Electrical conductivity of two phase liquid metal flow in magnetohydrodynamic generato

Aladyev, I. T.

Dodonov, L. D.

Gavrilova, N. D.

English

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https://ntrs.nasa.gov/search.jsp?R=19690003909 2020-03-12T08:08:58+00:00Z
it
N69-132 40
International Atomic Energy Agency
SYMPOSIUM ON THE PRODUCTION OF ELECTRICAL ENERGY BY MEANS OF MHD-GENERATORS
Warsaw, 24-30 July 1968
SM-107/153
THE EFFECTIVE ELECTRICAL CONDUCTIVITY OF A TWO-PHASE LIQUID-METAL FLOW At
by
N.D. Gavrilova, L.D. Dodonov, and I.T. Aladyev
G.M. Krzhizhanovsky Institute of Power Engineering, Moscow, USSR
At the present time scientific engineering problems associated with the
creation of high-temperature power plants using alkaline metals with
MHD generation of electric power are being intensely studied. If these
plants turn out to be profitable at the upper temperature of the cycle
T < 1500 °K, then their industrial realization will become feasible in
the next few years. The possibilities of creating [producing] a plant
with a single-phase (liquid) and a two-phase (vapor-liquid) flow in the
MHD generator are being examined. For the latter case, the study of
the characteristics [performance curves] of the MHD generator in the
presence of a vapor flow and the determination of the optimum vapor con-
tent in the duct is important. Since the generated power is proportional
to W2 a, the assumption of a certain vapor content can turn out to be
advantageous, since in this case alone with the decrease of the con-
ductivity of the flow (ali = (10 6 -10 )ava il ) at a given flow rate. The
velocity of the working medium is increaseg in the duct, and consequently,
the effective values are W 29 and o 2 q, corresponding to a maximum of
production W2 9e 29 . Moreover, in this case an increase in the efficiency
of the separator (injector-condenser) is possible and consequently of
the entire plant as a whole.
The range of change in the gas contents to which belong the optimum
values of W2 Tc 2 q) is defined experimentally. Data are limited on these
characteristics of the two-phase flow [ref. #1-61. They differ according
to working media and temperatures, shape of the ducts, the effect of
the magnetic field, as well as the values and character of the change
in conductivity. In this ppper the results are presented of the investi-
gation of the changes in the e.m.f. induced by vaporized potassium flow
(T = 1050°K in the MHD duct, along with the electrical conductivity of
this flow, a comparison and analysis of existing data.
If the liquid wets the surface of the duct, then the two-phase flow can
have one of the following five basic structures: bubble, emulsion, cork
(charge), annular (bar), diffuse-annular (disperse-film). In the first
four structures the entire liquid phase of the flow is in contact with
the wall of the duct and there are not discrete formations of liquid in
the vapor. These can be called "vapor-in-liquid" structures. In the
diffuse-annular structure, part of the liquid flows along the wall, and
another-part of it is sprayed `in the vapor in the form of discrete for-
mations (drops). When 6Zi > vvap, the drops are in practice electrically
G'
TRn#sc,a rr-,D f.,2 7C-T Potipu g s , a,J L/7t3 /BAs 7-ioo l^	 9^
isolated [insulated) from the liquid in the film and do not participate
in the generation of energy in the MHD duct.
structures of the two-phase flow in the ducts are basically defined
-by the volume flow rate of the vapor content S and the velocity of the
mix Wmix [ref. #7,81. Due to the relative velocity of the motions of
the phases which are a function of the structure of the flow and the
regime parameters, the actual (true) volume vapor content in the flow 9
differs from the flow rate S. Consequently, the effective velocity of
generation and the effective conductivity of the two-phase flow that
are a fucntion of the true parameters of the flow are also functions
of the structure of the flow. when QZiqq *# ava , the effective con-
ductivity for the different structures cif the low are expressed by the
following relationships:
A. For the bubble and emulsion structures of the two-phase flow, by
the Maxwell relationship
c Z3 — 2 + 9	 (1)6 2 lp	 2 1-9
B. For the purely annular structure
	
c_3 ° 1	 (2)
a 2qj 	1 -
C. For the diffuse-annular structure
c_iq 	 1	 (3)
c2lp 1 —
	
For this structure (2) is a limit function,
	
since due to the carrying
off of the moisture into the vapor nucleus the moisture content of the
flow, averaged along the duct cross section 1 -9, is greater than the
moisture content of the film 1-9*. In the presence of a substantial
conductivity of vapor Q2. increases and . aZiq/a2 9 decreases.
For the flows with a "vapor-in-liquid" structure, the effective velocity
of generation is equal to the mean true velocity of the liquid phase and
is defined by the relationship:
W29 	 Wo(1-x)	 (4)
	
