Annals of Nuclear Energy, Vol. 3, pp. 447 to 450. Pergamon Press, 1976. Printed in Northern Ireland

N E U T R O N PHYSICS A N A L Y S I S OF T H E R M I O N I C R E A C T O R S WITH U - 2 3 3 AS F U E L A N D B E R Y L L I U M AS M O D E R A T O R

SOMER ~AHiN Ege 0niversitesi, Miihendislik Bilimleri Fakiiltesi, Bornova, Izmir, Turkey

(Received 7 June 1976)

Abstract--Thermionic reactors with U-233 as fuel and Beryllium as moderator are appropriate as primary or secondary energy sources in space craft. In this paper, neutron physics analysis of such a reactor is presented. All neutron physics calculations have been carded out with the help of multigroup SN methods. 123 energy groups, $4-P3 approximation by one dimensional and 4 energy groups, $4-P1 approximation by two dimensional calculations have been used.

Some integral values and neutron production densities are given as characteristic properties of the reactor.

1. INTRODUCTION

The intensive development of the space research and technology obliges to seek new energy sources in space craft for their growing energy require- ments. For long mission periods thermionic reac- tors have a good chance to fulfill the requirements of space craft in a wide area (Htcker, 1968; Ther- mionikreaktoren, 1965; Int. Conf., 1968 Incore Therm., 1968; ~ahin, 1970; ~ahin, 1971]. They have a reasonable energy conversion efficiency (> 10%). As they do not have any moving parts, besides control instrumentations, they are prefera- ble to the conservative energy conversion systems, such as a generator driven by a mercury vapour turbine, in respect to the dynamical viewpoints.

Previous work was concentrated on thermionic reactors with U-235 as fuel and ZrH1,7 as mod- erator. We showed that a thermionic reactor with U-233 as fuel and Be as moderator will compete with the former ones (~ahin, 1974). In this paper we present the neutron physics analysis of such a reactor. As a typical thermionic fuel element we have chosen one which has been described in In- core therm. (1968), ~ahin (1970), and ~ahin (1971).

2. METHOD OF CALCULATIONS

In ~ahin (1974) we have found that a thermionic reactor with a ratio of Be/U-233 = 1200 has a good neutron economy. Thus the core of the reactor in this study will consist of this type of fuel elements. The study has been carried out in the following steps:

Multigroup lattice calculation to obtain nuclear data for homogenized reactor core

Multigroup reactor calculation with one space variable (r) to evaluate the neutron spectrum

Four-groups calculations to determine the critical reactor conditions with two space variables (r-z).

2.1. Multigroup lattice calculations

It is considered that the core of the thermionic reactor which is investigated in this paper, consists of a uniform type of fuel elements. In this case it is convenient to obtain the microstructure of the neutron spectrum with the help of a cylindrized lattice calculation.

In this study the lattice calculations have been carried out in cylindrical geometry in S4-Pa ap- proximation with 123 energy groups, solving the Boltzmann transport equation (~ahin, 1973) by the use of the computer code XSDRN (Greene, 1969) using the data set ENDF. VII.GP 123. SIGMAS. T 293 (Lucius, 1971; P. 100).

Using ENDF. VII GP 123. SIGMAS. T 293 it was possible to perform resonance self shielding calculations for Na, Nb, W. U-233, U-234, with the Nordheim integral method (Nordheim, 1961). After the neutron spectrum in the reactor lattice has been calculated, the cross sections have been weighted with this spectrum for the homogenized reactor calculations and recorded on a magnetic tape with XSDRN (Greene, 1969).

The mesh number was chosen as 40 to fit the heterogeneous structure of the fuel lattice.

2.2. One dimensional multigroup reactor calculation

In the next step one dimensional reactor calcula- tion in cylindrical geometry has been carried out using the computer code XSDRN in 123 energy

447

448 SUMER ~.AI'{[ N

1.4

- ~ 0 . 8

G r- ~ Moderotor

~ ° ~

G 0.4 / I C i Converter ond

Molybden i Fuel zone I cooling channel

o ~ ,~ ' ~ ~, ' ,o ,' ," ~ ,~ 2'0 Rodius, m m

Fig. 1. Neutron production in thermionic fuel cell.

G L2 v W S

~2

c l2x lO

~ lOxlO -5

1~16 X I0 -6

14x 10 -6

..~" 2 X i 0-6

5 X 1 0 - 4 %

2xlO "4

io-4 Core

!

Radius, cm

Fig. 2. Radial neutron production in the reactor.

i

r 48 52

I I t

44

,R = 0 0 0 (cm)

/R = 9.66(cm) ~ , 39(cm) O(cm)

Core Reflector

I i I I f J i I J I 0 4 8 12 16 20 24 28 32 36 40 44

Height, cm

Fig. 3. Radial neutron production in the reactor.

