For the small, high performance reactors required for space electric applications, adequate neutronic analysis is of crucial importance, but in terms of computational time consumed, nuclear calculations probably yield the least amount of detail for mission analysis study. It has been found possible, after generation of only a few designs of a reactor family in elaborate thermomechanical and nuclear detail to use simple curve fitting techniques to assure desired neutronic performance while still performing the thermomechanical analysis in explicit detail. The resulting speed-up in computation time permits a broad detailed examination of constraints by the mission analyst

Brown, N. J.

Mccauley, E. W.

English

NASA Technical Reports Server

NUCLEAR REACTOR DESCRIPTIONS FOR SPACE POWER SYSTEMS ANALYSIS*
E. W. McCauley and N. J. Brown
Lawrence Radiation Laboratory
University of California
Livermore, California
For the small, high performance reactors required for space electric
applications, adequate neutronic analysis is of crucial importance, but In
terms of computational time consumed, nuclear calculations probably yield the
least amount of detail for mission analysis study.
It has been found possible, after generation of only a few designs of a
reactor family in elaborate thermomechanical and nuclear detail to use simple
curve fitting techniques to assure desired neutronic performance while still
performing the thermomechanical analysis in explicit detail. The resulting
speed-up in computation time by three orders of magnitude, permits a broad
detailed examination of constraints by the mission analyst.
INTRODUCTION
Space research in general and Space nuclear
electric systems in particular are in a period of
priority reassessment and technological retrench-
ment. Even so, n_ concepts and different com-
binations of older concepts are being put forth
for possible application. In order to provide
any hope of progress, the mission analyst, faced
with a restricted list of missions and of vehic-
les, must develop a set of analyses more consis-
tent and credible than those to date. One of the
chief obstacles in his path is the state of
nuclear reactor heat source data which is usually
presented as a pointwise design or as a set of
parametric statements so overgeneralized as to be
effectively useless.
Mission analysis can hardly optimize a point,
or give a reasonable estimate of specific re-
search potential on systems where it has neither
breadth nor depth of knowledge. On the other
hand, the designer of the nuclear reactor heat
source has insufficient information to optimize
his system to the particular mission since it in
turn lacks definition.
To be effective, the reactor descriptions
must be presented to the mission analyst in con-
siderable detail. However, the parametric con-
straints must be held to an absolute minimum or
the surface to be fitted will be as full of con-
fusing depressions as a lunar landscape.
Some years ago the Lawrence Radiation
Laboratory developed a method of parallel-
optimization-path reactor design for cylindrical
reactors, which coupled thermo-mechanical design
to multi-group neutron transport analysis to allow
rapid assessment of the effects of acquired re-
search data and potential lines of research on
reactor performance. It was found practicable to
rapidly convert from one type of reactor to
another. Beyond this, the consistency inherent
in a single pass computerized design produced con-
figurations significantly superior to those that
the same group achieved by traditional reactor
design methods.
This method requires approximately 5 to lO
minutes of CDC-6600 time to produce a design point
which is too long to be suitable for inclusion in
mission analysis work. The neutronic routines are
called 30 to 40 times in a typical iterative de-
sign sequence and require three to four orders of
magnitude more computation time than the thermo-
mechanical portion.
The obvious approach is then to attempt to
eliminate the detailed neutronic analysis if pos-
sible. As a demonstration case, we have selected
a heatpipe-cooled reactor type previously studied
at LRL. _ We selected the criticality-limited de-
sign region and designed a family of 12 reactors
in detail at power levels of .6, 2., and 4.6 Mwth.
Fueled core aspect ratios (L/D) were chosen as
.8, 1.2, 1.6, and 2.0.
This paper purposely avoids extensive tables
and reactor descriptions so that it may not be
construed as a description of a particular reactor
system, but as an approach to a particular design
problem, applicable to a variety of systems,
whether liquid metal convectively cooled or heat-
pipe cooled cores for Rankine systems, or in- core
or out-of-core thermionic systems. However, it is
necessary to consider some parameters and features
of the system selected to demonstrate that the
study was not made on an over-simplified students
model.
DESCRIPTION OF THE HEAT SOURCE
Tilemodel selected was as detailed and sophis-
ticated as any published in connection with the LRL
Space Reactor Technology Program. The correspond-
