimum characteristics of the
MHD generator can be obtained by equating the respective
derivatives to zero:
a et
A -(a K)= 0
1..4
(2.13)
Let us consider some particular cases.
To.
1. LetA ANc which holds at >? 4. Then
N64
1,?
Kopt = 0.5. Equating allu = 0, we shall find the value of
the induction B at which the MHD generator ensures the
power spent on excitation:
4
E > , 2=
ac. LA 2, t411
ex.
PN
Then 'the optimum value of the flow rate can be found from
iow).., 0
OktfI
(2.15)
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Assuming the power dependence of the conductivity on
the flow parameters (2.5a) and remembering that the velocity
of sound a = X we reduce (2.15) to the form
2-.1-ec44p)
y-( -
{/k4 (.( + ? ikta.) =- 0
d lA
Hence, the the optimum value of Mach number
A.1
op+ 26/4 (t+is ifirq ?2 -(4741 ?1
(2.16)
Consequently, we can assume in a sufficiently narrow
temperature range that the optimum value of the flow rate
in the generator channel is constant /6/ and does not depend
on its load characteristics.
If the power spent on excitation cannot be neglected
the optimum Mach number will be
MI >M a+ Mop+
Wept- MeT+ a+ A4 i
of. (2.17)
3. If none of the terms in (2.12) may be neglected
optimisation in an analytical form becomes difficult.
However, a number of qualitative conclusions can be made
from (2.12). As was shown above, the maximum value of
AA1,14-4A/tx is attained at K = 0.5. The power required to drive
the compressor decreases monotonously when K increases
from 0 to 1. Therefore, the useful power of the unit with
a MHD generator reaches its maximum when K > 0.5. Fig. 3
illustrates the effect of K on the useful power of the
unit.
2.4. Let us dwell briefly on the choice of the opera-
ting conditions of the generator which will ensure the
maximum take-off of power from the unit of the channel
volume
(2.18)
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Then, the specific power of the unit will be
NIIA= i()ak421312, r 11 k 2'
LI': (2.19)
\12 4?1C 2c L.- - 4 6c po 2 .
When dtsic:&At`lie.A optimisation by the coefficient of
electric load gives the same result K = 0.5. If, besides,
414exANIA,t the optimum value of the flow rate can be deter-
mined from
(11).)z. 6
4L4.
Hence, with the power dependence of g (2.5a) we
obtain
A
AA 4=
or (2.20)
1-4 '-4
Accounting for the power spent on excitation the
result will be reversed (2.17). Indeed, it follows from
(2.19) that
MI 4. 4 Adt
op op ?
Op
a4- Mer-(4
t
a+ A4
or+
(2..21)
2.5. Above we considered the problems of selecting
the operating conditions for MHD generator which ensured
the minimum weight and size of the unit. For stationary
electric power installations the weight and size factors
determine the capital outlay and their efficiency becomes
the principal factor.
Let us consider the problem of selecting the opera-
ting conditions for MHD generator which ensure the max-
imum efficiency of the unit. For this purpose, we shall
reduce (2.12)-, with account taken of (2.9), to the following
form
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J_)
4
N:
where
P it(s V 271
/ bk al ? -----! 1(1-J(2.22)
44,41F...,
, 1' 2r4 '
f r-4
4 z b,cf,47;(it ? AA2)
(4-14)6t,e+ Fpe
K (-K)a .1
ws.7-
2,PI"
A detailed analysis of (2.22) is extremely complicat-
ed. Therefore, let us first consider a case in which the
effect of friction, heat transfer to the wall and the
power spent on exciting the magnetic field are disregardedv
Then
634,4
zcato_____[D+
s, P /4(0) To
(2.23)
Hence, it follows that with-the given parameters of the
cycle the efficiency of the unit will be determined only
by the coefficient of electric load K. Equating the deri-
vative from (2.23) by K to zero we shall obtain:
xatic.-2?(-1YLIA47-)
Y-4
Since 0 4 K 4 1, optimisation by K has no physical meaning,
i.e., the power of the unit is the highest when the coef-
ficient of electric load is at its maximum, i.e., at K = 1.