12 x I0-" ~ ~ H =O.O0(cm)

= ~ ~ / H=lO.9(cm , ~ LOx I0--" - ~ ~ ~ H =]9.9 (crn) ii ~ /~ :3o . , (cm)

~ 8~(10_~ " ~ H = 3 9 . 1 ( c m )

4 x I 0 -~ -

I , , , , , , 0 4 8 12 16 20 24 28 32 ;36 40

Radius, cm

Fig. 4. Axial neutron production in the reactor.

I 36

Neutron physics analysis of thermionic reactors

groups with $4-P3 approximation. The neutron leakage in the axial direction has been considered in form of a pseudo absorption (mode DY = height by XSDRN).

In this work a beryllium reflector with thickness of T = 12 cm has been used. This value was ob- tained as optimum by our previous work for U- 235/ZrH1.7 type reactors (~ahin, 1971; Chapter 2.4).

2.3. Collapsing the neutron data to [our energy groups to calculate the critical reactor dimen- sions

With the help of the neutron spectrum resulting On from multigroup one dimensional reactor calcula- tion, neutron data have been collapsed to 4 energy groups in order to perform 2-dimensional reactor calculations with reasonable computing efforts. As a compromise between accuracy and computer ex- penses the group collapsing has been performed as follows:

Table 1. Collapsing of the energy groups

Macrogroup Microgroup Energy boundaries

1 1-57 14.918-0.015034 MeV 2 58-93 15034-1.8591 eV 3 94-108 1.8591-0.02071 eV 4 109-123 0.2071-0 eV

The first macrogroup contains the fission spec- trum. The second macrogroup contains the reso- nance region and borders to the 94th microgroup where TERMOS (Honeck, 1961) cross-sections begin. The thermal region (E < 1.86 eV) is divided into 2 macrogroups due to its importance for a thermal reactor.

The four-group transport equations are solved with the help of DOT-III (Rhodas, 1973) in r-z geometry with S4-Px approximation (16 space angles).

The overall beryllium reflector thickness has been assumed as T = 12 cm.

All numerical calculations have been performed on the IBM-360/91 and IBM-360/75 computers at Oak Ridge National Laboratory, Radiation Shield- ing Information Center.

3. THE NUMERICAL RESULTS

Table 2 shows the technical values obtained through the numerical calculations.

449

Table 2. The technical values of Be moder- ated thermionic reactor with U-233 as nuc-

lear fuel

k,fr: 0.97369 Be/U-233:1200 Core radius: 33.282 cm Core height: 79.44 cm Height of reactor: 103.44 cm Reactor Mass: 1263 kg Fuel Mass (UO2): 11.85 kg Number of thermionic elements: 19x 12= 228 Electrical power output: 78 kW~l (by a uniform emitter heating of 10 W~l/crn 2)

Fig. 1 the neutron production density

f v(r, E) E (r, E)@(r, E) dE I

in the thermionic fuel cell has been illustrated as a function of cell radius. Due to the high neutron absorption in U-233 the penetration of neutrons in the fuel region is mostly hindered. Thus the ther- mal neutron spectrum of the lattice prevents to make effective use of the whole fuel investment.

Figure 2 shows the neutron production density from one dimensional reactor calculations (Section 2.2).

Figures 3 and 4 show the neutron production density resulted from two dimensional reactor cal- culations (Section 2.3).

4. DISCUSSION

With the help of highly sophisticated numerical neutron transport methods neutron physics analysis of a thermionic reactor with Be/U-233 = 1200 has been carried out. This reactor can be used as energy source in space craft with high electrical energy requirements. In this study the fuel distribu- tion in the core has been assumed uniform. At this point it is necessary to make a comment about the total electrical power output of the reactor. Hol- land has investigated the minimum degradation of power and efficiency due to nonuniform nuclear heating in thermionic reactors at optimized operat- ing conditions of series-parallel circuited cesium diodes. This degradation is quite high. In our previ- ous work we have presented a rational way to keep constant the emitter heating over the reactor vol- ume which would cause only a small increase of reactor diameter [~ahin, 1970; 1971; 1972]. There- fore we can assume that the technical values in the Table 2 are also similar to those of thermionie reactors with constant emitter heating, designed by the methods in ~ahin (1970, 1971).

450 SOMER SAHIN

Acknowledgements--The author wishes to thank Radia- tion Shielding Information Center in using the computer facilities at Oak Ridge National Laboratory; the Turkish Scientific and Technical Research Council for financial support of this research work by a postdoctoral research fellowship.

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