ing model here actually has its outermost radius
within the fueled core radius of the SPR-4 design,
yet it has been designed with a greater safety
margin.
A cross section is shown in Fig. l. Both the
reactor and the heatpipe boiler sections on the
ends w_re designed in the code. The design in-
cludes a dual control system, either of which could
carry the mission to completion. The core is not
represented by a simple fuel matrix but is designed
*'Work done under the auspices of the U. S. Atomic Energy Commission.
98
https://ntrs.nasa.gov/search.jsp?R=19720009963 2020-03-17T03:48:33+00:00Z
1.2 VERSION B
_'0.8
U VERSION A' " "
00.6
.-, FUEL LOADING, %
VERSION A VERSION B
__.0.4 I 2 I 2 3
U-233 24.7 44.5
:: 0.2 U-235 87.1 99.0 93.5 70.4 51.9
O U-238 12.9 1.0 6.5 4.9 3.6
z I I i I I I I
2 4 6 8 I0 12 14
CORE RADIUS - cm
16 18
.__Fig.2 Po_lerDensityProfiles
as a discrete number of fuel elements arranged in
a hexagonal pattern in a discrete number of
dodecagonal rows. Zonal boundaries coincide with
fuel element boundaries and fuel 1oadings of
U-238, U-235, and U-233 are varied to give radial
power flattening. Material properties are tem-
perature dependent and in cases where creep is
involved, both time and temperature dependent.
Fuel elements were designed with both thermal
stress and peak temperature limits. Provision was
made for differential thermal expansion and burn-
up dependent fuel swelling. The heatpipes for
each system were tailored to the reactor and
optimized for the specific ase, Their design
limits included peak or boiloff flux limits, and
a safety margin to carry the load on failure of
any single adjacent heatpipe as well as a I0%
factor for power surges, 20% for transport prop-
erty data scatter, and 10% for radial power
variations.
The units were designed to have a maximum
multiplication factor at room temperature of .96
when fully immersed in water and flooded in the
absence of blowoff side reflectors. Appropriate
neutron filters to accomplish this were placed
between core and pressure vessel in this case.
The design code could and in the past has, de-
signed these filters into the metallic structure
within the core as alloying elements or as
plating.
The design code also checks zero power tem-
perature coefficients as a function of temperature,
and power coefficients for control as a function
of lifetime including fuel burnup effects, pro-
duction of daughter fissile species, etc.
The pressure vessel and structure were de-
signed for each case using time and temperature
dependent creep data.
The remaining figures show additional details
of the system. Figure 2, previously published 2
shows the compactness and the degree of power
flattening achieved by the U-233, U-235 system
(version B) compared with the SPR-4 design
(version A). The remaining carpet plots,
Figures 3 - 10 show some of the more significant
parameters of the system. In particular the
readers attention is directed to the nonlinear be-
havior of many of the variables.
99
It should be obvious from the detail de-
scribed above that thermionic elements could have
been designed within the core instead of heat-
pipes, or outside the core in the boiler regions.
Similar families of liquid metal cooled reactors
have been designed to similar criteria and others
including specific pressure drops, coolant tem-
perature rises, etc. These have been even better
behaved than the heatpipe reactors shown. They
could just as easily have been gas cooled reactors
for Brayton cycle applications.
This listing of the detail considered in the
design is not presented with a view to convincing
the reader of the credibility of this particular
set of design calculations or the feasibility of
this particular design concept which has been
published in the past; it is presented as a demon-
stration that a rather complex design can be
described in considerable detail employing a
reasonable number of limits or weighting factors.
SHORT FORI,IOF THE COHPLETE SYSTEII
In place of the neutronic analysis we pre-
dicted the fuel mass using average core fuel
burnup data from the twelve designs• This was
purposely done in the simplest fashion by fitting
second order curves ti_rough the twelve data points
to produce expressions for burnup and the spacing
parameter _ as a function of power and aspect ratio.
The details of this fitting are shown in Appendix A.
Using these functionals to replace the neutronic
analysis, the thermo-mechanical code portion pro-
duced fifteen additional designs at points inter-
mediate to those of the previous detailed analysis.
These fifteen cases were repeated using the full
neutronic analysis and the data were compared.
They agreed within a few percent in all cases. We
therefore conclude that this analysis could be
used for this family of reactors within the
specified parameter ranges for mission studies.
Running times averaged less than I/lO second per
"fitted" design.
38
36
E
v
,.-
• 34
E
_ 32
J
_ _o
0
• 28
2,'.
Z 24
_ r--r-- I_T- _
+-----+- _
+__1+__ _
+___.+_ +.__+__ _ _
ii i
i o,.I- ÷--4.-
._...-+-.
Fig, 3. _eatsource Outside