This result is obvious since, with the specified AT0, the
power of the MHD generator does not depend on its operating
conditions and the power required to drive the compressor
is minimum at the highest possible Value of the internal
efficiency of the generator, i.e., at K = 1.
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Account for the friction and heat transfer when allex=
-=.0 leads us to the conclusion that the optimum value of K
decreases but is always greater than 0.5.
? If we disregard the heat transfer to the wall and
the capacity of the compressor we can find the coefficient
of electric load and the flow rate which ensure the maximum
power of the MUD generator. In this case)Kopt = 0.5 and
the optimum flow rate is determined from (2.16) and (2.17).
Thus, the optimum value of the coefficient of electric
load, at which ANu is maximum at the given iST09.will be
1 > Kopt > 0.5,
(2.224)
its value being dependent on the characteristics of the
magnetic system, cycle parameters and the flow of the
working substance through the channel of the MHD generator.
It is difficult to determine the optimum flow rate
from (2.22) analytically. However, an elementary considera-
tion shows that at M -? 1 the friction and heat transfer
to the wall reduce the optimum value of M found from (2.16)
and (2.17).
2.6. An analogous consideration of the effect produced
by the operating conditions of the MUD generator on its
internal efficiency
Nint
f-i
/ 4 (2.25)
in. dr To p
leads us to the following conclusions;
1. If the heat transfer to the wall and the friction
may be neglected K = 1 will be optimum and the flow rate
will affect the internal efficiency as follows:
? ivkl(4-1c)
(2.26)
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OEM
i.e., the maximum value of the internal efficiency will be
attained at 11-91.0. This result shows that a considerable
increase in M number in the channel of a MHD generator
is highly tndesirable from the energetic viewpoint.
2. The optimum value of K at which the internal effi-
ciency of the generator is maximum proves greater than the
value found from the condition of the maximum of the unit
useful power. This is due to the fact that the internal
efficiency accounts only for the dissipation of the energy
as a result of friction and Joule heat, while the useful
power also includes the heat transfer through the wall
and the power spent to excite the field.
3.1. The optimisation of the operating conditions
of the MED generator for an elementary cycle can be extended
to the unit as a whole. For this purpose let us break the
entire cycle of the unit into a number of elementary cycles
abed (Fig. 1). We can assert that if each elementary cycle
taken separately is optimumthen, to the first approximation,
the plant as a whole will operate at the optimum duty. It
should also be noted that the conclusions obtained above
allow a more judicious approach to the problem of selecting
the temperature at the output of the MHD generator.x
Indeed, if we equate (2.22) to zero, we can find such
value of the gas conductivity es at which the useful
power will not be generated, i.e., this condition determi-
nes the lower boundary of the expediency of utilising the
magnetohydrodynamic method of energy transformation. For-
mula (2.22) shows that the lower boundary of conductivity,
or of the temperature, drops as the gas flow is increased
through the generator channel.
x Literary sources usually indicate that the value
of the temperature at the output of the MHD generator
channel is selected from the condition of sufficient gas
conductivity and is specified at about 21000C.
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3.2. Even in the case of simplifying assumptions, an
analytical consideration of the integral formula ( 1.6)
encounters considerable difficulties. For this reason,
the calculations were performed by numerical integration
on a type M-20 computer. Below we give the results of the
variational calculations of the unit with a MMD generator
disregarding the power spent to excite the magnetic field.
The following parameters were assumed constant over
the length of the generator channel: G . 2 W/ m2; =
? = 0.5; ATw = To - Tw = 500?; U; k and the coefficient
of friction = 0.015. The working substance in the
channel of the MHD generator was a monoatomic gas (
1.67) with the molecular weight of p = 4 (Cp = 5,200
Joule) , The number Pr = 0.681.
The heat conductivity of the gas was determined from
kg ?K
the formula
A vl 4- di,
2?u
the viscosity
T?
/if Ale An
2?3
T
je.le
A. = 0. IQ
sec nt
-4 NI
/tie Is 0. 486 x4o
where
At large values of Tf = To + Tw we have
o.o.1311-0 4.-74 )
-r
'to +1:4
The electric conductivity of the gas was found from
the formula
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A
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a.
Plc
where 6 . lo mham is the conductivity of the gas at T
2073?K, P = 0.98x10522 , a = 12.
