TASK 4. REACTOR TECHNOLOGY

The nuclear analysis effort over the contract period was concerned with five principal activities:

1. Nuclear cross section data evaluation

2. Analytical methods development

3. Critical experiments and other physics measurements

4. Nuclear design of thermionic reactor cores

5. Nuclear analysis in support of the TFE test program.

Cross section studies were concentrated on the refractory metals and other nuclides important to thermionic reactor design which had not been extensively studied in other reactor programs. New evaluations were carried out for niobium, molybdenum, rhodium, samarium, rhenium, praseodymium, and dysprosium. As a result of the critical experiment program discussed below, discrepancies in the cross section data for U-235, tungsten, niobium, molybdenum, beryllium, oxygen, samarium, and dysprosium were identified and, in some cases, corrected in later evaluations.

The analytical methods development effort led to the development of a number of computer programs which were extensively used in design studies and critical experiment analysis. These include the GAF/GAR/GAND (References 1, 2 and 3) system for calculating neutron energy spectra and preparing multigroup cross section data, the GANDY (Reference 4) and FSDP3 (Reference 5) codes for calculating cross sections in the unresolved resonance energy region, the GAPER (References 6 and 7) transport perturbation theory program, and the 3DT three-dimensional transport theory code. These programs continue to be useful in fast reactor analysis.

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The earliest reactor physics experiments carried out consisted of spectrum measurements on non-multiplying and subcritical assemblies (Reference 8). The design of these one-dimensional assemblies of tungsten and U-235 formed the basis for several later spectrum experiments sponsored by other agencies, and initiated the extensive fast spectrum program at GGA. The tungsten measurements revealed spectral temperature dependence at high energies which had not been noted previously.

The major undertaking in the experimental reactor physics program was the design, construction, and licensing of the Thermionic Critical Facility (References 9, 10 and 11). This work included the design and fabrication of a full complement of neutronically homogeneous fuel elements for Assembly No. 1. A comprehensive series of experiments encompassing nearly the entire spectrum of fast reactor physics measurements was performed with Assembly No. 1 (References 12, 13, 14 and 15). In addition to the conventional critical mass measurement, the isothermal temperature coefficient, reactivity worths of individual fuel elements, and neutron lifetime (b /#) were measured. The neutron spectrum was measured by the pulsed neutron, time-of-flight method in a novel and calculable slab geometry configuration (Reference 13). Additionally, the reactivity worths of ~ 30 materials of interest to thermionics were measured in a unique experiment in which reactor flux perturbations were minimized (Reference 15). Reflector worths were also determined for thin slabs. The Doppler reactivity coefficients for samples of U-238, W, Ta, Nb, Dy₂O₃, and Sm₂O₃ were measured in a calculable spherical configuration by a new method in which the sample temperature was varied using a flowing stream of helium gas (Reference 16).

Assembly No. 1 of the Thermionic Critical Experiment was studied analytically in considerable depth, and the comparisons between calculation and experiment yielded considerable information relevant to thermionic reactor core design.

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Nuclear analysis of thermionic reactor systems was carried out for a wide variety of reactor designs for space and terrestrial applications (References 17 and 18). It was shown that a single TFE design, originally optimized for a fast reactor, could be used in systems with fast, intermediate, or thermal neutron energy spectra with satisfactory characteristics of critical size, power distribution, control margin and temperature coefficient. The latest study in this series is described below.

Finally, enrichment requirements and power distributions were calculated for all TFE and capsule tests irradiated in the TRIGA reactor.

The reactor design and analysis effort over the contract period has resulted in conceptual reactor designs for a variety of space and terrestrial electric power applications as well as for reactor experiments to be conducted in test facilities. This work was performed to establish reactor configurations for incorporation in power system designs and to analyze selected design parameters to establish performance parameters and feasibility of the particular concept.

Early reactor design work was focused on the "pancake" reactor concept (References 19 and 20) where the thermionic fuel elements are unit cells. The more recent work adopted the concept of the converters placed in series in a tube to form "flashlight^" fuel elements (References 21, 22 and 23). The pancake reactor configuration employed cross flowing liquid metal coolant while the flashlight reactor employs liquid metal coolant flow parallel to the axes of the flashlight fuel element.

Reactor applications included electric propulsion as well as auxiliary power (Reference 24). Reactors designed for electric propulsion are, generally, composed entirely of thermionic fuel elements and are characterized as fast neutron spectrum reactors. Auxiliary power reactors typically include the addition of driver fuel in the core to minimize core size. Both fast and moderated spectra have been studied, dependent upon the choice of driver fuel material.

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Water-cooled reactors were also studied for undersea application (Reference 18). These designs have a core composed of a mixture of thermionic fuel elements and UzRH fuel elements with surfaces exposed to the coolant of stainless steel construction.

Reactor designs for reactor ground tests were prepared at different times during the program. These reactors were intended to provide engineering data for use in design of reactors for space power (Reference 25).

The reactor test-conceptual design and cost task was concerned with the preparation of designs for a reactor test as well as cost estimates for the reactor test program.