1	 P
For the diffuse-annular structure and when cZi > Qva the effective
velocity of generation is defined by the relationship.
W2	 Wo(1-x*)
	(S)s 
1 - W
and is less than the cross- sectional mean true
Here Wo is the velocity of circulation, (1-x*)
content of the flow along the film.
Let us examine the results of the experimental
of two-phase flows.
In the paper [ref. #11 a change in cZiq /0 29 of
eutectic Na-K with nitrogen at low temperature,
velocity of the liquid.
is the mass moisture
research of conductivity
the mix[turel of the
s, Wp - 900 - 2000 kg/m2sec
2
and 9 < 0.6 (x < 0.02) at which structures of the "vapor-in-liquid"
flow are known to exist was investigated by the conduction-flowmeter
method (B = 6000-8000 gauss) in a flat duct of 50 X 6.7 mm having a
length of L = 115 mm. In the tests the 9-values were measured as to
the absorption of gamma rays at the input and output of the MHD duct.
The experimental data are approximated by :he relationship:
c ZS s exp 3.89
a2(p*
Figure 1 shows a comparison of this relationship with function ( 1), valid
inthe investigated range of 9 and confirmed by the authors of [ref.#1]
and the data with the air-water flow [ref. #2]. The cause of the
divergence of the data for Na-K--N2 [ref. #11 and the data for the air-
water flow [ref. #21, as indicated by the authors themselves in [ref-#31P
is the interaction of the flow with the magnetic field. However, the
actual cause is not the presence itself of a supplementary force effect
on the flow, but the fact that under its influence, the slippage of
the phases increases and consequently the volume vapor content of the
flow changes, and possibly even its structure. In the processing and
approximation of the results of [ref. #11, the T-values were used that
were in fact measured outside the magnetic field (at the input and out-
put of the duct), while obviously pondermotive forces in the flux affected
the changed e.m.f. The very effect of the pondermotive forces on water
water due to its small conductivity is negligible.
Maxwell's formula is the general [overall] relationship forthe effective
value of any characteristics of permeability (A, a, s) of a two-
phase medium consisting of a matrix and occlusions dispersed [diffused]
in it with a total relative volume 9 having a value of permeability
different from the permeability of'the matrix. Relationship (1) is
written .in values of electrical conductivity for the condition
aZiq > avap-
The paper [ref. #41 presents data on-the relative electrical capacity
of the two-phase vapor-water flow at atmospheric pressure as a function
of the true volume vapor content. These data which relate to the bubble
structure of the flow are transformed into values of relative electrical
conductivity and are shown in figure 1 for comparison. They agree well
with relationship (1).
The investigation of the characteristics of the two-phase flow of the
eutectic Na-K with argon purging have been conducted in the work [ref.#5j.
Measurements were made for the "gas-in-liquid" structures at the fol-
lowing regime parameters of flow: P = 1.5 atm abs, T = 320-920°K,
Wp = 330-600 kg/m 2 sec, ip < 0.65, p'/p" = 450-650. The flow was sampled
by the conduction-flowmeter method, the electrical-resistance method,
and the gamma-attenuation method. The results of the measurements by
the electrical-resistance and the conduction-flowmeter methods processed
as a function of the 9-values measured by the gamma-attenuation method
are presented in the form aliq/Q 2 = f(1-V) and are shown in figure 1
for comparison. As is seen from the graph, the data of [ref. #51
satisfy Maxwell's formula. The coincidence of the results of measure-
(6)
RPICEDiNG.. PAGE AA iTSiWV
where F 1 (RexlRin), F 2 (RexlRin) are functions of RexlRin• Here additional
information is necessary concerning the structure of the flow and its
true volume vapor contents. Due to the absence of such information, the
analysis was made as a function of the cross-sectional mean true volume
vapor contents of the flow at the input into the duct.
In an investigation that we performed earlier on the hydrodynamics of
a two-phase vapor-potassium flow [ref. #91, it was established that
the regularity of the change in the hydrodynamic characteristics of the
vapor-potassium flow are the same as for the vapor-water flow and
Armand's formulas is recommended for the calculation of the true volume
vapor contents [ref. #3I. In processing the data, we used 9-values
calculated after [ref. #81whose functions were obtained in the absence
of pondermotive forces, and consequently, the 9-values characterize the
state of the flow at the input into the MHD duct.
The results of the data processing are shown in figure 1. From the
graph it is evident that in the region (1 — 9 ) > 0.1, i.e., for a
"vapor-in-liquid" structure, there is sufficiently [fairly] good coin-
cidence of our data with [ref. #2, 4, 51 and function (1). This confirms
the fact that in our tests, due to the small length of the duct in
the magnetic field (L = 36 mm), the effect of the magnetic field on
the structure of the flow was small.
The boundary between the "vapor-in-liquid" structures and the diffuse-