The calculations were done within a wide range of
the working substance flow (m = 0.12 to 120 kg/sec), flow
rates (u = 500 to 2,000 m/sec), coefficients of electric
load (K = 0.3 to 0.9) and the temperature drops (Tm
To1 - T02 = 200 to 8000) employed in the MED generators.
The principal part of the calculations was performed for
T01 = 2273?K and P01 = 1.08x105-E2
m . The temperature of the
working substance at the compressor input was assumed equal
to Tlt = 308 K. The efficiency of the compressor was n =
0.85.
3.3. Fig. 4 shows the effect produced by the flow
Af
rate on the specific power of the MED generator EM . =
L
e-
?at m 0.12 kg/sec, K = 0.5. As can be seen the maximum
EMI, is attained at u. 1,100 na:/seirrespective of T02.
Moreover, the optimum value of the flow rate depends
? neither on the coefficient of electric load nor on the
flow of the working substance and is in a fairly good
agreement with formula (2.16) obtained from the considera-
tion of an elementary generator.
The effect of the flow rate on the specific take-off of
14,
the energy on the unit with MED generator E,41.=
is illustrated in Fig. 5. It can be seen from the compari-
son with Fig. 4 that in this case the maximum is noticeably
shifted towards u 0.5 and m = 1.2 kg/sec (Figs 9, 10) the curves
are above the "standard" curve, then at m = 120 kg/sec
(Figs 11 and 12) they are located below. This change in
Nit?ff..= f (k) owes its origin to the compression and the
dependence of the gas conductivity on pressure and also to
heat transfer to the wall. Indeed, if we neglect all the
losses, except the Joule losses, then as K increases, at
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? 19 ?
the fixed heat value, the pressure at the generator
output increases and the average gas conductivity is
therefore decreased in the generator channel. This shifts
?????
the maximum Nmv towards K 4 0.5, and, when K >0.5, Nmv
is located below the "standard" curve. This explains the
deviation of the curves NMv = f(k) at m = 120 kg/sec from
the "standard" curves.
At a lower gas flow rate the effect of friction in-
creases sharply, as a result of which the change in the
pressure at the generator output, depending on K, decreases
as can be seen from the curves NMv? For this reason, the
average value of the gas conductivity at K>. 0.5 decreases
less intensively and the curve Nmv = f(k) should approach
the "standard" curve. However, since the generator output
which operates less efficiently due to the reduced conduc-
tivity brought about by increased heat transfer to the
wall becomes much shorter at small flow rates, the curve
? ?
NMv = f(k) is in actual fact slightly above the "standard"
curve. This can also explain the effect of the flow rate
on the nature of NMv = f(k).
Figs 9, 10, 11 and 12 also show the curves of the
change in the specific power of the unit Nuv. It can be
easily seen that the optimum value of the coefficient of
electric load lies in the region K = 0.6 to 0.7 changing
but little in the case of a substantial alteration of the
used temperature drops, flow rates and the flow of the
working substance through the channel of the MID generator.
It should be pointed out, however, that as the gas flow
MO.
rate decreases the maximum attainable value of Nuv increases
somewhat and shifts towards greater K. An increase in the
flow rate will reduce N due to greater friction losses,
uv
i.e., the power required to drive the compressor.
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?
The above thesis is clearly illustrated in Figs.13 .
and 14 which show the change in the power of the MHD gene-
rator as referred to kg of gas EM = -- and the unit as a
whole E. The calculations show that the curve K = 0.5
at m = 120 kg/sec (Fig. 13) practically coincides with the
theoretical curve for the case involving no heat transfer
to the channel wall, i.e., in this case the relative share
of heat losses is negligibly small. As the coefficient of
electric load increases and the gas flow rate diminishes
the value of EM decreases in which case the greatest
deviation of the curves from the linear law LEmi.eral.
Is observed in the region of the smaller temperatures,
which can be explained by an increase in the relative share
of heat transfer through the walls. It is interesting to
note that at the small flow of the working substance the
decrease in T02 (increased temperature drop in the generat4
below a definite value does not increase the MHD generator
power. Hence, when the power of the MHD generators is
small it is irrational to increase the used heat content.