The most detailed study of a reactor test was performed assuming use of an existing facility at Los Alamos, New Mexico (References 25and 26). The reactor and facility were designed to facilitate removal and replacement of the fuel elements and other core components.

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4.1 NUCLEAR ANALYSIS (M. Merrill, A. Marshall, D. Mathews)

The objective of this task was the development and understanding of the neutronic characteristics of a thermionic reactor, including evaluation and refinement of cross section data, development of analytical methods for reactor physics design, and nuclear analysis in support of systems studies.

Past work has included nuclear analysis of fast and moderated thermionic reactors in support of systems studies. In addition, the task has been concerned with the analysis of data from critical experiment work performed at GGA and with the planning of future critical experiment programs.

4.1.1 Cross Section Maintenance

The processing of the Version III ENDF/B cross section data was completed for all nuclides of interest to thermionics except beryllium, for which modification of the existing processing codes would be required. The intended testing of the Version III data by re-calculation of the reactivity worth measurements in Assembly 1 of the Thermionic Critical Experiment (Reference 1.5) was not initiated.

4.1.2 Analytical Methods Development

Work was terminated on the development of a multi-region version of the MICROX cross section preparation code (Reference 27). Completion of this task would have required about three man-months of additional effort.

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4.1.3 Critical Experiment Planning

The work intended for this task in the second half of the fiscal year was not initiated. The Thermionic Critical Facility is being dismantled and de-licensed.

4.1.4 Reactor Design Studies

Nuclear analysis of a fast spectrum thermionic reactor for electric propulsion applications has been carried out over the past 17 months. A complete summary of this work is presented here, which includes some material from previous summary reports as well as the most recent work. Also included are the results of nuclear calculations for the Thermionic Reactor Experiment (TREX).

4.1.4.1 Introduction

The standard electric propulsion thermionic reactor was designed to produce 120 kWe with 162 UCZrC fueled thermionic fuel elements (TFEs).

Elevation and plan views of the reactor core are shown in Figures 4-1 and 4-2. The core consists of 162 TFEs of about 3.3 cm outer diameter arranged in a hexagonal lattice. The design of the UCZrC fueled TFE closely resembles that of the 6F series of prototype thermionic elements tested at GGA. A drawing of the 6F cell is given in Figure 4-3. The TFEs contain six thermionic diodes 5.1 cm in length arranged axially and separated by intercell connector regions 2.3 cm long (see Figure 4-4). Axial reflector pieces of BeO 10 cm long are included on each end of the TFEs. Additional TFE data are given in Tables 4-1 and 4-2.

Reactor control is provided by 11 cm thick BeO shutters which open out to increase core leakage (Figure 4-2). The core and reflector shutters are separated by a niobium pressure vessel. NaK coolant flows in the spaces between the TFEs.

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4.1.2.2 Calculational Methods

Multigroup neutron cross section sets were obtained with the GGC-5 code (Reference 28). For most calculations, an 11 broad group structure was used which is given below in Table 4-3.

The energy group structure was chosen to provide approximately equal flux in each energy group at the core-reflector interface. Some adjustment of the energy groups was then made to adequately treat the various types of reactions in the resolved and unresolved resonance range and in the fission source range.

The general procedure followed was to run separate GGC calculations for the core region and the radial reflector. The initial approximation is thus made that the neutron energy spectrum in these regions is that appropriate to an isolated homogeneous mixture of the materials in the region with a fission spectrum source and out-leakage represented by an energy-independent buckling. The adequacy of this approximation has been investigated with many-group one-dimensional calculations from which the actual region-dependent spectra can be approximately determined and used for cross section averaging in place of the GGC spectrum calculation.

The material volume fractions for the core region are given in Table 4-4. The GGC calculation for this region is complicated by the large number of resonance absorbing materials and the very heterogeneous arrangement. The principal resonance absorbers are U-235, U-238, tungsten, tantalum, and niobium. The latter three materials occur in a variety of shapes in the emitter, the collector sheath assembly, and the assorted connectors, spacers, springs, etc., of the intercell region. Only a few of these shapes resemble the spheres, slabs or cylinders for which escape probabilities are available in GGC.

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None of the resonance absorption treatments presently available in GGC-5 are adequate to treat the core region lattice. The most detailed spatial model available (the GAROL option for the resolved resonance range) allows only two regions, while to treat only the TFE fuel and its surrounding materials in one-dimensional cylindrical geometry requires a minimum of three regions (fuel, emitter, collector) and additional regions in the thick fuel body would be very desirable to improve on the flat source approximation in the escape probabilities. The TFE fuel bodies axe spaced sufficiently close that some form of Dancoff correction should be employed in the escape probabilities, but the standard formulation of this effect does not allow for the presence of fissile material and resonance absorbing materials between the regions being treated.

In the calculations actually done, most of this complexity was necessarily ignored. All resonance calculations were done with the GAMNIT-GANDY options of GGC-5, and because of expense, only one calculation was done for each resonant nuclide regardless of how many different geometries it occurs in. The resonance group cross sections of U-235 and U-238 were evaluated for the fuel body geometry, those of tungsten for the emitter, and those of niobium for the collector-sheath assembly. For tungsten and niobium, which occur as thin walled cylinders in the emitter and collector, the resonance calculations were done in cylindrical geometry by defining an equivalent solid cylinder with mean chord length.