annular structure of the flow in [ref. #21 is defined as 9 > 0.9. Our
estimates of this boundary with respect to the critical velocity of the
vapor [ref. #91 agree with the recommendation of [ref. #21. For the
disperion-film structure of the flow ((1-9) <0.1), the development
[processing] and representation of the data as a function of the cross-
sectional mean flow of the true volume vapor contents bear a conditional
character since, under the conditions of only liquid conducitivity of
the flow, only the film of the liquid takes part in generation, and
the mean moisture contents of the flow along the film are less than
the cross-sectional mean of the duct. However, such processing enables
us to compare the result=i with the limit function (2). From figure 1
it is evident that in this processing, our results for (1-9) < 0.1 lies
further to the right than the limit function (2) and consequently the
conductivity of the diffuse-annular vapor-potassium flow at temperatures
of approximately 1050°K is lower than the conductivity of the flow which
can be provided by the liquid phase of the two-phase flow under the
condition that it is entirely in contact with the electrodes. The above
presented indirect proof of that which our data, obtained without the
effect of the magnetic field (the effect of the pondermotive forces are
negligibly small) makes it possible to suggest that the deviation from
the limit function is caused by the carrying off of the liquid into the
nucleus of the flow.
For purposes of comparison figure 1 shows the results of the work [ref.#6]
developed [processed] according to the true volume vapor content at the
input into the duct, calculated after [ref. #81 (dark dots) and after
v = 0 (light open dots). From figure 1 it is evident that following
the data of [ref. #6] as well as following other data, the value QZig/029
5
are greater than the limit valuesa tia/Q2, = 1/(1-V) which are provided
only by the conductivity of the liquid in the flow.
A comparison of the data of Iref. #6] and ours processed by identical
methods- ,-according to the true volume vapor content at the input into
the du , A shows that they are located farther to the right of our data
and although there is a continuation of relationship (6) which according
to the magnetic effect is obtained at the close values B 2 L, that also
the data of [ref. #61, as discussed above, are plotted with respect to
the V-values at the input into the duct. This makes it possible to
judge the effect of the magnetic field as to 9, and consequently, to
the electrical conductivity of the flow.
The pondermotive forces in the two-phase flow, acting basically on the
liquid metal, increase the slippage of the phases and, as a result of
this, the carrying away of the liquid from the boundary-layer film to
the vapor nucleus of the flow should [must also] increase in the flow
of the diffuse-annular structure, and the conductivity of the flow
should decrease. This is well illustrated in figure 1 by a comparison
of our data and the data of [ref. #6] which differ only by the effect
of the magnetic field. Experimental research is necessary in a broad
range of change in the magnetic effect of B 2  and flow rate parameters
of the flow.
6
References
1. M. Petrik and K.Yu. Lee, "Characteristics of Liquid-Metal
MHD Generators. Magnetohydrodynamic Formations of Energy."
Proceedings of an International Symposium, Paris, 1964,
VINITI Publishing House, Moscow, 1966, .p. 543.
2. M.Petrik and K.Yu Lee, "MHD Generators in Tow-Phase Liquid
Metal Streams," Proceedings of an International Symposium,
Salzburg, Austria, 1966.
3. in English
4. in English
S. in English
6. P.L. Kirillov, V.I. Subbotin, and I.P. Stakhanov, "Measurements
of Electric Conductivity of Liquid Vapor Mixtures of Potassium,"
see, Proceedings of an International Symposium, Salzburg, 1966.
I. B.K. Koslov, Regimes and Forms of Motion of an Air-Water Mix-
ture in a Vertical Tube, Collection on "Hydrodynamics and Heat
Exchange while Boiling in a High-Pressure Vessel," Academy of
Sciences of the USSR, 1955.
8. A.A. Armand, "Resistance During the Motion of a Two-Phase Sys-
tem in a Horizontal Tube," Izvestiya VTI, No.l, 1946.
9. I.T. Alad'yev, N.D. Gavrilov, and L.D. Dodonov, "Hydrodynamics
of the Two-Phase Flow of Potassium in a Tube," Collection on
Investigations of Heat Exchange, Hydrodynamics, and Thermo-
physical Properties of Matter, Nauka Publishing House, Moscow,
1968.
Figures
1. Comparismn of the calculated formulas and
for the effective electrical conductivity
1. According to Maxwell's formula (1); 2.
ratio in Ref 2; 3. According to the ratio
imation of the data in Ref 1; 4. Given in
Ref.4; 6. Given in Ref 5; 7, and 8. Given
to the treatment for Oat the duct inlet &
by the authors.
experimental data
of two-phase flow.
According to the
in Ref.6 -- an approx-
Ref.2; 5. Given in
in Ref 6, corresponding
ad for 0-$; 9. Given
2. Relative change in the e.m.f. generated in a duct in the course
of a two-phase potassium vapor flow in a magnetic field depending
on xand Wmix*
1. Wp - 225 kg/m 2 sea,	 2. Wp - 415 kg/m 2 sec
7.


The effective electrical conductivity of a two-phase liquid-metal flow

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