To calculate the output characteristics and electrode temperature of thermionic emission electricity-generating
channels, one-dimensional stationary models of thermoelectroconduction processes, which are based on the principle of
additivity of the local current–voltage characteristic, are most widely used. The essence of this principle is the assumption
that the parameters of the discharge in the interelectrode space depend only on the local temperature of the electrodes and
the potential difference between them. This makes it possible to calculate the current density in the interelectrode gap by
interpolating the experimental dependence of the discharge current on the voltage between the electrodes and their temper-
ature, obtained in model thermionic emission converters with isothermal and equipotential electrodes.
However, mathematical modeling on a computer of the service life behavior of the electricity-generating channel,
reconstruction of its internal parameters from the output characteristics, and optimization requires repeated thermal-electri-
cal calculation of the channel. As a rule, the number of such calculations is quite large. The present communication presents
a method, developed to increase the efficiency of the computer programs used for calculating the electricity-generating chan-
nels by making a rational choice of model and using efficient numerical methods.
Mathematical Model. In the computational scheme of a multielement electricity-generating channel, shown in Fig. 1,
the hermetic inputs and connections between the electricity generating elements are represented as objects with lumped
parameters – equivalent electric and thermal resistances. The distribution of the temperature and electric potential over the
length of the electrodes of electricity generating elements is determined by a nonlinear boundary value problem for a system
of second-order ordinary differential equations which can be written in the form
(1)
(2)
with the boundary conditions
(3)
λF
dT
dx
TT
R
T
e
eec
i.c
⎛
⎝
⎜
⎞
⎠
⎟
=
+−
+
()
;
dV
dx
P
FF
j
2
2
=− +
⎛
⎝
⎜
⎞
⎠
⎟
e
e
e
c
c
ρρ
,
−−
⎛
⎝
⎜
⎞
⎠
⎟
+
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
−
−
ρρ ρρ
e
e
e
e
e
e
c
c
FF
I
dV
dx F F
q
1
2
;
d
dx
F
dT
dx
PTT TTj V
kT
e
e
e
ee
4
c
4
ec c
e
λεσ α χ
⎛
⎝
⎜
⎞
⎠
⎟
=−+−+++
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
−()()
2
Atomic Energy, Vol. 110, No. 3, July, 2011 (Russian Original Vol. 110, No. 3, March, 2011)
UDC 621.362+519.62
Research Institute and Scientific-Industrial Association Luch, Podolsk, Moscow Oblast. Translated from Atomnaya
Énergiya, Vol. 110, No. 3, pp. 175–178, March, 2011. Original article submitted December 20, 2010.
1063-4258/11/11003-0212
©
2011 Springer Science+Business Media, Inc.
212
A. A. Davydov and D. V. Shirokov
METHOD FOR CALCULATING THE OUTPUT
CHARACTERISTICS AND ELECTRODE
TEMPERATURE OF THERMIONIC EMISSION
ELECTRICITY-GENERATING CHANNELS