? = 4V/S_outer = 2(r_o² – r_i²)/r_o

Scattering materials inside the cylinder, such as the carbon in the UCZrC fuel are homogenized into the equivalent cylinder as an admixed moderator, e.g.,

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N_{carbon in W} = N_{carbon in UCZrC} x V_fuel/V_W

The choice of these approximations was carried over from earlier work. The accuracy of the method has not been confirmed by more detailed calculations for the present case.

The GGC for the radial reflector was run assuming a homogeneous mixture of the reflector materials. The material volume fractions for the reflectors axe also given in Table 4-4. A separate GGC was run for the axial reflector.

The various calculations described below were done with the one and two-dimensional transport theory codes 1DF (Reference 29) and TWOTRAN (Reference 30). The P₁S₄ approximation was used in all cases, except for the detailed Rq study which used the P₀S₄ approximation.

The one-dimensional cases may be run with almost any reasonable number of energy groups, while the two-dimensional cases were limited for reasons of economy to the standard 11 group structure.

The transverse leakage is represented in 1DF either by an adjusted fission spectrum (X’ = X - L/S)* or by reading in a single transverse dimension from which geometric bucklings are computed and used with the cross sections of each region to compute DB² for that region. For many radial cases for which the axial leakage did not significantly affect the desired results, the option of supplying a single transverse dimension was used. The value specified, 64 cm, which implies a 10 cm reflector savings, has been found to give reasonable results.

The two-dimensional calculations were done in r-z and r-q geometry. Because of limitations of core storage and budget, only portions of the core were represented in these models. For

_________

* X’ = the adjusted fission spectrum, X = the actual fission spectrum, and L/S is the neutron leakage per source neutron.

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example, the largest r-z model, used for power zoning, represents half the reactor in the axial direction. The differences between upper and lower grid plates and axial reflectors were considered to be less important in this problem relative to the need to have reasonably small mesh spacing in the core regions.

Individual temperature coefficient components were computed using the GAPER, and GAPER-2D codes (References 6 and 7). GAPER and GAPER-2D are, respectively, one-dimensional and two-dimensional P₁ transport perturbation theory codes. These codes use the direct and adjoint fluxes and currents, as computed by 1DF or TWOTRAN, to calculate the change in the inverse multiplication factor D (1/k) due to various perturbations in the macroscopic cross section sets.

4.1.4.3 Reactivity Requirements

The reactivity requirements assumed for the purpose of initial sizing studies were as follows:

Temperature defect, burnup 0.02 D r
Shutdown margin 0.04 D r
Uncertainty 0.03 D r
Control worth 0.09 D r

These requirements imply that the cold clean reactor should have a calculated multiplication factor of k_eff = 1.05 with all shutters closed. The temperature and uncertainty allowances are estimates based on previous studies. The shutdown margin includes an allowance for one control drive failure.

The calculations carried out to establish the critical size involved a sequence of four reference designs which will not be described in detail here. In the course of these studies, however,

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many results were obtained on the effect of various design changes on the core reactivity. These are summarized in Table 4-5. The excess reactivity is seen to be very sensitive to variations in reflector design, which affect leakage, and to uranium density. The sensitivity functions are for small changes; large changes may be quite non-linear. The excess reactivity of the final reference design was determined from a two dimensional (RZ) calculation for the unzoned core. This calculation included the following design changes, from the previous reference design, which affect reactivity:

1. Replace tantalum with niobium in the intercell region (+0.0106D r ).

2. Reduce pressure vessel side wall thickness to 0.090 inches (+0.0087D r ).

3. Replace control drums with full length control shutters.

The calculational model geometry is shown in Figure 4-5. Table 4-6 gives the volume fractions of the various materials used in the calculation. This calculation gave a multiplication factor for the unzoned core of 1.066. Two effects not included in the calculation are the effect of increasing the number of energy groups from 11 to 25 (+0.0027D r ) and the effect of including in the two-dimensional mesh the coolant plenum and pressure vessel head above and below the axial reflectors (+0.0043D r ). Including these effects would increase the multiplication factor to k_eff = 1.074.

Calculations were also made for the zoned core. The fuel zoning specified is shown in Figure 4-6 which gives the fractional theoretical density of the UCZrC fuel material in each axial and radial position. The multiplication factor of the zoned reactor was calculated to be 1.061. With the two corrections indicated

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above, this becomes k_eff = 1.069 which is the present best estimate for the zoned reference design arid gives a margin of nearly 0.05D k above the estimated requirement for temperature and burnup.

In the two-dimensional calculations mentioned above, the TFEs are all oriented in the same direction to facilitate the zoning calculations. In the actual design, one-half of the TFEs are inverted and in the initial design the TFEs were staggered in the axial direction. It was later decided that it was preferable to align the TFEs and stagger the end reflector pieces. This has the advantage of increasing the reactivity (0.01D r ) relative to the previous reference design and being more consistent with the calculational model used above.