We cannot but fail to notice the fact that the
referred power of the unit E.sp (Fig. 14) at in >12 kg/sec
is greater at K 0.7 to 0.9, whereas at m 412 kg/sec
the maximum is attained at K = 0.5. This can be explained
by the fact that at in 4. 12 kg/sec the predominant role
is played by the dissipation friction losses and the
heat transfer to the wall, whereas at m,> 12 kg/sec the
main losses are due to the dissipation of the Joule heat.
Therefore, an increase in K essentially reduces the rela-
tive consumption of the power produced by the MHD generator
.to drive. the compressor. It should be noted in conclusion
that at small flow rates we observe an insufficiently
expressed maximum of the referred power of the unit E .
sp
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3.5. The effect of the flow rate, the coefficient of
electric load and the gas temperature at the generator
channel output on the internal efficiency n . of the
? Jo,
energy transformation process is shown in Figs 15 and 16.
It can be seen that as K increases and the flow rate of
the working substance and the temperature at the output T02
decrease, the effect of the flow rate on )1: increases
/0
noticeably, which can be attributed to the greater role
played by the dissipation heat losses. It should be
noted that if at K = 0.5 an increase in the used temperature
drop (decrease of T02) somewhat increases ,,; then, at
K = 0.9,we observe the decrease inn . in which case as
/04
the flow rate increases and T02 diminishes, the curves
9
. f(T02) for K = 0.5 and K = 0.9 draw near to each 0;
other, especially when m = 12 kg/sec.
Fig. 17 shows the change in the internal efficiency
of the MED generator depending on_K. The figure shows
that there is an optimum value of K at which n is at
its maximum, the optimum K shifting towards the smaller
values with the decrease in the gas flow and the increase
in the flow rate. Analogous curves for the specific power
NL
of the unit tc are given in Fig. 18, where I increa-
ses essentially at a higher gas flow. The optimum value
of K increases with the increase in m. The presence of the
maximum II and E is due to the effect produced by
Jo; sp
friction and heat transfer to the wall. Indeed, as K
increases, the length of the generator becomes much longer
and, with K ?01, the length of the generator in the
absence of heat transfer to the wall grows infinitely
large, i.e., the friction losses increase intensively.
In Fig. 18 the dotted lines show)by way of comparison.)
the change in the internal efficiency. It follows from
????
this that the maximum E can be attained at smaller
sp
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Declassified in Part - Sanitized Copy Approved for Release 2014/03/06: CIA-RDP80-00247A003400170001-4
- 22 -
values of K. As has been shown above, this can be attributed
to the fact that the internal efficiency accounts only for the
dissipation losses, whereas the useful power of the unit
is also determined by the heat transfer to the walls of
the generator channel. If we also take into account the
ONO
power spent to excite the field, the maximum Esp will be
displaced still more towards the smaller values of the
coefficient of electric load.
This results shows beyond all doubt that the role
of the internal efficienty of the process, as a criteria
of the efficiency of the unit as a whole, is considerably
reduced in magnetohydrodynamic units and the value of the
useful power of the unit, as referred to the flow of the
working substance, becomes the principal factor. Herein
lies the main difficulty of optimisation of the parameters
of the unit with a MHD generator.
References
1. J.Neuringer, J.Fluid Mech. 7,.pt 2, 1960.
2. Energy Conversion for Space Power. Academic Press,
New-York, London 1961.
3. N.I.Polsky, G.M.Shchegolev. Thermal Physics of High
Temperatures, No. 1, 1964.
4. N.I.Polsky, Thermal Physics of High Temperatures, No. 2.
1964.
5. R.J.Rosa. Phys. Fluids, 4, No. 2, 1961.
6. A.E.Sheindlin, A.B.Gubarev, V.I.Kovbasyuk, V.A.Prokudin.
Proceedings of the USSR Academy of Sciences, Energetics
and Automatics, No. 6, 1962.
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Yo ? 2, ?
C.
P"o2
F&:
AN
A N M
1111
.4
I N lc
."%...
r--
A /7g
0
q4
q2
0,2
01/
0,6
0,8
3fne
kz:20001'
9 ,
45 .
lEnne
00 ,
li
: 3
The effect of the coefficient
of electric load on the useful
power of the unit with an MHD
generator with a specified
length of the channel.