Diameter
L
6--_--- /
2.O
4 ...... I 1.0
i
2 _+ k _----
\-J \ ....
j ,...o/
--- o.s _
I I
Fig. 6, Heatplpe Inside
Diameter
4;
3.oi
i 2.5
2.0
h5
hO
.s
o
Fig. 4. Average Fuel 8urnup
+ .
........ //
/
.._+
Fig, 7. _um_r of Fuel
Elemnts
0.7
o+
_.... +._. __.
_"o.'_ \I __
_ .4 _
_ 0.3
0.2
0.1 ....
0 .......
1I-o
I
Fig. 5. Spacing Parameter, B.
1--
200_
180_
| ,4o_-
-_120
:_ 100
'° i
60
40 ¸
r_ i i
J t\_
Fig. 8, Total Uranium Mass
ioo
3O
2.C
25
2O
m
.M
0
i 15
e)
f,4
!
-!
\
\
k
_W
\
\
0.6 6%
\
\ \
\\
\
\ \
,,\ \
, \.
\ \
%
%
2
\ :b--%
.,,,.,. -
-o.
),8
\
%
Table I shows typical results. These data
were selected from the larger set as quantities of
particular interest to the mission analyst, re-
actor physicist, and engineer. For the mission
analyst fueled core radius, maximum package radius,
and reactor-boiler mass were selected. For the
physicist the hot-core full-power start of life
and cold-core water-immersed and flooded multipli-
cation factors are presented. For the engineer the
heatpipe inside radius and a fuel element porosity
parameter were selected as variables representative
of areas subject to possible future constraints in
view of, e.g., fabrication difficulties. The
factors shown in percentages are the maximum and
rms deviation of the predicted value from that
established by the complete analysis. Also shown
where applicable is the ratio of the maximum value
of the parameter to the minimum encountered in the
field, demonstrating that we were not fitting near
constants. Fuel mass varied by a factor of 5.4.
Table I
Core React Keff Keff Heatpipe Bfa_,_Radius Radius Mass Hot _ Radius
Max Oev % 2.74 2.57 5.86 2.52 2.21 .255 2.39
Rms Dev % 1.27 1.13 3.20 1.62 1.23 .12 1.13
F max/F rain 1.79 1.60 5.18 2.89 1.80
(a)B is a fuel element porosity parameter representative of a design detail
and is the ratio of the fuel inside radius to the outside hexagonal-flat
radius.
Fig. 9. U-233 Mass
CONCLUSIONS
2.5
l.5
1.0 _-._
Fig 10 Reflector Thickness --
As a demonstration the results indicate the
promise of the method. This becomes n_re evident
when the reactors are examined in detail. The
simplicity of the fitting method selected is not
meant to apply to the designs. The simplest possi-
ble representation was used to predict a complex
design, to get across the point that it is neither
impossible nor impractical to implicitly formulate
reactor designs so that they can be meaningfully
employed by the mission analyst. It is obvious
that a more sophisticated set of formulae could be
developed covering such parameters as reflector
thickness, zone loading fraction, etc., to give even
closer predictions. As an example of this, the
parameter B was included above as a starting point
to reduce the number of iterations in the thernw)-
mechanical analyses.
By using these methods, reactor analysis and
reactor system surveys can be broadened in scope so
as to pass from company and academic circles to
interact meaningfully and credibly with the space
systems analysts who must provide input data for tile
decision making process.
BIBLIOGRAPHY
I. Brown, N.J.; and HcCauley, E.W.: Fast Reactor Desiqn Analysis Codes,
Lawrence Radiation Laboratory, Livermore, Rept. UCRL-50429 (1968).
2. Walter, C.E.; Brown, N.J; Hampel, V.E.; McCauleym E.W.; and Wilcox, T.P., Jr.;
An Advanced 2000 kWth Nuclear Heat Source, Lawrence Radiation
Laboratory, Livermore, Rept. UCRL-70978 (1968).
I01
Appendix A
THE FITTED FUNCTIONALSB AND BU
In order to providea direct path to the
explicit, mechanical characterizationof an
implicitly critical and optimized nuclear reactor
heat source of power Q and ratio L/Do it is
necessary to describe the spacing paran_ter, B
and the burnup fraction, BU as functionals. The
data used are abstracted from the detailed
analyses.
As is clear from Figure 5, B is a function of
L/D and Q, or
B = B(LID,Q) = D(Q) + E(Q)(L/D) + F(Q)(L/D)2
with
2
D(Q) = _ diQi
i=O
2
_-_
E(O) = 2. eiQ1
i=0
2
fiQiF(Q) = L
i=O
where, for constant Q,
2
B (L/D)Q = /_.
j=O
1.1
1,2
gi(L/D)J 1,3
Performing the indicated least squares fit in
equation 1.3, the gi are used to fit the dl, el,
and f_, respectively, of equations 1.2 thu_
producing the coefficients of equation l.l. They
are listed, for reference, in Table A.l.
The burnup (Figure4) is treated in a similar
manner with
BU = BU(L/D,Q) = A(Q) + B(Q)(L/D) + C(Q)(L/D)z
1.4
where
2
A(Q) = _ akQk
k=O
2
B(Q) : _ bkQk
k=O
2
C(Q) = _ ckQk
k:O
and
2
BU(LID)Q : _. _ (LID)_
_:0
The resulting coefficients of equation 1.4 are
listed in Table A.2.
Table A.I
The. Functional_.Coefficients of
i=O
D 2.59217E-I
(d)
, ml m i
E 4.27773E-2
(e)
, i i
F -8.41595E-2
(f)
i
i=I i=2
m.
1.23627E-I -l.19133E-2
i i
3.74926E-2 -7.96442E-3
-l,06819E-2 2.64808E-3
i i i llmli i
Table A.2
The..Functional Coefficients of BU
k=O k=l k=2
i i m m ii i
A l.20680E-2 2.39719E-2 -3.53083E-3
(a)
i • u i i l
B -I.07593E-2 -l.36532E-2 2.53387E-3
(b)
i ii m lilmllll
C 3.09971E-3 2.41979E-3 -5.07874E-4
(c)
i m i i i
*Burn Up
102


Nuclear reactor descriptions for space power systems analysis

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