4.1.4.4 Power Distribution Studies

The RZ calculation, described above for the zoned core case, provided the two-dimensional power distribution for the reference core. As shown in Figure 4-6, the diodes are represented radially as rings of unit cells in a hexagonal array and axially as the 5.1 cm fueled and 2.3 cm unfueled zones.

The axial power distribution in the core zone was flattened, relative to the unzoned core, by varying the density of UC-ZrC in each diode zone as shown in Figure 4-6. These densities represent the fraction of theoretical density inside the fuel cavity, with the average density maintained at 64.8% theoretical density. Finding the correct densities is an iterative procedure involving a computer code called ZONE which evaluates thermionic performance for an input power distribution and specifies fuel density adjustments to obtain uniform emitter temperatures. If the density changes required were significant, a second nuclear calculation would be required.

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The relative power distribution in the diodes in the zoned core is given in Figure 4-6 normalized to an average power in the diodes of 1.0. The highest axial max/min power ratio was 1.08. Further variations in the diode fuel density would reduce this max/min power, but would result in a somewhat lower average fuel density, with a corresponding loss in core reactivity.

The power distributions discussed here were computed with the shutters closed. The power distribution with the shutters in an operating position, i.e., partially opened, has not been evaluated.

The RZ calculations cannot accurately treat the power distribution in the TFEs adjacent to the reflector. In order to determine the adequacy of the RZ calculation in this region, an Rq calculation was made which explicitly described a TFE adjacent to the reflector. The geometric model used is shown in Figure 4-7.

A series of one-dimensional calculations were made which confirmed the adequacy of the mesh size and of the homogenization of the emitter and collector used in the Rq model. The one dimensional calculations also compared the power distributions from a .25 group calculation (5 thermal groups) with an 11 group calculation (1 thermal group). The one-thermal group calculation badly underestimated the power peak at the core reflector interface.

Because the Rq problem was larger than any previously run case, and because of no prior experience with the CDC-7600 computer on which it was planned to run, the first Rq calculation was run with one thermal group using the P₀S₄ approximation. The P₀ approximation probably slightly overpredicts the power peak in the outer TFE, while the use of one thermal energy group is known to produce a definite underprediction of the peak. A P₁S₄, multi-thermal group Rq calculation was planned for a future calculation

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to complete the study. The transverse leakage was represented by using a core height of 64 cm to compute the buckling. This leakage approximation was verified by comparing a one-dimensional radial problem, using an input 64 cm core height for the buckling, with an RZ calculation.

Figure 4-8 compares the Rq relative power, for a traverse across the radial center line of the outer TFE, with that obtained from an 11 group, P₁S₄ RZ calculation. Relative power is defined here as the power in a mesh interval divided by the lowest mesh interval power in the TFE. It is seen in this comparison that the RZ calculation overpredicts the power distribution relative to the Rq calculation. It is expected that a similar comparison with multi-thermal groups would also show that the power peaking predicted by an RZ calculation is conservative; further investigation is required, however, to verify this prediction. A contour plot of the power distribution from the Rq calculation is given in Figure 4-9.

4.1.4.5 Control Worth Studies

An investigation was made early in the design study to find a control system that would provide adequate control with a minimum reflector thickness. Calculations were done for two control concepts: rotating BeO drums with B₄C absorber segments (the original), and BeO shutters which open out to increase core leakage.

Calculations for a preliminary design with 5-inch diameter drums indicated a control worth of 0.06 D r with natural boron and 0.09 D r with B¹⁰ for an absorber segment one-sixth of the drum diameter in thickness. It would be desirable to use natural boron instead of B¹⁰ for reasons of cost. Fully enriched boron (93.1 wt.% B¹⁰) costs around $3/g. However, using a larger poison segment of natural B₄C would reduce the excess reactivity in the drums-out configuration.

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The possibility of adding hydrogen to the poison segments of control drums was considered with the idea of slowing down a greater fraction of the reflector neutrons into the energy range where the boron cross section is largest. This idea was tested with some calculations in which hydrogen atom densities of 0.03 and 0.06 atoms/bn-cm were assumed in the poison segments in place of the carbon (0.06 is roughly the hydrogen density in H₂O or ZrH_1.7; an actual material suitable for the temperature requirements has not been selected). The density of natural boron was unchanged. The results are as follows:

k_eff (drums out) k_eff (drums in) D r

Original design 1.0384 0.9782 0.0593
N_H = 0.03 1.038 0.9531 0.8558

N_H = 0.06 1.0377 0.9375 0.1030

The method is seen to be quite effective. With the drums full out, the excess reactivity is hardly affected, since neutrons which reach thermal energies far out in the reflector have little chance of returning to the core.

Another control alternative is to use opening shutters in place of rotating drums. Since the motion of the shutters opens up large streaming paths, multi-dimensional calculations are required to determine the control swing.