176r : 4
The effect of the flow rate on
the specific power of an MUD
generator
EN
ML v., L
2
(T01 = 22730K,
F01 = 1.1 ata,
m = 0.12 kg/sec, K = 0.5)
4/00 600 800 1000 1200 /400 /600 MAC
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Declassified in Part - Sanitized Copy Approved for Release 2014/03/06: CIA-RDP80-00247A003400170001-4
3e
- 24 -
4,00 600 800
9
a
7
6
5
3
The effect of the flow rate on
.the specific take-off of energy
from the unit with an MHD
,generator N,
Egi..=
1
i( 01 = 22730K, P01 = 1.1 ata,
0.12 kg/sec, K = 0.5)
/000 1200 1400 1600 m
Nmv
cilc
-.....m
4 Q??
17" ' 11....
400
600
800 1000
F: : 6
The effect of the flow rate on
the specific power of an MHD
generator wm
(T01 = 22730K? P01 = 1.1 ate.,
m = 0.12 kg/sec, K = 0.5)
400
1000
6
00
800 1200A00
The effect of the
flow rate on the spe-
cific power of the
unit
- 4/4
kv -
V
7 ?
(701 . 2273?K, P01 =
1.1 ata, m = 0.12
kg/sec, K = 0.5)
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Declassified in Part - Sanitized Copy Approved for Release 2014/03/06: CIA-RDP80-00247A003400170001-4
- 25 -
6
5
Ij
3
2
42
4
a
/1/.yv
2Q ?k
0 0
I
?
?
NO
17
1601
sao 600 800 /009 1200
The effect of the flow rate on the specific power
- N?
of the unit Nvv-v
(T01 = 2273?K, 201 = 1
1.1
K = 0.5).
1 00
,
?
--.
7,'
/
.
?
\
of
........4:-
%.
\
v
-.4
"43..
..,, "yr
?
....
r
g?
.
,...
.
7
ie
-'441
43
Od
as
OS
as
The effect of the coefficient of
electric load on -the specific
power of the unit lc
(T01 = T02=
2273oK, 18000K,
.
P01 = 1.1 ata, m = 1.2 .kg/sec)
ata, m = 120 kg/sec,
iFy: /0
The effect of the coefficient of
electric load on the specific
power of the unit Wv
(T01 = 22730K, T02 = 1600?K?
- 1.1 ata, m = 1.2 kg/sec)
P01 -
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Declassified in Part - Sanitized Copy Approved for Release 2014/03/06: CIA-RDP80-00247A003400170001-4
? 26 ?
e
?
Cv .?
At' .h, ?
1.
't
Ax
\
',..
?
e
/
.
/
N
\ ?
\
40,
4X ?4
P
we
?
A, ,
' 1
?,e,
Alln?"
S.\
ad
-
t11)17
....
_
P
I?,
.
40.4,
go
.?
.A.
02
!4
a
? CU
06
as
OS
02
44
/737:1/
The effect of the coefficient of electric load
??????
on the specific power of the unit Nv
?K, T = 1800?K,
(To1 = 2273 02 = 1.1 ata,
m = 120 kg/sec).
It
11
1\
..\
',.
?
c" ?
\ %
y":?
,
5,,
e
?
_. ?
.
....
r\
/
/
/
/C,,y
\
N
6.
.?
'
.
.'...4
N
\
.
i
A7sv
144 : ' ?
N4,1
000? 4 ito*,
,
.?';,....
'.5_S.'
0
i
i
....7.Z.7.%,
W.
K
4v
alf 41.'
.3
3
4V
The effect of the coefficient of electric load
on the specific power of the unit Nv
P
(To1. o1 =
= 2273?K, To2 = 1600?K, 1.1 ata,
kg/sec).
? (,/S00 ??13
o or 861:7. m IS
lit u z/vo ri. is
4 v./400.gs
..... eft ?449 NI /3
---4-0 c/2,1491$
---cort2 sovs
.....?..m rale Kg It
Arool5
+ ll./70:2' on Is
# II6c1219 m/i
M.49
ei447.S
..............ir......
d44.9
?
! ,,011'.
&-.L.19_*"140
--db??
.
3........1....e.?....a?-?..........---.