Calculations of the control shutter worth have been done in RZ geometry since the streaming with the shutters open is primarily in the axial direction. A correction for the radial streaming is obtained from an Rq geometry calculation. The reference shutters closed configuration was calculated for the unzoned core before the inclusion of the three design changes discussed above. The calculational results are the following:

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k_eff D k

1. RZ, Unzoned Core, Shutters Closed 1.033

2. RZ, Unzoned Core, Shutters Open 1.5 in. 0.981 0.052

3. RZ, Unzoned Core, Shutters Open 3.0 in. 0.936 0.097

4. Rq , Unzoned Core, Shutters Open 3.0 in. 0.907 0.126

The Rq calculation, Case 4, includes transverse leakages (DB² cross sections) from Case 3. Further iteration of leakages between Cases 3 and 4 should be done, but the final control worth should be closer to 0.12 D k. Most of the design changes, e.g., removal of Ta, thinner pressure vessel and longer axial shutters, will change the multiplication factor of the shutters-open case less than that of the shutters-closed case. It is, therefore, concluded that ample control margin is available in the shutter design.

Since shutter control provides adequate control margin with a minimum reflector thickness, the shutter control concept was chosen for the reference design.

4.l.4.6 Water Flooding Studies

During shipment or launch of an electric propulsion reactor, the control shutters would be either removed or in the full-open position (7.6 cm displacement of center-of-reflector mass). If an accident occurs in which the reactor is immersed in water and either the core or the leakage gaps between shutters are filled with water, a potential criticality problem exists. One-dimensional radial calculations (10 fast groups, 5 thermal groups) were done for several conditions of water flooding to investigate this problem. The results are as follows:

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It seems apparent that some means would have to be provided to avoid criticality in the case of accidents which lead to flooding. In the pre-launch phases of a mission, this could take the form of a poison material between the core and shutters. For situations involving re-entry and flooding after removal of this poison, some means of breaking up the core beyond simply blowing off the shutters may be required. The alternative of incorporating sufficient resonance and thermal poisons to assure sub-criticality after intact re-entry and flooding may penalize the excess reactivity of the unflooded system to an unacceptable degree, although this has not been established by calculations.

4.1.4.7 Other Nuclear Characteristics

Table 4-6 gives some miscellaneous nuclear characteristics calculated for the electric propulsion reactor.

4.1.4.8 240 kWe Reactor Studies

Some one-dimensional calculations were done for a 240 kWe electric propulsion design as part of a separate study. Three concepts were investigated: 1) a 240 TFE reactor, 2) a moderated 240 TFE reactor, and 5) two coupled 120 kWe reactors.

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The 240 TEE reactor is simply an enlarged version of the 162 TFE reference design. It has adequate excess reactivity if the fuel density is reduced by 10-12% from the 162 TFE design. Control is satisfactory with 4.5 in. diameter drums with B¹⁰C segments occupying one-third of the drum diameter. (The spacecraft design in this case favors drums over shutters.) Because of the higher power density, lower fuel density, and higher radial flux peak, the maximum fast fluence at 10⁴ hr is about 30% higher than in the 162 TFE design.

If it were necessary to reduce the fluence for a long mission, it could be brought to the level of the reference design (2.4 x 10²¹ nvt per 10⁴ hr) by the inclusion of about 10 volume percent ZrH in the core. In this case the fuel density is reduced about 14% from the 162 TFE reference design. The cell geometry assumed for this case is shown in Figure 4-10.

The use of multiple 120 kWe thermionic reactors was considered as a method of obtaining higher powers without building larger cores. In addition to development cost savings, this concept avoids the problems of higher fast fluence and reduced control margin encountered in larger diameter cores. An upper limit estimate of the reactivity coupling between adjacent 120 kWe reactors was made by replacing the vacuum boundary condition at the outer reflector surface by a reflecting boundary condition. This calculation, which essentially represents a close-packed infinite array of reactors, gives a reactivity increase of 0.12 D k for reactors controlled with poison drums. It can be concluded that an arrangement of two or more drum-controlled reactors would be very weakly coupled and is, therefore, a feasible concept.

4.1.4.9 TREX Temperature Coefficient Studies

Nuclear calculations were done for the Thermionic Reactor Experiment with the objective of comparing the dynamic behavior of an all-TFE TREX with that of a design using a smaller number of TFEs and a driver fuel.

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The latter design is attractive from the standpoint of economy, but it must be determined to what extent its dynamic behavior is affected by the relative magnitudes of the reactivity temperature coefficients of the TFEs and the driver fuel. The objective was to find a design for which the dynamic response in one or more types of transient experiments is dominated by the reactivity feedback from the TFEs.

As a start, the Doppler coefficients of TFEs and driver fuel were calculated for a variety of design options. For all cases, it was assumed that there are 60 TFEs and that the amount of driver fuel is adjusted to give a multiplication factor of 1.05. Design options included (1) locating the TFEs at the core center or at the core edge, (2) using 3-inch or 5-inch thick BeO-B₄C control drums and (3) using a close-packed driver fuel lattice or a cluster type driver element. The cluster type driver element is a group of seven driver pins inside a tube of the same outer diameter as a TFE. The driver fuel pin for both close-packed and cluster-type elements is fully enriched UO₂ clad with stainless steel with an outer diameter of 0.368 inches. The geometry of both fuel types is illustrated in Figure 4-11.

Doppler coefficients were determined by (1) obtaining direct and adjoint fluxes and currents for the desired configurations from one-dimensional transport calculations, (2) obtaining macroscopic cross sections at a variety of temperatures, and (3) using the fluxes, currents, and cross sections in a first order perturbation theory calculation to obtain the reactivity perturbation.

The principal results for all cases are summarized in Table 4-7. Detailed results for Case 7 are given in Table 4-8. Note that the definition of a "prompt" coefficient depends on the nature of the transient considered, e.g., whether the initial perturbation is in the electrical load, the position of a control drum, or the coolant temperature. For the present purposes of comparison, we define the TFE prompt coefficient as the Doppler coefficients of U-235 and U-238 and half of the Doppler

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coefficient of tungsten. Approximately half of the tungsten is in the intercell region and has a more delayed time response than the emitter itself. The definition of the prompt coefficient given here is particularly appropriate for transients initiated by electrical load changes or step reactivity perturbations. The isothermal coefficient of the driver fuel is composed of the U-235 and U-258 Doppler coefficients and would have a time response comparable to the TFE prompt coefficient for step reactivity perturbations.

The principal conclusion to be noted from preliminary analysis of these results is the desirability of having the TFEs in the outer region and having as thick a reflector as can be allowed by power peaking considerations. With outer TFEs, the close-pack driver arrangement gives substantially larger TFE coefficients than the cluster arrangement.

In most small fast spectrum reactors, the axial expansion temperature coefficient is of comparable magnitude to the Doppler coefficient. If the driver fuel in the TREX design is not axially segmented in some way, the axial expansion coefficient of the driver fuel is expected to dominate the dynamic response of the reactor. A brief study was made to determine what effect axial segmentation had on the axial expansion coefficient of the driver fuel. Two-dimensional calculations were made using the core configuration given in Case 7 of the Doppler coefficient study. It is assumed in these studies that the driver fuel is held rigid at the top and bottom of the core and permitted to expand at the point of segmentation.

It was observed that a gap at the axial center of the driver fuel gave an expansion coefficient (D r /D T(° )) of about +4 x 10^-7. For a gap at a point 11 cm above the axial center, the coefficient is +9 x 10^-8. Previous calculations for unsegmented driver fuel (Reference) gave an expansion coefficient of about -l x 10^-6. It is obvious from these calculations that a significant reduction in the driver axial expansion coefficient can be obtained by segmentation. Further studies are necessary, however, to optimize the segmentation in order to reduce the axial expansion coefficient to a minimum.

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4.2 REACTOR DESIGN AND ANALYSIS

The objective of this subtask is the mechanical, thermal, and hydraulic analysis and design of the reactor core, reflector, core vessel, and control drive system. The requirements of the design are set by system specifications.

The approach to reactor design at this stage of reactor development is to do sufficient analysis to assure the basic feasibility of the conceptual designs and to develop analytical tools for use in these calculations, when necessary.

Past work in this subtask included conceptual designs of fast reactors at 100 and 300 kWe power levels and moderated reactors in the 5-100 kWe power range. Thermionic reactors containing fast driver fuels were also studied.

The most recent past work has been concerned with the 120-kWe NEP (nuclear electric propulsion) reactor in the side thrust system configuration. This is a fast liquid metal cooled reactor with 162 TFEs producing 22 volts. The reactor is controlled by movement of the radially located beryllium oxide reflector. Eighteen reflector elements rotate towards and away from the core to regulate openings for neutron leakage which controls the reactor. The latest status of the 120 kWe NEP system design, including reactor parameters, is described in Reference 9.

4.2.1 Layout and Specifications for the 120 kWe NEP Reactor (D. Allen)

The axial configuration of the core and reflector was defined in greater detail. This more detailed specification is required for more precise nuclear analysis of the core and for system shielding analysis. Since the core and axial reflector are completely defined by the TFE detail, the NEP Reactor TFE has been designed.

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The typical TFE is illustrated in Figure 4-12. In order to produce the reactor output voltage of 22 V, 6 such TFEs must be connected in series. To accomplish the series connection, the string of six converters in each TFE is oriented alternatively as shown in Figure 4-12, or upside down from that configuration. Two types of TFE result - the N and P types - identified according to whether the top lead of the TFE is connected to the negative or positive side (collector or emitter) of the top converter. Two-thirds of the TFEs are connected in pairs (one N and one P-type) through a connection housing at the end opposite the end welded to the reactor vessel. The TFEs are connected in the groups of six as shown in Figure 4-13. To cross-connect all of the TFE strings at their mid-potential, they are grounded to the NaK coolant. The 27 groups of 6 TFEs are located in radial rings in the core so that nuclear power input to the TFEs in each group will be approximately the same. This connection scheme is illustrated in the inset to Figure 4-13.

To accomplish the maximum fuel density in the core, the TFEs must be arranged so that the fueled regions of each emitter are aligned axially. This configuration has a calculated advantage in multiplication factor of 0.01 D k over the alignment of TFEs so that the planes bounding all of the converters line up (See Section 4.1.4.2). Since the fuel is not axially centered in the converter, the resulting interface between converters and the axial reflector blocks is irregular. The TFE end details in Figures 4-14 and 4-15 indicate the configuration resulting. The reflector blocks are alternatively 88.3 mm (3.475 in.) or 115.0 mm (4.525 in.) long. The overall axial layout of the reactor by zones, significant to the nuclear analyst, is given in Figure 4-16.