_,,,7,...
? --T..-
.04$
?
.,,
-
..1b.
+
+
d??.?
422
2/
19 a
Is
42-'?dd
717:f3
The effect of T02 and the gas flow on the ref?
_ ntm
=
erred power of tt,IiIHD generator
im _ 00.7101( _ = 1.1 ata).
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Declassified in Part - Sanitized Copy Approved for Release 2014/03/06: CIA-RDP80-00247A003400170001-4
- 27 -
/0
49
0,13
q7
0,6
4,4
43
q2
41
4? 25
. 4104? J
40
15
?40
45
3y9
In z 120 t 5i ?
rnz .i1 K5 1 /1
r :0,7
---.
---
...,..,, m. ve A,.9 is
r
.?
?
t..0.9
.
.
-'
.
? :r.07 : ...,..i
-..?::.-.7.---17----1. _14-.45
... -- .... i
---- . .
,...,
,...........--
,..i...,
I'.
/,..,..
, ' 0:: ..' . ,..1?..
...? ?,t,.?....-?
.
. ...
,....
..??. -
........ ....
11......?
.......
..,..-
... . .
/--......
... .,.......
.... ...
........
-
.
,.........? ? . ? ...rums
. ?
...- - -I- -. _.t..? ........___i.r, 49
.
ow 40..,.r. ,er,juns.n?muirt 43 .
.
A., 9
...."?' ? ??????
? ?
"'????? ?????? ? .....t ........il q
I ma
. _ . _
Zs
41
20
1.9
? K
- .--i- 036
?. _ ? ? --4Z7;?--;.? - .....t... ?
_4_0044
.- . -? ..,A -- ...7,?eritoolidigii,
1
. ;,...cr4. --.........
?44.1;:g.% -.f.
)?
____.. ..7...r.. . j
. .. `".-2.,..?.....t.464-r. - .
64sr:Aga,fth:;'"-Aoo
-0-2.11-7"---3,4679
..._H- .
-......?04.
?
*
49
4,5
47
4
45
43
4/
"" req9
0,3
-1 _ _?.
-r
? 1.1.500
a r 800 m /
? 1100
st 1400ti-
??? 1700 m s
4- 2000 m
To:
711:14
Change in the referred'
power in the unit With
an EID generator depend-
ing on 102 and the gas
flow (T01 = 22730K, P01
= 1.1 ata, u = 500 to
800 m/sec)
2,2 2,1
104k
The effect of T02 and
the flow rate on the
internal efficiency of
an MH]) generator (T01 =
2273?K, P01 = 1.1 ata,
in = 12 kg/sec)
20 48 t7 t5 41/ y /04,t
-7:30,c,
-relifir
,..i2.2..
--kr---:?--7
7.--71-6-.
?
-
--.?..14.--:.
....
mi---3?
?
--"'
g4X'
-e-1,-;
#00 ra /J- ?
m a
n' is
?
V
?OW
ni /5
?
. ?
Szs....52_
.
.
.
.
? 500 rn / s
0 827 m / j
Ill lag m/
t/ 4v m 1 s
4/70v m 1,
S. AMP nt 1 s .
43
Ze
e/
20
X7
46
7;y:16
The effect of T02 and
the flow rate on the
internal efficiency of
an MHD generator (T01 =
2273?K,201 = 1.1 ata,
in = 120 kg/sec)
0.,030/r
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Declassified in Part - Sanitized Copy Approved for Release 2014/03/06: CIA-RDP80-00247A003400170001-4
? 28 ?
The effect
f? : 17
of the coefficient
of electric load
on the internal efficiency of PHD generator
= 2273?K, P 1.1 ata,
(To1o1T2 = 1473?K)
A 1
339
2,2
20
0
1.2
0
0,8
46
44
42
0,9
m141011 12?'
/77.1TAI
147
;45
,Zct
rnza
? -144
!6:3
inla .1
I ki
'I
02 03
44,
as 46 V
48
0,9 1,0
I'7: 18
The effect Of the coefficient of electric load
on the referred power of the unit with MHD
? W.,
generator E
(T01 = 2273?K, To2 = 1590?K, P01 = 1,1 ata, u =
1,100 kg/sec) .
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