It can be noted from the TFE end details of Figures 4-14 and 4-15, that the reflector blocks are shaped to accommodate the TFE leads, the pump-out lines for the inter-electrode space and the fission gas port tube. The TFE insulator-seal is configured to the same design as the converter insulator seal. Three tubes emerge from the TFE. They are

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the cesium tube to be connected to the cesium reservoir, the fission product tube to be connected to the fission product trap and the fission product space pump-out tube, which is pinched closed after fabrication. The details of the connection housing at the ends of two-thirds of the TFEs can be seen. The connection is to be made with electron beam welds from the end on. All but the last weld are circular. The last weld, sealing the TFEs at that end is an ogival weld.

Design work on the details of the reactor and NEP TFE configurations should not proceed further until their fabrication practice is demonstrated.

4.2.2 Mechanical Design for 120 kWe Reactor (E.J. Steeger)

4.2.2.1 Effect of Isothermal and Self Heating on the Reflector Element Assembly

If the reflector elements are heated isothermally for bake-out or heated by coolant circulation in the reactor, differential dimensional changes between the niobium can and the BeO will take place. These are shown as Figures 4-17 and 4-18.

Insertion of a Bellville spring at either or both ends of the BeO will serve to accommodate the differential axial dimension changes. If the spring preload is greater than the expected load during the launch sequence, then contact between surfaces will be maintained. Figure 4-19 shows the design of a spring and the spring stress and deflection with load.

A thermal analysis of the reflector element assembly with self heating was done in order to determine the temperatures during reactor operation. The GGA computer code TAC2D was used for this analysis. The self heating of BeO was taken as 0.04 W/cm³/megawatt(th). Since part of the element is looking at a section of insulation and part is looking at the heat exchanger (radiator), the problem was broken up for solution.

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Also, the design of the element allows a 0.38 mm (0.15 inch) clearance between the BeO and. The can when at ambient temperature.

Since some contact between the BeO and the can will take place, the following assumptions were used for the analysis:

1. Elements in the "open" and closed positions.

2. Elements looking at the thermal insulation and the heat exchanger.

3. One-fourth of the BeO surface in contact with the Nb can.

4. A gap between the BeO surface and the Nb can.

Figures 4-20 through 4-23 show the results of the analysis. The ambient temperature for all cases was 1055°K.

The highest BeO and niobium can temperatures occur with the elements in the closed position with the assumption that a radiation gap exists between the BeO and the can.

If the worst case is chosen, the BeO temperature will be about 1300°K with a radial temperature gradient of 14°K. The can will have a radial temperature difference of 60°K

The temperature difference across the can of 60°K would result in a displacement inwardly of .010" (.025 cm) at the center of the element.

For the condition of 60°K D T across the niobium can, the BeO has a D T of 14°K. The tensile stress induced by the D T is

S_T = s ED T = 40.7 MN/m² (5900 psi)

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If the BeO is assumed to be in contact with the can during this condition then the radial D T is 8°C resulting in a stress of 23.2 MN/m² (3370 psi).

4.2.2.2 Control Element under Launch Shock and Vibration

For the control element and its support structure, the most severe projected launch loading is the requirement to withstand 15 Gs along the three axes. No sinusoidal excitation at or above resonant frequencies are called out in the qualification specification.

The configuration and mass distribution are shown in Figure 4-24.

If it is assumed that the BeO "pucks" carry no load, sideways static loading of 15 Gs results in bending stresses in the 0.76 mm thick can of 22.8 MN/m² (3310 psi). The factor of safety for this condition based on the proportional limit of Nb-1Zr is eleven. The angular deflection at the end supports under the acceleration is 0.048°, and the centerline deflection 0.17 mm (0.0066 in.).

An axial acceleration of 15 Gs produces a tensile stress in the can of 9.0 MN/m² (1308 psi) which corresponds to a factor of safety of twenty-eight. Maximum shear stress where the element supports meet the bearing shaft is 1.8 MN/m² (2577 psi) which is a factor of fourteen above the limit.

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The control element bearings are subjected to a stress of 3.6 MN/m² (518 psi) in compression due to lateral acceleration, and shear and compressive stresses of 4.2 MN/m² (602 psi) and 17.3 MN/m² (2467 psi), respectively, under axial acceleration.

The calculated natural frequency of the control element is to be 174 Hz. The sinusoidal input specified for qualification spans the range of 4 to 35 Hz. However, random acceleration is specified over a range up to 2000 Hz.

Launch load conditions on the control element and its supporting parts appear to be moderate. No potential problem areas should be expected for this component from a mechanical standpoint.

4.2.2.5 Design of Control Element Snubber

The control element deceleration snubber is designed to act within the last 10 of control element travel to absorb the inertial energy stored in the system and stop the drive in the control rod full out position. The item as designed is illustrated in Figure 4-25.

The cylinder is divided into two chambers with one portion a bellows. Initially, with a gas pressure of 34.5 kN/m² (5.0 psia) the force exerted by the piston rod against the snubber arm almost balances the spring torque. As the control element moves toward an "in" position, the piston will travel 8.9 mm (0.35 in.) (10° of control rod movement) to a stop. An orifice through the piston allows the gas to come to equilibrium within the system.

As the control elements are spring driven during scram, the snubber arm will contact the piston rod 10° before the full out position. The gas to the right of the piston is essentially trapped and will be compressed. If the orifice is designed correctly, the inertial energy can be dissipated in flow work as the gas is transferred through the piston and there will be no tendency to bounce.

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The snubber was designed to absorb the energy from a 52° "in" position with a 8.9 mm (0.35 in.) travel. From any position less than 52° , the snubber will not bottom from energy absorption, but will stop the control element and then go to the full-out position as the gas in the two chambers reaches equilibrium.

Figure 4-26 shows the energy absorption versus piston travel with the energy stored in one control element indicated and Figure 4-27 is the calculated pressure in the snubbing chamber.

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1. Mathews, D. R., and Archibald, R. J., "GAF. A Computer Program for Calculation of Neutron Spectra and Average Cross Sections in the High Energy Region," USAEC Report GA-7169, Gulf General Atomic, January 20, 1967.

2. Shanstrom, R. T., et.al., "GAF and GAR, New Computer Programs for the Calculation of Neutron Spectra, Treatment of Resonance Effects, and Averaging of Group Cross Sections for Fast Reactor Analysis, USAEC Report GA-7920, Gulf General Atomic, March 31, 1967.

3. Archibald, R. J. and Mathews, D. R., "The GAF/GAB/GAMD Fast Reactor Cross Section Preparation System. Vol.1. GAFGAR- A Program for the Calculation of Neutron Spectra and Group-Averaged Cross Sections," USAEC Report GA-7542, Gulf General Atomic, January 22, 1968.

4. Cohen, S. C. and Koch, P. K., "GANDY. A Computer Program for the Evaluation of Effective Cross Sections in the Unresolved Resonance Region," USAEC Report GA-8003, Gulf General Atomic, May 22, 1967.

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7. Archibald, R. J. and Sargis, D. A., "GAPER-2D. A Two Dimensional Transport Perturbation Theory Program," USAEC Report GA-10103, Gulf General Atomic, April 29, 1970.

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10. Cohen, S. C., "Thermionic Critical Experiment Program", USAEC Report GA-8309, Gulf General Atomic, November 28, 1967.

11. Cohen, S., et.al., "Conceptual Design of a Thermionic Critical Experiment for Doppler Coefficient Measurements," USAEC Report GA-7472, Gulf General Atomic, November 15, 1966.

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12. Cohen, S. C., et.al. , "Fast Critical Experiments in Support of Thermionic Reactor Physics", Presented at the Thermionic Specialist Conference, October 1968.

13. Cohen, S. C., et.al., "The Neutron Spectrum for a Subcritical Section of the Thermionic Critical Experiment. Assembly No. 1", USAEC Report GA-9100, Gulf General Atomic, December 13, 1968.

14. Cohen, S. C., Moore, R. A., Sargis, D. A., "Analysis of Fuel Block Worth Measurements in the Thermionic Critical Experiment", USAEC Report GA-8866, Gulf General Atomic, October 21, 1968

15. Moore, R. A., et.al. "Reactivity Worth Measurements and Analysis in the Thermionic Critical Experiment. Assembly No. 1" USAEC Report GA-9377, Gulf General Atomic, May 16, 1969.

16. Sargis, D. A., et.al., "Measurement and Analysis of Doppler Reactivities in the Thermionic Critical Experiment Assembly No. 1", USAEC Report GA-10152, Gulf General Atomic, July 1, 1970.

17. Shanstrom, R. T., et.al., "Neutronic Aspects of the Thermionic Reactor Experiment", USAEC Report GA-6107, Gulf General Atomic, March 15, 1965.

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19. Allen, D. T., et.al., "A Design Study of the Unit-Cell Thermionic Reactor for Space Application. Final Report", USAEC Report GA-8917, Gulf General Atomic, January 13, 1969.

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22. Homeyer, W. G., "The Performance of Thermionic Reactors for 50 to 100 kWe," Presented at the Thermionic Conversion Specialist Conference, November 1969.

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23. Fisher, C. R., and Merrill, M. H., "A Comparison of Thermionic Reactor Designs Employing a Common Thermionic Fuel Element," Presented at the 3rd International Conference on Thermionic Electrical Power Generation, Julich, Germany, March 22, 1972.

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27. Walti, P., and Koch, P., "MICROX, A Two-Region Flux Spectrum Code for the Efficient Calculation of Group Cross Sections", USAEC Report GA-A10827, Gulf General Atomic, April 14, 1972.

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29. Archibald, R., et.al., "1-DFX-A Revised Version of the 1-DF (DTF-IV) SN Transport Theory Code", USAEC Report GA-B10820, Gulf General Atomic, September 1971.

30. "Theory and Use of the General-Geometry TWOTRAN Program, USAEC Report LA-4432, Los Alamos Scientific Laboratory, May 1970.

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